@inproceedings{19858, abstract = {Given a graph G that undergoes a sequence of edge insertions and deletions, we study the Maximum k-Edge Coloring problem (MkEC): Having access to k different colors, color as many edges of G as possible such that no two adjacent edges share the same color. While this problem is different from simply maintaining a b-matching with b = k, the two problems are related. However, maximum b-matching can be solved efficiently in the static setting, whereas MkEC is NP-hard and even APX-hard for k ≥ 2. We present new results on both problems: For b-matching, we show a new integrality gap result and we adapt Wajc’s matching sparsification scheme [David Wajc, 2020] for the case where b is a constant. Using these as basis, we give three new algorithms for the dynamic MkEC problem: Our MatchO algorithm builds on the dynamic (2+ε)-approximation algorithm of Bhattacharya, Gupta, and Mohan [Sayan Bhattacharya et al., 2017] for b-matching and achieves a (2+ε)(k+1)/k-approximation in O(poly(log n, ε^-1)) update time against an oblivious adversary. Our MatchA algorithm builds on the dynamic (7+ε)-approximation algorithm by Bhattacharya, Henzinger, and Italiano [Sayan Bhattacharya et al., 2015] for fractional b-matching and achieves a (7+ε)(3k+3)/(3k-1)-approximation in O(poly(log n, ε^-1)) update time against an adaptive adversary. Moreover, our reductions use the dynamic b-matching algorithm as a black box, so any future improvement in the approximation ratio for dynamic b-matching will automatically translate into a better approximation ratio for our algorithms. Finally, we present a greedy algorithm with O(Δ+k) update time, which guarantees a 2.16 approximation factor.}, author = {El-Hayek, Antoine and Hanauer, Kathrin and Henzinger, Monika H}, booktitle = {4th Symposium on Algorithmic Foundations of Dynamic Networks}, isbn = {9783959773683}, issn = {1868-8969}, location = {Liverpool, United Kingdom}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{On b-matching and fully-dynamic maximum k-edge coloring}}, doi = {10.4230/LIPIcs.SAND.2025.4}, volume = {330}, year = {2025}, } @inproceedings{20253, abstract = {A quantitative word automaton (QWA) defines a function from infinite words to values. For example, every infinite run of a limit-average QWA 𝒜 obtains a mean payoff, and every word w ∈ Σ^ω is assigned the maximal mean payoff obtained by nondeterministic runs of 𝒜 over w. We introduce quantitative language automata (QLAs) that define functions from language generators (i.e., implementations) to values, where a language generator can be nonprobabilistic, defining a set of infinite words, or probabilistic, defining a probability measure over infinite words. A QLA consists of a QWA and an aggregator function. For example, given a QWA 𝒜, the infimum aggregator maps each language L ⊆ Σ^ω to the greatest lower bound assigned by 𝒜 to any word in L. For boolean value sets, QWAs define boolean properties of traces, and QLAs define boolean properties of sets of traces, i.e., hyperproperties. For more general value sets, QLAs serve as a specification language for a generalization of hyperproperties, called quantitative hyperproperties. A nonprobabilistic (resp. probabilistic) quantitative hyperproperty assigns a value to each set (resp. distribution) G of traces, e.g., the minimal (resp. expected) average response time exhibited by the traces in G. We give several examples of quantitative hyperproperties and investigate three paradigmatic problems for QLAs: evaluation, nonemptiness, and universality. In the evaluation problem, given a QLA 𝔸 and an implementation G, we ask for the value that 𝔸 assigns to G. In the nonemptiness (resp. universality) problem, given a QLA 𝔸 and a value k, we ask whether 𝔸 assigns at least k to some (resp. every) language. We provide a comprehensive picture of decidability for these problems for QLAs with common aggregators as well as their restrictions to ω-regular languages and trace distributions generated by finite-state Markov chains.}, author = {Henzinger, Thomas A and Kebis, Pavol and Mazzocchi, Nicolas Adrien and Sarac, Naci E}, booktitle = {36th International Conference on Concurrency Theory}, isbn = {9783959773898}, issn = {1868-8969}, location = {Aarhus, Denmark}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Quantitative language automata}}, doi = {10.4230/LIPIcs.CONCUR.2025.21}, volume = {348}, year = {2025}, } @inproceedings{20290, abstract = {We consider equilibria in multiplayer stochastic graph games with terminal-node rewards. In such games, Nash equilibria are defined assuming that each player seeks to maximise their expected payoff, ignoring their aversion or tolerance to risk. We therefore study risk-sensitive equilibria (RSEs), where the expected payoff is replaced by a risk measure. A classical risk measure in the literature is the entropic risk measure, where each player has a real valued parameter capturing their risk-averseness. We introduce the extreme risk measure, which corresponds to extreme cases of entropic risk measure, where players are either extreme optimists or extreme pessimists. Under extreme risk measure, every player is an extremist: an extreme optimist perceives their reward as the maximum payoff that can be achieved with positive probability, while an extreme pessimist expects the minimum payoff achievable with positive probability. We argue that the extreme risk measure, especially in multi-player graph based settings, is particularly relevant as they can model several real life instances such as interactions between secure systems and potential security threats, or distributed controls for safety critical systems. We prove that RSEs defined with the extreme risk measure are guaranteed to exist when all rewards are non-negative. Furthermore, we prove that the problem of deciding whether a given game contains an RSE that generates risk measures within specified intervals is decidable and NP-complete for our extreme risk measure, and even PTIME-complete when all players are extreme optimists, while that same problem is undecidable using the entropic risk measure or even the classical expected payoff. This establishes, to our knowledge, the first decidable fragment for equilibria in simple stochastic games without restrictions on strategy types or number of players.}, author = {Brice, Léonard and Henzinger, Thomas A and Thejaswini, K. S.}, booktitle = {50th International Symposium on Mathematical Foundations of Computer Science}, isbn = {9783959773881}, issn = {1868-8969}, location = {Warsaw, Poland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Finding equilibria: Simpler for pessimists, simplest for optimists}}, doi = {10.4230/LIPIcs.MFCS.2025.30}, volume = {345}, year = {2025}, } @inproceedings{20291, abstract = {We define and study classes of ω-regular automata for which the nondeterminism can be resolved by a policy that uses a combination of memory and randomness on any input word, based solely on the prefix read so far. We examine two settings for providing the input word to an automaton. In the first setting, called adversarial resolvability, the input word is constructed letter-by-letter by an adversary, dependent on the resolver’s previous decisions. In the second setting, called stochastic resolvability, the adversary pre-commits to an infinite word and reveals it letter-by-letter. In each setting, we require the existence of an almost-sure resolver, i.e., a policy that ensures that as long as the adversary provides a word in the language of the underlying nondeterministic automaton, the run constructed by the policy is accepting with probability 1. The class of automata that are adversarially resolvable is the well-studied class of history-deterministic automata. The case of stochastically resolvable automata, on the other hand, defines a novel class. Restricting the class of resolvers in both settings to stochastic policies without memory introduces two additional new classes of automata. We show that the new automata classes offer interesting trade-offs between succinctness, expressivity, and computational complexity, providing a fine gradation between deterministic automata and nondeterministic automata.}, author = {Henzinger, Thomas A and Prakash, Aditya and Thejaswini, K. S.}, booktitle = {50th International Symposium on Mathematical Foundations of Computer Science}, isbn = {9783959773881}, issn = {1868-8969}, location = {Warsaw, Poland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Resolving nondeterminism with randomness}}, doi = {10.4230/LIPIcs.MFCS.2025.57}, volume = {345}, year = {2025}, } @inproceedings{20533, abstract = {We give an introduction into differential privacy in the dynamic setting, called the continual observation setting.}, author = {Henzinger, Monika H and Safavi Hemami, Roodabeh}, booktitle = {33rd Annual European Symposium on Algorithms}, isbn = {9783959773959}, issn = {1868-8969}, location = {Warsaw, Poland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Securing dynamic data: A primer on differentially private data structures}}, doi = {10.4230/LIPIcs.ESA.2025.2}, volume = {351}, year = {2025}, } @inproceedings{20534, abstract = {A non-trivial minimum cut (NMC) sparsifier is a multigraph Ĝ that preserves all non-trivial minimum cuts of a given undirected graph G. We introduce a flexible data structure for fully dynamic graphs that can efficiently provide an NMC sparsifier upon request at any point during the sequence of updates. We employ simple dynamic forest data structures to achieve a fast from-scratch construction of the sparsifier at query time. Based on the strength of the adversary and desired type of time bounds, the data structure comes with different guarantees. Specifically, let G be a fully dynamic simple graph with n vertices and minimum degree δ. Then our data structure supports an insertion/deletion of an edge to/from G in n^o(1) worst-case time. Furthermore, upon request, it can return w.h.p. an NMC sparsifier of G that has O(n/δ) vertices and O(n) edges, in Ô(n) time. The probabilistic guarantees hold against an adaptive adversary. Alternatively, the update and query times can be improved to Õ(1) and Õ(n) respectively, if amortized-time guarantees are sufficient, or if the adversary is oblivious. Throughout the paper, we use Õ to hide polylogarithmic factors and Ô to hide subpolynomial (i.e., n^o(1)) factors. We discuss two applications of our new data structure. First, it can be used to efficiently report a cactus representation of all minimum cuts of a fully dynamic simple graph. Building this cactus for the NMC sparsifier instead of the original graph allows for a construction time that is sublinear in the number of edges. Against an adaptive adversary, we can with high probability output the cactus representation in worst-case Ô(n) time. Second, our data structure allows us to efficiently compute the maximal k-edge-connected subgraphs of undirected simple graphs, by repeatedly applying a minimum cut algorithm on the NMC sparsifier. Specifically, we can compute with high probability the maximal k-edge-connected subgraphs of a simple graph with n vertices and m edges in Õ(m+n²/k) time. This improves the best known time bounds for k = Ω(n^{1/8}) and naturally extends to the case of fully dynamic graphs.}, author = {Henzinger, Monika H and Kosinas, Evangelos and Münk, Robin and Räcke, Harald}, booktitle = {33rd Annual European Symposium on Algorithms}, isbn = {9783959773959}, issn = {1868-8969}, location = {Warsaw, Poland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Efficient contractions of dynamic graphs - with applications}}, doi = {10.4230/LIPIcs.ESA.2025.36}, volume = {351}, year = {2025}, } @inproceedings{20535, abstract = {Many differentially private and classical non-private graph algorithms rely crucially on determining whether some property of each vertex meets a threshold. For example, for the k-core decomposition problem, the classic peeling algorithm iteratively removes a vertex if its induced degree falls below a threshold. The sparse vector technique (SVT) is generally used to transform non-private threshold queries into private ones with only a small additive loss in accuracy. However, a naive application of SVT in the graph setting leads to an amplification of the error by a factor of n due to composition, as SVT is applied to every vertex. In this paper, we resolve this problem by formulating a novel generalized sparse vector technique which we call the Multidimensional AboveThreshold (MAT) Mechanism which generalizes SVT (applied to vectors with one dimension) to vectors with multiple dimensions. When applied to vectors with n dimensions, we solve a number of important graph problems with better bounds than previous work. Specifically, we apply our MAT mechanism to obtain a set of improved bounds for a variety of problems including k-core decomposition, densest subgraph, low out-degree ordering, and vertex coloring. We give a tight local edge differentially private (LEDP) algorithm for k-core decomposition that results in an approximation with O(ε^{-1} log n) additive error and no multiplicative error in O(n) rounds. We also give a new (2+η)-factor multiplicative, O(ε^{-1} log n) additive error algorithm in O(log² n) rounds for any constant η > 0. Both of these results are asymptotically tight against our new lower bound of Ω(log n) for any constant-factor approximation algorithm for k-core decomposition. Our new algorithms for k-core decomposition also directly lead to new algorithms for the related problems of densest subgraph and low out-degree ordering. Finally, we give novel LEDP differentially private defective coloring algorithms that use number of colors given in terms of the arboricity of the graph.}, author = {Dhulipala, Laxman and Henzinger, Monika H and Li, George Z. and Liu, Quanquan C. and Sricharan, A. R. and Zhu, Leqi}, booktitle = {33rd Annual European Symposium on Algorithms}, isbn = {9783959773959}, issn = {1868-8969}, location = {Warsaw, Poland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Near-optimal differentially private graph algorithms via the Multidimensional AboveThreshold Mechanism}}, doi = {10.4230/LIPIcs.ESA.2025.91}, volume = {351}, year = {2025}, } @inproceedings{20536, abstract = {Uniquely represented (UR) data structures represent each logical state with a unique storage state. We study the problem of maintaining a dynamic set of n keys from a totally ordered universe in this context. UR structures are also called "strongly history independent" structures in the literature. We introduce a two-layer data structure called (α,ε)-Randomized Block Search Tree (RBST) that is uniquely represented and suitable for external memory (EM). Though RBSTs naturally generalize the well-known binary Treaps, several new ideas are needed to analyze the expected search, update, and storage efficiency in terms of block-reads, block-writes, and blocks stored. We prove that searches have O(ε^{-1} + log_α n) block-reads, that dynamic updates perform O(ε^{-1} + log_α(n)/α) block-writes and O(ε^{-2}+(1+(ε^{-1}+log n)/α)log_α n) block-reads, and that (α, ε)-RBSTs have an asymptotic load-factor of at least (1-ε) for every ε ∈ (0,1/2]. Thus (α, ε)-RBSTs improve on the known, uniquely represented B-Treap [Golovin; ICALP'09]. Compared with non-UR structures, the RBST is also, to the best of our knowledge, the first external memory structure that is storage-efficient and has a non-amortized, write-efficient update bound.}, author = {Safavi Hemami, Roodabeh and Seybold, Martin P.}, booktitle = {19th International Symposium on Algorithms and Data Structures}, isbn = {9783959773980}, issn = {1868-8969}, location = {Toronto, Canada}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{B-Treaps revised: Write efficient randomized block search trees with high load}}, doi = {10.4230/LIPIcs.WADS.2025.47}, volume = {349}, year = {2025}, } @inproceedings{19281, abstract = {In this work, we consider the list-decodability and list-recoverability of codes in the zero-rate regime. Briefly, a code 𝒞 ⊆ [q]ⁿ is (p,𝓁,L)-list-recoverable if for all tuples of input lists (Y₁,… ,Y_n) with each Y_i ⊆ [q] and |Y_i| = 𝓁, the number of codewords c ∈ 𝒞 such that c_i ∉ Y_i for at most pn choices of i ∈ [n] is less than L; list-decoding is the special case of 𝓁 = 1. In recent work by Resch, Yuan and Zhang (ICALP 2023) the zero-rate threshold for list-recovery was determined for all parameters: that is, the work explicitly computes p_*: = p_*(q,𝓁,L) with the property that for all ε > 0 (a) there exist positive-rate (p_*-ε,𝓁,L)-list-recoverable codes, and (b) any (p_*+ε,𝓁,L)-list-recoverable code has rate 0. In fact, in the latter case the code has constant size, independent on n. However, the constant size in their work is quite large in 1/ε, at least |𝒞| ≥ (1/(ε))^O(q^L). Our contribution in this work is to show that for all choices of q,𝓁 and L with q ≥ 3, any (p_*+ε,𝓁,L)-list-recoverable code must have size O_{q,𝓁,L}(1/ε), and furthermore this upper bound is complemented by a matching lower bound Ω_{q,𝓁,L}(1/ε). This greatly generalizes work by Alon, Bukh and Polyanskiy (IEEE Trans. Inf. Theory 2018) which focused only on the case of binary alphabet (and thus necessarily only list-decoding). We remark that we can in fact recover the same result for q = 2 and even L, as obtained by Alon, Bukh and Polyanskiy: we thus strictly generalize their work. Our main technical contribution is to (a) properly define a linear programming relaxation of the list-recovery condition over large alphabets; and (b) to demonstrate that a certain function defined on a q-ary probability simplex is maximized by the uniform distribution. This represents the core challenge in generalizing to larger q (as a binary simplex can be naturally identified with a one-dimensional interval). We can subsequently re-utilize certain Schur convexity and convexity properties established for a related function by Resch, Yuan and Zhang along with ideas of Alon, Bukh and Polyanskiy.}, author = {Resch, Nicolas and Yuan, Chen and Zhang, Yihan}, booktitle = {16th Innovations in Theoretical Computer Science Conference}, isbn = {9783959773614}, issn = {1868-8969}, location = {New York, NY, United States}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Tight bounds on list-decodable and list-recoverable zero-rate codes}}, doi = {10.4230/LIPIcs.ITCS.2025.82}, volume = {325}, year = {2025}, } @inproceedings{21412, abstract = {Payment channel networks (PCNs) are a promising technology that alleviates blockchain scalability by shifting the transaction load from the blockchain to the PCN. Nevertheless, the network topology has to be carefully designed to maximise the transaction throughput in PCNs. Additionally, users in PCNs also have to make optimal decisions on which transactions to forward and which to reject to prolong the lifetime of their channels. In this work, we consider an input sequence of transactions over p parties. Each transaction consists of a transaction size, source, and target, and can be either accepted or rejected (entailing a cost). The goal is to design a PCN topology among the p cooperating parties, along with the channel capacities, and then output a decision for each transaction in the sequence to minimise the cost of creating and augmenting channels, as well as the cost of rejecting transactions. Our main contribution is an 𝒪(p) approximation algorithm for the problem with p parties. We further show that with some assumptions on the distribution of transactions, we can reduce the approximation ratio to 𝒪(√p). We complement our theoretical analysis with an empirical study of our assumptions and approach in the context of the Lightning Network.}, author = {Chatterjee, Krishnendu and Křišťan, Jan Matyáš and Schmid, Stefan and Svoboda, Jakub and Yeo, Michelle X}, booktitle = {39th International Symposium on Distributed Computing}, isbn = {9783959774024}, issn = {1868-8969}, location = {Berlin, Germany}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Boosting payment channel network liquidity with topology optimization and transaction selection}}, doi = {10.4230/LIPIcs.DISC.2025.23}, volume = {356}, year = {2025}, } @inproceedings{20587, abstract = {The blocks in the Bitcoin blockchain "record" the amount of work W that went into creating them through proofs of work. When honest parties control a majority of the work, consensus is achieved by picking the chain with the highest recorded weight. Resources other than work have been considered to secure such longest-chain blockchains. In Chia, blocks record the amount of disk-space S (via a proof of space) and sequential computational steps V (through a VDF). In this paper, we ask what weight functions Γ(S,V,W) (that assign a weight to a block as a function of the recorded space, speed, and work) are secure in the sense that whenever the weight of the resources controlled by honest parties is larger than the weight of adversarial parties, the blockchain is secure against private double-spending attacks. We completely classify such functions in an idealized "continuous" model: Γ(S,V,W) is secure against private double-spending attacks if and only if it is homogeneous of degree one in the "timed" resources V and W, i.e., αΓ(S,V,W) = Γ(S,α V, α W). This includes the Bitcoin rule Γ(S,V,W) = W and the Chia rule Γ(S,V,W) = S ⋅ V. In a more realistic model where blocks are created at discrete time-points, one additionally needs some mild assumptions on the dependency on S (basically, the weight should not grow too much if S is slightly increased, say linear as in Chia). Our classification is more general and allows various instantiations of the same resource. It provides a powerful tool for designing new longest-chain blockchains. E.g., consider combining different PoWs to counter centralization, say the Bitcoin PoW W₁ and a memory-hard PoW W₂. Previous work suggested to use W₁+W₂ as weight. Our results show that using e.g., √{W₁}⋅ √{W₂} or min{W₁,W₂} are also secure, and we argue that in practice these are much better choices.}, author = {Baig, Mirza Ahad and Günther, Christoph Ullrich and Pietrzak, Krzysztof Z}, booktitle = {7th Conference on Advances in Financial Technologies}, isbn = {9783959774000}, issn = {1868-8969}, location = {Pittsburgh, PA, United States}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Nakamoto consensus from multiple resources}}, doi = {10.4230/LIPIcs.AFT.2025.16}, volume = {354}, year = {2025}, } @inproceedings{18066, abstract = {Graph games lie at the algorithmic core of many automated design problems in computer science. These are games usually played between two players on a given graph, where the players keep moving a token along the edges according to pre-determined rules (turn-based, concurrent, etc.), and the winner is decided based on the infinite path (aka play) traversed by the token from a given initial position. In bidding games, the players initially get some monetary budgets which they need to use to bid for the privilege of moving the token at each step. Each round of bidding affects the players' available budgets, which is the only form of update that the budgets experience. We introduce bidding games with charging where the players can additionally improve their budgets during the game by collecting vertex-dependent monetary rewards, aka the "charges." Unlike traditional bidding games (where all charges are zero), bidding games with charging allow non-trivial recurrent behaviors. For example, a reachability objective may require multiple detours to vertices with high charges to earn additional budget. We show that, nonetheless, the central property of traditional bidding games generalizes to bidding games with charging: For each vertex there exists a threshold ratio, which is the necessary and sufficient fraction of the total budget for winning the game from that vertex. While the thresholds of traditional bidding games correspond to unique fixed points of linear systems of equations, in games with charging, these fixed points are no longer unique. This significantly complicates the proof of existence and the algorithmic computation of thresholds for infinite-duration objectives. We also provide the lower complexity bounds for computing thresholds for Rabin and Streett objectives, which are the first known lower bounds in any form of bidding games (with or without charging), and we solve the following repair problem for safety and reachability games that have unsatisfiable objectives: Can we distribute a given amount of charge to the players in a way such that the objective can be satisfied?}, author = {Avni, Guy and Goharshady, Ehsan Kafshdar and Henzinger, Thomas A and Mallik, Kaushik}, booktitle = {35th International Conference on Concurrency Theory}, isbn = {9783959773393}, issn = {1868-8969}, location = {Calgary, Canada}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Bidding games with charging}}, doi = {10.4230/LIPIcs.CONCUR.2024.8}, volume = {311}, year = {2024}, } @inproceedings{18067, abstract = {An automaton 𝒜 is history-deterministic if its nondeterminism can be resolved on the fly, only using the prefix of the word read so far. This mild form of nondeterminism has attracted particular attention for its applications in synthesis problems. An automaton 𝒜 is guidable with respect to a class C of automata if it can fairly simulate every automaton in C, whose language is contained in that of 𝒜. In other words, guidable automata are those for which inclusion and simulation coincide, making them particularly interesting for model-checking. We study the connection between these two notions, and specifically the question of when they coincide. For classes of automata on which they do, deciding guidability, an otherwise challenging decision problem, reduces to deciding history-determinism, a problem that is starting to be well-understood for many classes. We provide a selection of sufficient criteria for a class of automata to guarantee the coincidence of the notions, and use them to show that the notions coincide for the most common automata classes, among which are ω-regular automata and many infinite-state automata with safety and reachability acceptance conditions, including vector addition systems with states, one-counter nets, pushdown-, Parikh-, and timed-automata. We also demonstrate that history-determinism and guidability do not always coincide, for example, for the classes of timed automata with a fixed number of clocks.}, author = {Boker, Udi and Henzinger, Thomas A and Lehtinen, Karoliina and Prakash, Aditya}, booktitle = {35th International Conference on Concurrency Theory}, isbn = {9783959773393}, issn = {1868-8969}, location = {Calgary, Canada}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{History-determinism vs fair simulation}}, doi = {10.4230/LIPIcs.CONCUR.2024.12}, volume = {311}, year = {2024}, } @inproceedings{18068, abstract = {We study the following refinement relation between nondeterministic state-transition models: model ℬ strategically dominates model 𝒜 iff every deterministic refinement of 𝒜 is language contained in some deterministic refinement of ℬ. While language containment is trace inclusion, and the (fair) simulation preorder coincides with tree inclusion, strategic dominance falls strictly between the two and can be characterized as "strategy inclusion" between 𝒜 and ℬ: every strategy that resolves the nondeterminism of 𝒜 is dominated by a strategy that resolves the nondeterminism of ℬ. Strategic dominance can be checked in 2-ExpTime by a decidable first-order Presburger logic with quantification over words and strategies, called resolver logic. We give several other applications of resolver logic, including checking the co-safety, co-liveness, and history-determinism of boolean and quantitative automata, and checking the inclusion between hyperproperties that are specified by nondeterministic boolean and quantitative automata.}, author = {Henzinger, Thomas A and Mazzocchi, Nicolas Adrien and Sarac, Naci E}, booktitle = {35th International Conference on Concurrency Theory}, isbn = {9783959773393}, issn = {1868-8969}, location = {Calgary, Canada}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Strategic dominance: A new preorder for nondeterministic processes}}, doi = {10.4230/LIPIcs.CONCUR.2024.29}, volume = {311}, year = {2024}, } @inproceedings{18156, abstract = {Privately counting distinct elements in a stream is a fundamental data analysis problem with many applications in machine learning. In the turnstile model, Jain et al. [NeurIPS2023] initiated the study of this problem parameterized by the maximum flippancy of any element, i.e., the number of times that the count of an element changes from 0 to above 0 or vice versa. They give an item-level (ε,δ)-differentially private algorithm whose additive error is tight with respect to that parameterization. In this work, we show that a very simple algorithm based on the sparse vector technique achieves a tight additive error for item-level (ε,δ)-differential privacy and item-level ε-differential privacy with regards to a different parameterization, namely the sum of all flippancies. Our second result is a bound which shows that for a large class of algorithms, including all existing differentially private algorithms for this problem, the lower bound from item-level differential privacy extends to event-level differential privacy. This partially answers an open question by Jain et al. [NeurIPS2023].}, author = {Henzinger, Monika H and Sricharan, A. R. and Steiner, Teresa Anna}, booktitle = {International Conference on Approximation Algorithms for Combinatorial Optimization Problems }, isbn = {9783959773485}, issn = {1868-8969}, location = {London, United Kingdom}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Private counting of distinct elements in the turnstile model and extensions}}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2024.40}, volume = {317}, year = {2024}, } @inproceedings{18175, abstract = {Large-scale software repositories are a source of insights for software engineering. They offer an unmatched window into the software development process at scale. Their sheer number and size holds the promise of broadly applicable results. At the same time, that very size presents practical challenges for scaling tools and algorithms to millions of projects. A reasonable approach is to limit studies to representative samples of the population of interest. Broadly applicable conclusions can then be obtained by generalizing to the entire population. The contribution of this paper is a standardized experimental design methodology for choosing the inputs of studies working with large-scale repositories. We advocate for a methodology that clearly lays out what the population of interest is, how to sample it, and that fosters reproducibility. Along the way, we discourage researchers from using extrinsic attributes of projects such as stars, that measure some unclear notion of popularity.}, author = {Maj, Petr and Muroya Lei, Stefanie and Siek, Konrad and Di Grazia, Luca and Vitek, Jan}, booktitle = {38th European Conference on Object-Oriented Programming}, isbn = {9783959773416}, issn = {1868-8969}, location = {Vienna, Austria}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{The fault in our stars: Designing reproducible large-scale code analysis experiments}}, doi = {10.4230/LIPIcs.ECOOP.2024.27}, volume = {313}, year = {2024}, } @inproceedings{18308, abstract = {We study in this paper the problem of maintaining a solution to k-median and k-means clustering in a fully dynamic setting. To do so, we present an algorithm to efficiently maintain a coreset, a compressed version of the dataset, that allows easy computation of a clustering solution at query time. Our coreset algorithm has near-optimal update time of Õ(k) in general metric spaces, which reduces to Õ(d) in the Euclidean space ℝ^d. The query time is O(k²) in general metrics, and O(kd) in ℝ^d. To maintain a constant-factor approximation for k-median and k-means clustering in Euclidean space, this directly leads to an algorithm with update time Õ(d), and query time Õ(kd + k²). To maintain a O(polylog k)-approximation, the query time is reduced to Õ(kd).}, author = {La Tour, Max Dupré and Henzinger, Monika H and Saulpic, David}, booktitle = {32nd Annual European Symposium on Algorithms}, isbn = {9783959773386}, issn = {1868-8969}, location = {London, United Kingdom}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Fully dynamic k-means coreset in near-optimal update time}}, doi = {10.4230/LIPIcs.ESA.2024.100}, volume = {308}, year = {2024}, } @inproceedings{18309, abstract = {The problem of designing connectivity oracles supporting vertex failures is one of the basic data structures problems for undirected graphs. It is already well understood: previous works [Duan-Pettie STOC'10; Long-Saranurak FOCS'22] achieve query time linear in the number of failed vertices, and it is conditionally optimal as long as we require preprocessing time polynomial in the size of the graph and update time polynomial in the number of failed vertices. We revisit this problem in the paradigm of algorithms with predictions: we ask if the query time can be improved if the set of failed vertices can be predicted beforehand up to a small number of errors. More specifically, we design a data structure that, given a graph G = (V,E) and a set of vertices predicted to fail D̂ ⊆ V of size d = |D̂|, preprocesses it in time Õ(d|E|) and then can receive an update given as the symmetric difference between the predicted and the actual set of failed vertices D̂△D = (D̂ ⧵ D) ∪ (D ⧵ D̂) of size η = |D̂△D|, process it in time Õ(η⁴), and after that answer connectivity queries in G ⧵ D in time O(η). Viewed from another perspective, our data structure provides an improvement over the state of the art for the fully dynamic subgraph connectivity problem in the sensitivity setting [Henzinger-Neumann ESA'16]. We argue that the preprocessing time and query time of our data structure are conditionally optimal under standard fine-grained complexity assumptions.}, author = {Hu, Bingbing and Kosinas, Evangelos and Polak, Adam}, booktitle = {32nd Annual European Symposium on Algorithms}, isbn = {9783959773386}, issn = {1868-8969}, location = {London, United Kingdom}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Connectivity oracles for predictable vertex failures}}, doi = {10.4230/LIPIcs.ESA.2024.72}, volume = {308}, year = {2024}, } @inproceedings{18556, abstract = {Given a finite set, A ⊆ ℝ², and a subset, B ⊆ A, the MST-ratio is the combined length of the minimum spanning trees of B and A⧵B divided by the length of the minimum spanning tree of A. The question of the supremum, over all sets A, of the maximum, over all subsets B, is related to the Steiner ratio, and we prove this sup-max is between 2.154 and 2.427. Restricting ourselves to 2-dimensional lattices, we prove that the sup-max is 2, while the inf-max is 1.25. By some margin the most difficult of these results is the upper bound for the inf-max, which we prove by showing that the hexagonal lattice cannot have MST-ratio larger than 1.25.}, author = {Cultrera di Montesano, Sebastiano and Draganov, Ondrej and Edelsbrunner, Herbert and Saghafian, Morteza}, booktitle = {32nd International Symposium on Graph Drawing and Network Visualization}, isbn = {9783959773430}, issn = {1868-8969}, location = {Vienna, Austria}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{The Euclidean MST-ratio for bi-colored lattices}}, doi = {10.4230/LIPIcs.GD.2024.3}, volume = {320}, year = {2024}, } @inproceedings{18557, abstract = {Broadcast and Consensus are most fundamental tasks in distributed computing. These tasks are particularly challenging in dynamic networks where communication across the network links may be unreliable, e.g., due to mobility or failures. Over the last years, researchers have derived several impossibility results and high time complexity lower bounds for these tasks. Specifically for the setting where in each round of communication the adversary is allowed to choose one rooted tree along which the information is disseminated, there is a lower as well as an upper bound that is linear in the number n of nodes for Broadcast and for n ≥ 3 the adversary can guarantee that Consensus never happens. This setting is called the oblivious message adversary for rooted trees. Also note that if the adversary is allowed to choose a graph that does not contain a rooted tree, then it can guarantee that Broadcast and Consensus will never happen. However, such deterministic adversarial models may be overly pessimistic, as many processes in real-world settings are stochastic in nature rather than worst-case. This paper studies Broadcast on stochastic dynamic networks and shows that the situation is very different to the deterministic case. In particular, we show that if information dissemination occurs along random rooted trees and directed Erdős–Rényi graphs, Broadcast completes in O(log n) rounds of communication with high probability. The fundamental insight in our analysis is that key variables are mutually independent. We then study two adversarial models, (a) one with Byzantine nodes and (b) one where an adversary controls the edges. (a) Our techniques without Byzantine nodes are general enough so that they can be extended to Byzantine nodes. (b) In the spirit of smoothed analysis, we introduce the notion of randomized oblivious message adversary, where in each round, an adversary picks k ≤ 2n/3 edges to appear in the communication network, and then a graph (e.g. rooted tree or directed Erdős–Rényi graph) is chosen uniformly at random among the set of all such graphs that include these edges. We show that Broadcast completes in a finite number of rounds, which is, e.g., O(k+log n) rounds in rooted trees. We then extend these results to All-to-All Broadcast, and Consensus, and give lower bounds that show that most of our upper bounds are tight.}, author = {El-Hayek, Antoine and Henzinger, Monika H and Schmid, Stefan}, booktitle = {38th International Symposium on Distributed Computing}, isbn = {9783959773522}, issn = {1868-8969}, location = {Madrid, Spain}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Broadcast and Consensus in stochastic dynamic networks with Byzantine nodes and adversarial edges}}, doi = {10.4230/LIPIcs.DISC.2024.21}, volume = {319}, year = {2024}, }