---
_id: '551'
abstract:
- lang: eng
text: 'Evolutionary graph theory studies the evolutionary dynamics in a population
structure given as a connected graph. Each node of the graph represents an individual
of the population, and edges determine how offspring are placed. We consider the
classical birth-death Moran process where there are two types of individuals,
namely, the residents with fitness 1 and mutants with fitness r. The fitness indicates
the reproductive strength. The evolutionary dynamics happens as follows: in the
initial step, in a population of all resident individuals a mutant is introduced,
and then at each step, an individual is chosen proportional to the fitness of
its type to reproduce, and the offspring replaces a neighbor uniformly at random.
The process stops when all individuals are either residents or mutants. The probability
that all individuals in the end are mutants is called the fixation probability,
which is a key factor in the rate of evolution. We consider the problem of approximating
the fixation probability. The class of algorithms that is extremely relevant for
approximation of the fixation probabilities is the Monte-Carlo simulation of the
process. Previous results present a polynomial-time Monte-Carlo algorithm for
undirected graphs when r is given in unary. First, we present a simple modification:
instead of simulating each step, we discard ineffective steps, where no node changes
type (i.e., either residents replace residents, or mutants replace mutants). Using
the above simple modification and our result that the number of effective steps
is concentrated around the expected number of effective steps, we present faster
polynomial-time Monte-Carlo algorithms for undirected graphs. Our algorithms are
always at least a factor O(n2/ log n) faster as compared to the previous algorithms,
where n is the number of nodes, and is polynomial even if r is given in binary.
We also present lower bounds showing that the upper bound on the expected number
of effective steps we present is asymptotically tight for undirected graphs. '
alternative_title:
- LIPIcs
article_number: '61'
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Rasmus
full_name: Ibsen-Jensen, Rasmus
id: 3B699956-F248-11E8-B48F-1D18A9856A87
last_name: Ibsen-Jensen
orcid: 0000-0003-4783-0389
- first_name: Martin
full_name: Nowak, Martin
last_name: Nowak
citation:
ama: 'Chatterjee K, Ibsen-Jensen R, Nowak M. Faster Monte Carlo algorithms for fixation
probability of the Moran process on undirected graphs. In: Leibniz International
Proceedings in Informatics. Vol 83. Schloss Dagstuhl - Leibniz-Zentrum für
Informatik; 2017. doi:10.4230/LIPIcs.MFCS.2017.61'
apa: 'Chatterjee, K., Ibsen-Jensen, R., & Nowak, M. (2017). Faster Monte Carlo
algorithms for fixation probability of the Moran process on undirected graphs.
In Leibniz International Proceedings in Informatics (Vol. 83). Aalborg,
Denmark: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.MFCS.2017.61'
chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Martin Nowak. “Faster
Monte Carlo Algorithms for Fixation Probability of the Moran Process on Undirected
Graphs.” In Leibniz International Proceedings in Informatics, Vol. 83.
Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. https://doi.org/10.4230/LIPIcs.MFCS.2017.61.
ieee: K. Chatterjee, R. Ibsen-Jensen, and M. Nowak, “Faster Monte Carlo algorithms
for fixation probability of the Moran process on undirected graphs,” in Leibniz
International Proceedings in Informatics, Aalborg, Denmark, 2017, vol. 83.
ista: 'Chatterjee K, Ibsen-Jensen R, Nowak M. 2017. Faster Monte Carlo algorithms
for fixation probability of the Moran process on undirected graphs. Leibniz International
Proceedings in Informatics. MFCS: Mathematical Foundations of Computer Science
(SG), LIPIcs, vol. 83, 61.'
mla: Chatterjee, Krishnendu, et al. “Faster Monte Carlo Algorithms for Fixation
Probability of the Moran Process on Undirected Graphs.” Leibniz International
Proceedings in Informatics, vol. 83, 61, Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2017, doi:10.4230/LIPIcs.MFCS.2017.61.
short: K. Chatterjee, R. Ibsen-Jensen, M. Nowak, in:, Leibniz International Proceedings
in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017.
conference:
end_date: 2017-08-25
location: Aalborg, Denmark
name: 'MFCS: Mathematical Foundations of Computer Science (SG)'
start_date: 2017-08-21
date_created: 2018-12-11T11:47:08Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2021-01-12T08:02:34Z
day: '01'
ddc:
- '004'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.MFCS.2017.61
file:
- access_level: open_access
checksum: 2eed5224c0e4e259484a1d71acb8ba6a
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:18:04Z
date_updated: 2020-07-14T12:47:00Z
file_id: '5322'
file_name: IST-2018-924-v1+1_LIPIcs-MFCS-2017-61.pdf
file_size: 535077
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file_date_updated: 2020-07-14T12:47:00Z
has_accepted_license: '1'
intvolume: ' 83'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
publication: Leibniz International Proceedings in Informatics
publication_identifier:
isbn:
- 978-395977046-0
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7263'
pubrep_id: '924'
quality_controlled: '1'
scopus_import: 1
status: public
title: Faster Monte Carlo algorithms for fixation probability of the Moran process
on undirected graphs
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: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 83
year: '2017'
...
---
_id: '552'
abstract:
- lang: eng
text: 'Graph games provide the foundation for modeling and synthesis of reactive
processes. Such games are played over graphs where the vertices are controlled
by two adversarial players. We consider graph games where the objective of the
first player is the conjunction of a qualitative objective (specified as a parity
condition) and a quantitative objective (specified as a meanpayoff condition).
There are two variants of the problem, namely, the threshold problem where the
quantitative goal is to ensure that the mean-payoff value is above a threshold,
and the value problem where the quantitative goal is to ensure the optimal mean-payoff
value; in both cases ensuring the qualitative parity objective. The previous best-known
algorithms for game graphs with n vertices, m edges, parity objectives with d
priorities, and maximal absolute reward value W for mean-payoff objectives, are
as follows: O(nd+1 . m . w) for the threshold problem, and O(nd+2 · m · W) for
the value problem. Our main contributions are faster algorithms, and the running
times of our algorithms are as follows: O(nd-1 · m ·W) for the threshold problem,
and O(nd · m · W · log(n · W)) for the value problem. For mean-payoff parity objectives
with two priorities, our algorithms match the best-known bounds of the algorithms
for mean-payoff games (without conjunction with parity objectives). Our results
are relevant in synthesis of reactive systems with both functional requirement
(given as a qualitative objective) and performance requirement (given as a quantitative
objective).'
alternative_title:
- LIPIcs
article_number: '39'
article_processing_charge: No
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- 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: Alexander
full_name: Svozil, Alexander
last_name: Svozil
citation:
ama: 'Chatterjee K, Henzinger MH, Svozil A. Faster algorithms for mean-payoff parity
games. In: Leibniz International Proceedings in Informatics. Vol 83. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik; 2017. doi:10.4230/LIPIcs.MFCS.2017.39'
apa: 'Chatterjee, K., Henzinger, M. H., & Svozil, A. (2017). Faster algorithms
for mean-payoff parity games. In Leibniz International Proceedings in Informatics
(Vol. 83). Aalborg, Denmark: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.MFCS.2017.39'
chicago: Chatterjee, Krishnendu, Monika H Henzinger, and Alexander Svozil. “Faster
Algorithms for Mean-Payoff Parity Games.” In Leibniz International Proceedings
in Informatics, Vol. 83. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017. https://doi.org/10.4230/LIPIcs.MFCS.2017.39.
ieee: K. Chatterjee, M. H. Henzinger, and A. Svozil, “Faster algorithms for mean-payoff
parity games,” in Leibniz International Proceedings in Informatics, Aalborg,
Denmark, 2017, vol. 83.
ista: 'Chatterjee K, Henzinger MH, Svozil A. 2017. Faster algorithms for mean-payoff
parity games. Leibniz International Proceedings in Informatics. MFCS: Mathematical
Foundations of Computer Science (SG), LIPIcs, vol. 83, 39.'
mla: Chatterjee, Krishnendu, et al. “Faster Algorithms for Mean-Payoff Parity Games.”
Leibniz International Proceedings in Informatics, vol. 83, 39, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2017, doi:10.4230/LIPIcs.MFCS.2017.39.
short: K. Chatterjee, M.H. Henzinger, A. Svozil, in:, Leibniz International Proceedings
in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017.
conference:
end_date: 2017-08-25
location: Aalborg, Denmark
name: 'MFCS: Mathematical Foundations of Computer Science (SG)'
start_date: 2017-08-21
date_created: 2018-12-11T11:47:08Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2023-02-14T10:06:46Z
day: '01'
ddc:
- '004'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.MFCS.2017.39
ec_funded: 1
file:
- access_level: open_access
checksum: c67f4866ddbfd555afef1f63ae9a8fc7
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:57Z
date_updated: 2020-07-14T12:47:00Z
file_id: '5248'
file_name: IST-2018-923-v1+1_LIPIcs-MFCS-2017-39.pdf
file_size: 610339
relation: main_file
file_date_updated: 2020-07-14T12:47:00Z
has_accepted_license: '1'
intvolume: ' 83'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/3.0/
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
publication: Leibniz International Proceedings in Informatics
publication_identifier:
isbn:
- 978-395977046-0
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7262'
pubrep_id: '923'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Faster algorithms for mean-payoff parity games
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 83
year: '2017'
...
---
_id: '553'
abstract:
- lang: eng
text: 'We consider two player, zero-sum, finite-state concurrent reachability games,
played for an infinite number of rounds, where in every round, each player simultaneously
and independently of the other players chooses an action, whereafter the successor
state is determined by a probability distribution given by the current state and
the chosen actions. Player 1 wins iff a designated goal state is eventually visited.
We are interested in the complexity of stationary strategies measured by their
patience, which is defined as the inverse of the smallest non-zero probability
employed. Our main results are as follows: We show that: (i) the optimal bound
on the patience of optimal and -optimal strategies, for both players is doubly
exponential; and (ii) even in games with a single non-absorbing state exponential
(in the number of actions) patience is necessary. '
alternative_title:
- LIPIcs
article_number: '55'
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Kristofer
full_name: Hansen, Kristofer
last_name: Hansen
- first_name: Rasmus
full_name: Ibsen-Jensen, Rasmus
id: 3B699956-F248-11E8-B48F-1D18A9856A87
last_name: Ibsen-Jensen
orcid: 0000-0003-4783-0389
citation:
ama: 'Chatterjee K, Hansen K, Ibsen-Jensen R. Strategy complexity of concurrent
safety games. In: Leibniz International Proceedings in Informatics. Vol
83. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017. doi:10.4230/LIPIcs.MFCS.2017.55'
apa: 'Chatterjee, K., Hansen, K., & Ibsen-Jensen, R. (2017). Strategy complexity
of concurrent safety games. In Leibniz International Proceedings in Informatics
(Vol. 83). Aalborg, Denmark: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.MFCS.2017.55'
chicago: Chatterjee, Krishnendu, Kristofer Hansen, and Rasmus Ibsen-Jensen. “Strategy
Complexity of Concurrent Safety Games.” In Leibniz International Proceedings
in Informatics, Vol. 83. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2017. https://doi.org/10.4230/LIPIcs.MFCS.2017.55.
ieee: K. Chatterjee, K. Hansen, and R. Ibsen-Jensen, “Strategy complexity of concurrent
safety games,” in Leibniz International Proceedings in Informatics, Aalborg,
Denmark, 2017, vol. 83.
ista: 'Chatterjee K, Hansen K, Ibsen-Jensen R. 2017. Strategy complexity of concurrent
safety games. Leibniz International Proceedings in Informatics. MFCS: Mathematical
Foundations of Computer Science (SG), LIPIcs, vol. 83, 55.'
mla: Chatterjee, Krishnendu, et al. “Strategy Complexity of Concurrent Safety Games.”
Leibniz International Proceedings in Informatics, vol. 83, 55, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2017, doi:10.4230/LIPIcs.MFCS.2017.55.
short: K. Chatterjee, K. Hansen, R. Ibsen-Jensen, in:, Leibniz International Proceedings
in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017.
conference:
end_date: 2017-08-25
location: Aalborg, Denmark
name: 'MFCS: Mathematical Foundations of Computer Science (SG)'
start_date: 2017-08-21
date_created: 2018-12-11T11:47:08Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2021-01-12T08:02:35Z
day: '01'
ddc:
- '004'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.MFCS.2017.55
file:
- access_level: open_access
checksum: 7101facb56ade363205c695d72dbd173
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:09:29Z
date_updated: 2020-07-14T12:47:00Z
file_id: '4753'
file_name: IST-2018-922-v1+1_LIPIcs-MFCS-2017-55.pdf
file_size: 549967
relation: main_file
file_date_updated: 2020-07-14T12:47:00Z
has_accepted_license: '1'
intvolume: ' 83'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1506.02434
month: '11'
oa: 1
oa_version: Published Version
publication: Leibniz International Proceedings in Informatics
publication_identifier:
isbn:
- 978-395977046-0
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publist_id: '7261'
pubrep_id: '922'
quality_controlled: '1'
scopus_import: 1
status: public
title: Strategy complexity of concurrent safety games
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: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 83
year: '2017'
...