@inproceedings{9620,
  abstract     = {In this note, we introduce a distributed twist on the classic coupon collector problem: a set of m collectors wish to each obtain a set of n coupons; for this, they can each sample coupons uniformly at random, but can also meet in pairwise interactions, during which they can exchange coupons. By doing so, they hope to reduce the number of coupons that must be sampled by each collector in order to obtain a full set. This extension is natural when considering real-world manifestations of the coupon collector phenomenon, and has been remarked upon and studied empirically (Hayes and Hannigan 2006, Ahmad et al. 2014, Delmarcelle 2019).

We provide the first theoretical analysis for such a scenario. We find that “coupon collecting with friends” can indeed significantly reduce the number of coupons each collector must sample, and raises interesting connections to the more traditional variants of the problem. While our analysis is in most cases asymptotically tight, there are several open questions raised, regarding finer-grained analysis of both “coupon collecting with friends,” and of a long-studied variant of the original problem in which a collector requires multiple full sets of coupons.},
  author       = {Alistarh, Dan-Adrian and Davies, Peter},
  booktitle    = {Structural Information and Communication Complexity},
  isbn         = {9783030795269},
  issn         = {1611-3349},
  location     = {Wrocław, Poland},
  pages        = {3--12},
  publisher    = {Springer Nature},
  title        = {{Collecting coupons is faster with friends}},
  doi          = {10.1007/978-3-030-79527-6_1},
  volume       = {12810},
  year         = {2021},
}

@inproceedings{9823,
  abstract     = {Approximate agreement is one of the few variants of consensus that can be solved in a wait-free manner in asynchronous systems where processes communicate by reading and writing to shared memory. In this work, we consider a natural generalisation of approximate agreement on arbitrary undirected connected graphs. Each process is given a vertex of the graph as input and, if non-faulty, must output a vertex such that
all the outputs are within distance 1 of one another, and

each output value lies on a shortest path between two input values.

From prior work, it is known that there is no wait-free algorithm among   𝑛≥3  processes for this problem on any cycle of length   𝑐≥4 , by reduction from 2-set agreement (Castañeda et al. 2018).

In this work, we investigate the solvability and complexity of this task on general graphs. We give a new, direct proof of the impossibility of approximate agreement on cycles of length   𝑐≥4 , via a generalisation of Sperner’s Lemma to convex polygons. We also extend the reduction from 2-set agreement to a larger class of graphs, showing that approximate agreement on these graphs is unsolvable. On the positive side, we present a wait-free algorithm for a class of graphs that properly contains the class of chordal graphs.},
  author       = {Alistarh, Dan-Adrian and Ellen, Faith and Rybicki, Joel},
  booktitle    = {Structural Information and Communication Complexity},
  isbn         = {9783030795269},
  issn         = {1611-3349},
  location     = {Wrocław, Poland},
  pages        = {87--105},
  publisher    = {Springer Nature},
  title        = {{Wait-free approximate agreement on graphs}},
  doi          = {10.1007/978-3-030-79527-6_6},
  volume       = {12810},
  year         = {2021},
}