---
OA_place: publisher
_id: '17208'
abstract:
- lang: eng
text: "Can current quantum computers provide a speedup over their classical counterparts
for some kinds of problems? In this thesis, with a focus on ground state search/preparation,
we address some of the challenges that both quantum annealing and variational
quantum algorithms suffer from, hindering any possible practical speedup in comparison
to the best classical counterparts. \r\n\r\nIn the first part of the thesis, we
study the performance of quantum annealing for solving a particular combinatorial
optimization problem called 3-XOR satisfability (3-XORSAT). The classical problem
is mapped into a ground state search of a 3-local classical Hamiltonian $H_C$.
We consider how modifying the initial problem, by adding more interaction terms
to the corresponding Hamiltonian, leads to the emergence of a first-order phase
transition during the annealing process. This phenomenon causes the total annealing
duration, $T$, required to prepare the ground state of $H_C$ with a high probability
to increase exponentially with the size of the problem. Our findings indicate
that with the growing complexity of problem instances, the likelihood of encountering
first-order phase transitions also increases, making quantum annealing an impractical
solution for these types of combinatorial optimization problems.\r\n\r\nIn the
second part, we focus on the problem of barren plateaus in generic variational
quantum algorithms. Barren plateaus correspond to flat regions in the parameter
space where the gradient of the cost function is zero in expectation, and with
the variance decaying exponentially with the system size, thus obstructing an
efficient parameter optimization. We propose an algorithm to circumvent Barren
Plateaus by monitoring the entanglement entropy of k-local reduced density matrices,
alongside a method for estimating entanglement entropy via classical shadow tomography.
We illustrate the approach with the paradigmatic example of the variational quantum
eigensolver, and show that our algorithm effectively avoids barren plateaus in
the initialization as well as during the optimization stage. \r\n\r\nLastly, in
the last two Chapters of this thesis, we focus on the quantum approximate optimization
algorithm (QAOA), originally introduced as an algorithm for solving generic combinatorial
optimization problems in near-term quantum devices. Specifically, we focus on
how to develop rigorous initialization strategies with guarantee improvement.
Our motivation for this study lies in that for random initialization, the optimization
typically leads to local minima with poor performance. Our main result corresponds
to the analytical construction of index-1 saddle points or transition states,
stationary points with a single direction of descent, as a tool for systematically
exploring the QAOA optimization landscape. This leads us to propose a novel greedy
parameter initialization strategy that guarantees for the energy to decrease with
an increasing number of circuit layers. Furthermore, with precise estimates for
the negative Hessian eigenvalue and its eigenvector, we establish a lower bound
for energy improvement following a QAOA iteration."
acknowledged_ssus:
- _id: ScienComp
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Raimel A
full_name: Medina Ramos, Raimel A
id: CE680B90-D85A-11E9-B684-C920E6697425
last_name: Medina Ramos
orcid: 0000-0002-5383-2869
citation:
ama: Medina Ramos RA. Exploring the optimization landscape of variational quantum
algorithms. 2024. doi:10.15479/at:ista:17208
apa: Medina Ramos, R. A. (2024). Exploring the optimization landscape of variational
quantum algorithms. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17208
chicago: Medina Ramos, Raimel A. “Exploring the Optimization Landscape of Variational
Quantum Algorithms.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17208.
ieee: R. A. Medina Ramos, “Exploring the optimization landscape of variational quantum
algorithms,” Institute of Science and Technology Austria, 2024.
ista: Medina Ramos RA. 2024. Exploring the optimization landscape of variational
quantum algorithms. Institute of Science and Technology Austria.
mla: Medina Ramos, Raimel A. Exploring the Optimization Landscape of Variational
Quantum Algorithms. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17208.
short: R.A. Medina Ramos, Exploring the Optimization Landscape of Variational Quantum
Algorithms, Institute of Science and Technology Austria, 2024.
corr_author: '1'
date_created: 2024-07-09T09:14:24Z
date_published: 2024-07-09T00:00:00Z
date_updated: 2026-04-07T12:43:22Z
day: '09'
ddc:
- '539'
degree_awarded: PhD
department:
- _id: GradSch
- _id: MaSe
doi: 10.15479/at:ista:17208
ec_funded: 1
file:
- access_level: closed
checksum: 6f45273d04f4418bc2adc018baed0525
content_type: application/zip
creator: rmedinar
date_created: 2024-07-09T09:21:44Z
date_updated: 2024-07-10T11:34:09Z
file_id: '17212'
file_name: Raimel_Thesis-Final.zip
file_size: '14218691'
relation: source_file
- access_level: open_access
checksum: 6724a95bec772dbabc0111b9f08a805e
content_type: application/pdf
creator: rmedinar
date_created: 2024-07-17T09:23:24Z
date_updated: 2024-07-17T09:23:24Z
file_id: '17275'
file_name: Raimel_Thesis-20_pdfa.pdf
file_size: 11253627
relation: main_file
success: 1
file_date_updated: 2024-07-17T09:23:24Z
has_accepted_license: '1'
keyword:
- Quantum computing
- Variational Quantum Algorithms
- Optimization
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: '133'
project:
- _id: 23841C26-32DE-11EA-91FC-C7463DDC885E
call_identifier: H2020
grant_number: '850899'
name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '10545'
relation: part_of_dissertation
status: public
- id: '10067'
relation: part_of_dissertation
status: public
- id: '17222'
relation: part_of_dissertation
status: public
- id: '13125'
relation: part_of_dissertation
status: public
- id: '11471'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Maksym
full_name: Serbyn, Maksym
id: 47809E7E-F248-11E8-B48F-1D18A9856A87
last_name: Serbyn
orcid: 0000-0002-2399-5827
title: Exploring the optimization landscape of variational quantum algorithms
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
_id: '10004'
abstract:
- lang: eng
text: 'Markov chains are the de facto finite-state model for stochastic dynamical
systems, and Markov decision processes (MDPs) extend Markov chains by incorporating
non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization
criterion is the maximal expected total reward where the MDP stops after T steps,
which can be computed by a simple dynamic programming algorithm. We consider a
natural generalization of the problem where the stopping times can be chosen according
to a probability distribution, such that the expected stopping time is T, to optimize
the expected total reward. Quite surprisingly we establish inter-reducibility
of the expected stopping-time problem for Markov chains with the Positivity problem
(which is related to the well-known Skolem problem), for which establishing either
decidability or undecidability would be a major breakthrough. Given the hardness
of the exact problem, we consider the approximate version of the problem: we show
that it can be solved in exponential time for Markov chains and in exponential
space for MDPs.'
acknowledgement: We are grateful to the anonymous reviewers of LICS 2021 and of a
previous version of this paper for insightful comments that helped improving the
presentation. This research was partially supported by the grant ERC CoG 863818
(ForM-SMArt).
article_processing_charge: No
arxiv: 1
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Laurent
full_name: Doyen, Laurent
last_name: Doyen
citation:
ama: 'Chatterjee K, Doyen L. Stochastic processes with expected stopping time. In:
Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science.
Institute of Electrical and Electronics Engineers; 2021:1-13. doi:10.1109/LICS52264.2021.9470595'
apa: 'Chatterjee, K., & Doyen, L. (2021). Stochastic processes with expected
stopping time. In Proceedings of the 36th Annual ACM/IEEE Symposium on Logic
in Computer Science (pp. 1–13). Rome, Italy: Institute of Electrical and Electronics
Engineers. https://doi.org/10.1109/LICS52264.2021.9470595'
chicago: Chatterjee, Krishnendu, and Laurent Doyen. “Stochastic Processes with Expected
Stopping Time.” In Proceedings of the 36th Annual ACM/IEEE Symposium on Logic
in Computer Science, 1–13. Institute of Electrical and Electronics Engineers,
2021. https://doi.org/10.1109/LICS52264.2021.9470595.
ieee: K. Chatterjee and L. Doyen, “Stochastic processes with expected stopping time,”
in Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science,
Rome, Italy, 2021, pp. 1–13.
ista: 'Chatterjee K, Doyen L. 2021. Stochastic processes with expected stopping
time. Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science.
LICS: Logic in Computer Science, 1–13.'
mla: Chatterjee, Krishnendu, and Laurent Doyen. “Stochastic Processes with Expected
Stopping Time.” Proceedings of the 36th Annual ACM/IEEE Symposium on Logic
in Computer Science, Institute of Electrical and Electronics Engineers, 2021,
pp. 1–13, doi:10.1109/LICS52264.2021.9470595.
short: K. Chatterjee, L. Doyen, in:, Proceedings of the 36th Annual ACM/IEEE Symposium
on Logic in Computer Science, Institute of Electrical and Electronics Engineers,
2021, pp. 1–13.
conference:
end_date: 2021-07-02
location: Rome, Italy
name: 'LICS: Logic in Computer Science'
start_date: 2021-06-29
date_created: 2021-09-12T22:01:25Z
date_published: 2021-07-07T00:00:00Z
date_updated: 2025-09-08T14:54:13Z
day: '07'
department:
- _id: KrCh
doi: 10.1109/LICS52264.2021.9470595
ec_funded: 1
external_id:
arxiv:
- '2104.07278'
isi:
- '000947350400036'
isi: 1
keyword:
- Computer science
- Heuristic algorithms
- Memory management
- Automata
- Markov processes
- Probability distribution
- Complexity theory
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2104.07278
month: '07'
oa: 1
oa_version: Preprint
page: 1-13
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
publication: Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer
Science
publication_identifier:
eisbn:
- 978-1-6654-4895-6
isbn:
- 978-1-6654-4896-3
issn:
- 1043-6871
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
related_material:
record:
- id: '18630'
relation: later_version
status: public
scopus_import: '1'
status: public
title: Stochastic processes with expected stopping time
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '11675'
abstract:
- lang: eng
text: 'We consider the problems of maintaining an approximate maximum matching and
an approximate minimum vertex cover in a dynamic graph undergoing a sequence of
edge insertions/deletions. Starting with the seminal work of Onak and Rubinfeld
(in: Proceedings of the ACM symposium on theory of computing (STOC), 2010), this
problem has received significant attention in recent years. Very recently, extending
the framework of Baswana et al. (in: Proceedings of the IEEE symposium on foundations
of computer science (FOCS), 2011) , Solomon (in: Proceedings of the IEEE symposium
on foundations of computer science (FOCS), 2016) gave a randomized dynamic algorithm
for this problem that has an approximation ratio of 2 and an amortized update
time of O(1) with high probability. This algorithm requires the assumption of
an oblivious adversary, meaning that the future sequence of edge insertions/deletions
in the graph cannot depend in any way on the algorithm’s past output. A natural
way to remove the assumption on oblivious adversary is to give a deterministic
dynamic algorithm for the same problem in O(1) update time. In this paper, we
resolve this question. We present a new deterministic fully dynamic algorithm
that maintains a O(1)-approximate minimum vertex cover and maximum fractional
matching, with an amortized update time of O(1). Previously, the best deterministic
algorithm for this problem was due to Bhattacharya et al. (in: Proceedings of
the ACM-SIAM symposium on discrete algorithms (SODA), 2015); it had an approximation
ratio of (2+ε) and an amortized update time of O(logn/ε2). Our result can be generalized
to give a fully dynamic O(f3)-approximate algorithm with O(f2) amortized update
time for the hypergraph vertex cover and fractional hypergraph matching problem,
where every hyperedge has at most f vertices.'
article_processing_charge: No
article_type: original
author:
- first_name: Sayan
full_name: Bhattacharya, Sayan
last_name: Bhattacharya
- first_name: Deeparnab
full_name: Chakrabarty, Deeparnab
last_name: Chakrabarty
- first_name: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
citation:
ama: Bhattacharya S, Chakrabarty D, Henzinger M. Deterministic dynamic matching
in O(1) update time. Algorithmica. 2020;82(4):1057-1080. doi:10.1007/s00453-019-00630-4
apa: Bhattacharya, S., Chakrabarty, D., & Henzinger, M. (2020). Deterministic
dynamic matching in O(1) update time. Algorithmica. Springer Nature. https://doi.org/10.1007/s00453-019-00630-4
chicago: Bhattacharya, Sayan, Deeparnab Chakrabarty, and Monika Henzinger. “Deterministic
Dynamic Matching in O(1) Update Time.” Algorithmica. Springer Nature, 2020.
https://doi.org/10.1007/s00453-019-00630-4.
ieee: S. Bhattacharya, D. Chakrabarty, and M. Henzinger, “Deterministic dynamic
matching in O(1) update time,” Algorithmica, vol. 82, no. 4. Springer Nature,
pp. 1057–1080, 2020.
ista: Bhattacharya S, Chakrabarty D, Henzinger M. 2020. Deterministic dynamic matching
in O(1) update time. Algorithmica. 82(4), 1057–1080.
mla: Bhattacharya, Sayan, et al. “Deterministic Dynamic Matching in O(1) Update
Time.” Algorithmica, vol. 82, no. 4, Springer Nature, 2020, pp. 1057–80,
doi:10.1007/s00453-019-00630-4.
short: S. Bhattacharya, D. Chakrabarty, M. Henzinger, Algorithmica 82 (2020) 1057–1080.
date_created: 2022-07-27T14:31:06Z
date_published: 2020-04-01T00:00:00Z
date_updated: 2024-11-06T12:07:43Z
day: '01'
doi: 10.1007/s00453-019-00630-4
extern: '1'
intvolume: ' 82'
issue: '4'
keyword:
- Dynamic algorithms
- Data structures
- Graph algorithms
- Matching
- Vertex cover
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00453-019-00630-4
month: '04'
oa: 1
oa_version: Published Version
page: 1057-1080
publication: Algorithmica
publication_identifier:
eissn:
- 1432-0541
issn:
- 0178-4617
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Deterministic dynamic matching in O(1) update time
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 82
year: '2020'
...
---
_id: '11676'
abstract:
- lang: eng
text: We study the problem of maximizing a monotone submodular function with viability
constraints. This problem originates from computational biology, where we are
given a phylogenetic tree over a set of species and a directed graph, the so-called
food web, encoding viability constraints between these species. These food webs
usually have constant depth. The goal is to select a subset of k species that
satisfies the viability constraints and has maximal phylogenetic diversity. As
this problem is known to be NP-hard, we investigate approximation algorithms.
We present the first constant factor approximation algorithm if the depth is constant.
Its approximation ratio is (1−1e√). This algorithm not only applies to phylogenetic
trees with viability constraints but for arbitrary monotone submodular set functions
with viability constraints. Second, we show that there is no (1−1/e+ϵ)-approximation
algorithm for our problem setting (even for additive functions) and that there
is no approximation algorithm for a slight extension of this setting.
acknowledgement: "The research leading to these results has received funding from
the European Research\r\nCouncil under the European Union’s Seventh Framework Programme
(FP/2007-2013)/ERC Grant Agreement No. 340506."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Wolfgang
full_name: Dvořák, Wolfgang
last_name: Dvořák
- first_name: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
- first_name: David P.
full_name: Williamson, David P.
last_name: Williamson
citation:
ama: Dvořák W, Henzinger M, Williamson DP. Maximizing a submodular function with
viability constraints. Algorithmica. 2017;77(1):152-172. doi:10.1007/s00453-015-0066-y
apa: Dvořák, W., Henzinger, M., & Williamson, D. P. (2017). Maximizing a submodular
function with viability constraints. Algorithmica. Springer Nature. https://doi.org/10.1007/s00453-015-0066-y
chicago: Dvořák, Wolfgang, Monika Henzinger, and David P. Williamson. “Maximizing
a Submodular Function with Viability Constraints.” Algorithmica. Springer
Nature, 2017. https://doi.org/10.1007/s00453-015-0066-y.
ieee: W. Dvořák, M. Henzinger, and D. P. Williamson, “Maximizing a submodular function
with viability constraints,” Algorithmica, vol. 77, no. 1. Springer Nature,
pp. 152–172, 2017.
ista: Dvořák W, Henzinger M, Williamson DP. 2017. Maximizing a submodular function
with viability constraints. Algorithmica. 77(1), 152–172.
mla: Dvořák, Wolfgang, et al. “Maximizing a Submodular Function with Viability Constraints.”
Algorithmica, vol. 77, no. 1, Springer Nature, 2017, pp. 152–72, doi:10.1007/s00453-015-0066-y.
short: W. Dvořák, M. Henzinger, D.P. Williamson, Algorithmica 77 (2017) 152–172.
date_created: 2022-07-27T14:37:24Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2024-11-06T12:07:55Z
day: '01'
doi: 10.1007/s00453-015-0066-y
extern: '1'
external_id:
arxiv:
- '1611.05753'
intvolume: ' 77'
issue: '1'
keyword:
- Approximation algorithms
- Submodular functions
- Phylogenetic diversity
- Viability constraints
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1611.05753
month: '01'
oa: 1
oa_version: Preprint
page: 152-172
publication: Algorithmica
publication_identifier:
eissn:
- 1432-0541
issn:
- 0178-4617
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Maximizing a submodular function with viability constraints
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 77
year: '2017'
...
---
_id: '11668'
abstract:
- lang: eng
text: "We study multiple keyword sponsored search auctions with budgets. Each keyword
has multiple ad slots with a click-through rate. The bidders have additive valuations,
which are linear in the click-through rates, and budgets, which are restricting
their overall payments. Additionally, the number of slots per keyword assigned
to a bidder is bounded.\r\n\r\nWe show the following results: (1) We give the
first mechanism for multiple keywords, where click-through rates differ among
slots. Our mechanism is incentive compatible in expectation, individually rational
in expectation, and Pareto optimal. (2) We study the combinatorial setting, where
each bidder is only interested in a subset of the keywords. We give an incentive
compatible, individually rational, Pareto-optimal, and deterministic mechanism
for identical click-through rates. (3) We give an impossibility result for incentive
compatible, individually rational, Pareto-optimal, and deterministic mechanisms
for bidders with diminishing marginal valuations."
article_number: '2'
article_processing_charge: No
article_type: original
author:
- first_name: Riccardo
full_name: Colini-Baldeschi, Riccardo
last_name: Colini-Baldeschi
- first_name: Stefano
full_name: Leonardi, Stefano
last_name: Leonardi
- first_name: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
- first_name: Martin
full_name: Starnberger, Martin
last_name: Starnberger
citation:
ama: Colini-Baldeschi R, Leonardi S, Henzinger M, Starnberger M. On multiple keyword
sponsored search auctions with budgets. ACM Transactions on Economics and Computation.
2015;4(1). doi:10.1145/2818357
apa: Colini-Baldeschi, R., Leonardi, S., Henzinger, M., & Starnberger, M. (2015).
On multiple keyword sponsored search auctions with budgets. ACM Transactions
on Economics and Computation. Association for Computing Machinery. https://doi.org/10.1145/2818357
chicago: Colini-Baldeschi, Riccardo, Stefano Leonardi, Monika Henzinger, and Martin
Starnberger. “On Multiple Keyword Sponsored Search Auctions with Budgets.” ACM
Transactions on Economics and Computation. Association for Computing Machinery,
2015. https://doi.org/10.1145/2818357.
ieee: R. Colini-Baldeschi, S. Leonardi, M. Henzinger, and M. Starnberger, “On multiple
keyword sponsored search auctions with budgets,” ACM Transactions on Economics
and Computation, vol. 4, no. 1. Association for Computing Machinery, 2015.
ista: Colini-Baldeschi R, Leonardi S, Henzinger M, Starnberger M. 2015. On multiple
keyword sponsored search auctions with budgets. ACM Transactions on Economics
and Computation. 4(1), 2.
mla: Colini-Baldeschi, Riccardo, et al. “On Multiple Keyword Sponsored Search Auctions
with Budgets.” ACM Transactions on Economics and Computation, vol. 4, no.
1, 2, Association for Computing Machinery, 2015, doi:10.1145/2818357.
short: R. Colini-Baldeschi, S. Leonardi, M. Henzinger, M. Starnberger, ACM Transactions
on Economics and Computation 4 (2015).
date_created: 2022-07-27T11:54:56Z
date_published: 2015-12-05T00:00:00Z
date_updated: 2024-11-06T12:06:41Z
day: '05'
doi: 10.1145/2818357
extern: '1'
intvolume: ' 4'
issue: '1'
keyword:
- Algorithms
- Economics
- Clinching ascending auction
- auctions with budgets
- Sponsored search auctions
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://eprints.cs.univie.ac.at/3510/
month: '12'
oa: 1
oa_version: Submitted Version
publication: ACM Transactions on Economics and Computation
publication_identifier:
eissn:
- 2167-8383
issn:
- 2167-8375
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: On multiple keyword sponsored search auctions with budgets
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 4
year: '2015'
...
---
_id: '11679'
abstract:
- lang: eng
text: "We are given a set T = {T 1 ,T 2 , . . .,T k } of rooted binary trees, each
T i leaf-labeled by a subset L(Ti)⊂{1,2,...,n} . If T is a tree on {1,2, . . .,n
}, we let T|L denote the minimal subtree of T induced by the nodes of L and all
their ancestors. The consensus tree problem asks whether there exists a tree T
* such that, for every i , T∗|L(Ti) is homeomorphic to T i .\r\n\r\nWe present
algorithms which test if a given set of trees has a consensus tree and if so,
construct one. The deterministic algorithm takes time min{O(N n 1/2 ), O(N+ n
2 log n )}, where N=∑i|Ti| , and uses linear space. The randomized algorithm takes
time O(N log3 n) and uses linear space. The previous best for this problem was
a 1981 O(Nn) algorithm by Aho et al. Our faster deterministic algorithm uses a
new efficient algorithm for the following interesting dynamic graph problem: Given
a graph G with n nodes and m edges and a sequence of b batches of one or more
edge deletions, then, after each batch, either find a new component that has just
been created or determine that there is no such component. For this problem, we
have a simple algorithm with running time O(n 2 log n + b 0 min{n 2 , m log n
}), where b 0 is the number of batches which do not result in a new component.
For our particular application, b0≤1 . If all edges are deleted, then the best
previously known deterministic algorithm requires time O(mn−−√) to solve this
problem. We also present two applications of these consensus tree algorithms which
solve other problems in computational evolutionary biology."
article_processing_charge: No
article_type: original
author:
- first_name: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
- first_name: V.
full_name: King, V.
last_name: King
- first_name: T.
full_name: Warnow, T.
last_name: Warnow
citation:
ama: Henzinger M, King V, Warnow T. Constructing a tree from homeomorphic subtrees,
with applications to computational evolutionary biology. Algorithmica.
1999;24:1-13. doi:10.1007/pl00009268
apa: Henzinger, M., King, V., & Warnow, T. (1999). Constructing a tree from
homeomorphic subtrees, with applications to computational evolutionary biology.
Algorithmica. Springer Nature. https://doi.org/10.1007/pl00009268
chicago: Henzinger, Monika, V. King, and T. Warnow. “Constructing a Tree from Homeomorphic
Subtrees, with Applications to Computational Evolutionary Biology.” Algorithmica.
Springer Nature, 1999. https://doi.org/10.1007/pl00009268.
ieee: M. Henzinger, V. King, and T. Warnow, “Constructing a tree from homeomorphic
subtrees, with applications to computational evolutionary biology,” Algorithmica,
vol. 24. Springer Nature, pp. 1–13, 1999.
ista: Henzinger M, King V, Warnow T. 1999. Constructing a tree from homeomorphic
subtrees, with applications to computational evolutionary biology. Algorithmica.
24, 1–13.
mla: Henzinger, Monika, et al. “Constructing a Tree from Homeomorphic Subtrees,
with Applications to Computational Evolutionary Biology.” Algorithmica,
vol. 24, Springer Nature, 1999, pp. 1–13, doi:10.1007/pl00009268.
short: M. Henzinger, V. King, T. Warnow, Algorithmica 24 (1999) 1–13.
date_created: 2022-07-27T15:02:28Z
date_published: 1999-05-01T00:00:00Z
date_updated: 2024-11-04T11:41:23Z
day: '01'
doi: 10.1007/pl00009268
extern: '1'
intvolume: ' 24'
keyword:
- Algorithms
- Data structures
- Evolutionary biology
- Theory of databases
language:
- iso: eng
month: '05'
oa_version: None
page: 1-13
publication: Algorithmica
publication_identifier:
eissn:
- 1432-0541
issn:
- 0178-4617
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '11927'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Constructing a tree from homeomorphic subtrees, with applications to computational
evolutionary biology
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '1999'
...