7 Search Results for "Svoboda, Jakub"

Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.9
ε-Stationary Nash Equilibria in Multi-Player Stochastic Graph Games

Authors: Ali Asadi, Léonard Brice, Krishnendu Chatterjee, and K. S. Thejaswini

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
A strategy profile in a multi-player game is a Nash equilibrium if no player can unilaterally deviate to achieve a strictly better payoff. A profile is an ε-Nash equilibrium if no player can gain more than ε by unilaterally deviating from their strategy. In this work, we use ε-Nash equilibria to approximate the computation of Nash equilibria. Specifically, we focus on turn-based, multiplayer stochastic games played on graphs, where players are restricted to stationary strategies - strategies that use randomness but not memory. The problem of deciding the constrained existence of stationary Nash equilibria - where each player’s payoff must lie within a given interval - is known to be ∃ℝ-complete in such a setting (Hansen and Sølvsten, 2020). We extend this line of work to stationary ε-Nash equilibria and present an algorithm that solves the following promise problem: given a game with a Nash equilibrium satisfying the constraints, compute an ε-Nash equilibrium that ε-satisfies those same constraints - satisfies the constraints up to an ε additive error. Our algorithm runs in FNP^NP time. To achieve this, we first show that if a constrained Nash equilibrium exists, then one exists where the non-zero probabilities are at least an inverse of a double-exponential in the input. We further prove that such a strategy can be encoded using floating-point representations, as in the work of Frederiksen and Miltersen (2013), which finally gives us our FNP^NP algorithm. We further show that the decision version of the promise problem is NP-hard. Finally, we show a partial tightness result by proving a lower bound for such techniques: if a constrained Nash equilibrium exists, then there must be one where the probabilities in the strategies are double-exponentially small.
Cite as

Ali Asadi, Léonard Brice, Krishnendu Chatterjee, and K. S. Thejaswini. ε-Stationary Nash Equilibria in Multi-Player Stochastic Graph Games. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{asadi_et_al:LIPIcs.FSTTCS.2025.9,
  author =	{Asadi, Ali and Brice, L\'{e}onard and Chatterjee, Krishnendu and Thejaswini, K. S.},
  title =	{{\epsilon-Stationary Nash Equilibria in Multi-Player Stochastic Graph Games}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.9},
  URN =		{urn:nbn:de:0030-drops-250897},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.9},
  annote =	{Keywords: Nash Equilibria, \epsilon-Nash equilibria, Approximation, Existential Theory of Reals}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.39
Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules

Authors: Shuichi Hirahara, Naoto Ohsaka, Tatsuhiro Suga, Akira Suzuki, Yuma Tamura, and Xiao Zhou

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
In reconfiguration problems, we are given two feasible solutions to a graph problem and asked whether one can be transformed into the other via a sequence of feasible intermediate solutions under a given reconfiguration rule. While earlier work focused on modifying a single element at a time, recent studies have started examining how different rules impact computational complexity. Motivated by recent progress, we study Independent Set Reconfiguration (ISR) and Vertex Cover Reconfiguration (VCR) under the k-Token Jumping (k-TJ) and k-Token Sliding (k-TS) models. In k-TJ, up to k vertices may be replaced, while k-TS additionally requires a perfect matching between removed and added vertices. It is known that the complexity of ISR crucially depends on k, ranging from PSPACE-complete and NP-complete to polynomial-time solvable. In this paper, we further explore the gradient of computational complexity of the problems. We first show that ISR under k-TJ with k = |I| - μ remains NP-hard when μ is any fixed positive integer and the input graph is restricted to graphs of maximum degree 3 or planar graphs of maximum degree 4, where |I| is the size of feasible solutions. In addition, we prove that the problem belongs to NP not only for μ = O(1) but also for μ = O(log |I|). In contrast, we show that VCR under k-TJ is in XP when parameterized by μ = |S| - k, where |S| is the size of feasible solutions. Furthermore, we establish the PSPACE-completeness of ISR and VCR under both k-TJ and k-TS on several graph classes, for fixed k as well as superconstant k relative to the size of feasible solutions.
Cite as

Shuichi Hirahara, Naoto Ohsaka, Tatsuhiro Suga, Akira Suzuki, Yuma Tamura, and Xiao Zhou. Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hirahara_et_al:LIPIcs.ISAAC.2025.39,
  author =	{Hirahara, Shuichi and Ohsaka, Naoto and Suga, Tatsuhiro and Suzuki, Akira and Tamura, Yuma and Zhou, Xiao},
  title =	{{Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{39:1--39:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.39},
  URN =		{urn:nbn:de:0030-drops-249474},
  doi =		{10.4230/LIPIcs.ISAAC.2025.39},
  annote =	{Keywords: combinatorial reconfiguration, extended reconfiguration rule, independent set reconfiguration, vertex cover reconfiguration, PSPACE-completeness, NP-completeness}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.23
Boosting Payment Channel Network Liquidity with Topology Optimization and Transaction Selection

Authors: Krishnendu Chatterjee, Jan Matyáš Křišťan, Stefan Schmid, Jakub Svoboda, and Michelle Yeo

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

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.
Cite as

Krishnendu Chatterjee, Jan Matyáš Křišťan, Stefan Schmid, Jakub Svoboda, and Michelle Yeo. Boosting Payment Channel Network Liquidity with Topology Optimization and Transaction Selection. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chatterjee_et_al:LIPIcs.DISC.2025.23,
  author =	{Chatterjee, Krishnendu and K\v{r}i\v{s}\v{t}an, Jan Maty\'{a}\v{s} and Schmid, Stefan and Svoboda, Jakub and Yeo, Michelle},
  title =	{{Boosting Payment Channel Network Liquidity with Topology Optimization and Transaction Selection}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{23:1--23:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.23},
  URN =		{urn:nbn:de:0030-drops-248402},
  doi =		{10.4230/LIPIcs.DISC.2025.23},
  annote =	{Keywords: Blockchains, Cryptocurrencies, Payment Channel Networks, Throughput, Optimisation, Graph Algorithms, Approximation Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.95
ARRIVAL: Recursive Framework & 𝓁₁-Contraction

Authors: Sebastian Haslebacher

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
ARRIVAL is the problem of deciding which out of two possible destinations will be reached first by a token that moves deterministically along the edges of a directed graph, according to so-called switching rules. It is known to lie in NP ∩ CoNP, but not known to lie in 𝖯. The state-of-the-art algorithm due to Gärtner et al. (ICALP `21) runs in time 2^{𝒪(√n log n)} on an n-vertex graph. We prove that ARRIVAL can be solved in time 2^{𝒪(k log² n)} on n-vertex graphs of treewidth k. Our algorithm is derived by adapting a simple recursive algorithm for a generalization of ARRIVAL called G-ARRIVAL. This simple recursive algorithm acts as a framework from which we can also rederive the subexponential upper bound of Gärtner et al. Our second result is a reduction from G-ARRIVAL to the problem of finding an approximate fixed point of an 𝓁₁-contracting function f : [0, 1]ⁿ → [0, 1]ⁿ. Finding such fixed points is a well-studied problem in the case of the 𝓁₂-metric and the 𝓁_∞-metric, but little is known about the 𝓁₁-case. Both of our results highlight parallels between ARRIVAL and the Simple Stochastic Games (SSG) problem. Concretely, Chatterjee et al. (SODA `23) gave an algorithm for SSG parameterized by treewidth that achieves a similar bound as we do for ARRIVAL, and SSG is known to reduce to 𝓁_∞-contraction.
Cite as

Sebastian Haslebacher. ARRIVAL: Recursive Framework & 𝓁₁-Contraction. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 95:1-95:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{haslebacher:LIPIcs.ICALP.2025.95,
  author =	{Haslebacher, Sebastian},
  title =	{{ARRIVAL: Recursive Framework \& 𝓁₁-Contraction}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{95:1--95:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.95},
  URN =		{urn:nbn:de:0030-drops-234723},
  doi =		{10.4230/LIPIcs.ICALP.2025.95},
  annote =	{Keywords: ARRIVAL, G-ARRIVAL, Deterministic Random Walk, Rotor-Routing, 𝓁₁-Contraction, Banach Fixed Point}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2024.5
Concurrent Stochastic Games with Stateful-Discounted and Parity Objectives: Complexity and Algorithms

Authors: Ali Asadi, Krishnendu Chatterjee, Raimundo Saona, and Jakub Svoboda

Published in: LIPIcs, Volume 323, 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)

Abstract
We study two-player zero-sum concurrent stochastic games with finite state and action space played for an infinite number of steps. In every step, the two players simultaneously and independently choose an action. Given the current state and the chosen actions, the next state is obtained according to a stochastic transition function. An objective is a measurable function on plays (or infinite trajectories) of the game, and the value for an objective is the maximal expectation that the player can guarantee against the adversarial player. We consider: (a) stateful-discounted objectives, which are similar to the classic discounted-sum objectives, but states are associated with different discount factors rather than a single discount factor; and (b) parity objectives, which are a canonical representation for ω-regular objectives. For stateful-discounted objectives, given an ordering of the discount factors, the limit value is the limit of the value of the stateful-discounted objectives, as the discount factors approach zero according to the given order. The computational problem we consider is the approximation of the value within an arbitrary additive error. The above problem is known to be in EXPSPACE for the limit value of stateful-discounted objectives and in PSPACE for parity objectives. The best-known algorithms for both the above problems are at least exponential time, with an exponential dependence on the number of states and actions. Our main results for the value approximation problem for the limit value of stateful-discounted objectives and parity objectives are as follows: (a) we establish TFNP[NP] complexity; and (b) we present algorithms that improve the dependency on the number of actions in the exponent from linear to logarithmic. In particular, if the number of states is constant, our algorithms run in polynomial time.
Cite as

Ali Asadi, Krishnendu Chatterjee, Raimundo Saona, and Jakub Svoboda. Concurrent Stochastic Games with Stateful-Discounted and Parity Objectives: Complexity and Algorithms. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{asadi_et_al:LIPIcs.FSTTCS.2024.5,
  author =	{Asadi, Ali and Chatterjee, Krishnendu and Saona, Raimundo and Svoboda, Jakub},
  title =	{{Concurrent Stochastic Games with Stateful-Discounted and Parity Objectives: Complexity and Algorithms}},
  booktitle =	{44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-355-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{323},
  editor =	{Barman, Siddharth and Lasota, S{\l}awomir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024.5},
  URN =		{urn:nbn:de:0030-drops-221942},
  doi =		{10.4230/LIPIcs.FSTTCS.2024.5},
  annote =	{Keywords: Concurrent Stochastic Games, Parity Objectives, Discounted-sum Objectives}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2022.11
Complexity of Spatial Games

Authors: Krishnendu Chatterjee, Rasmus Ibsen-Jensen, Ismaël Jecker, and Jakub Svoboda

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

Abstract
Spatial games form a widely-studied class of games from biology and physics modeling the evolution of social behavior. Formally, such a game is defined by a square (d by d) payoff matrix M and an undirected graph G. Each vertex of G represents an individual, that initially follows some strategy i ∈ {1,2,…,d}. In each round of the game, every individual plays the matrix game with each of its neighbors: An individual following strategy i meeting a neighbor following strategy j receives a payoff equal to the entry (i,j) of M. Then, each individual updates its strategy to its neighbors' strategy with the highest sum of payoffs, and the next round starts. The basic computational problems consist of reachability between configurations and the average frequency of a strategy. For general spatial games and graphs, these problems are in PSPACE. In this paper, we examine restricted setting: the game is a prisoner’s dilemma; and G is a subgraph of grid. We prove that basic computational problems for spatial games with prisoner’s dilemma on a subgraph of a grid are PSPACE-hard.
Cite as

Krishnendu Chatterjee, Rasmus Ibsen-Jensen, Ismaël Jecker, and Jakub Svoboda. Complexity of Spatial Games. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chatterjee_et_al:LIPIcs.FSTTCS.2022.11,
  author =	{Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Jecker, Isma\"{e}l and Svoboda, Jakub},
  title =	{{Complexity of Spatial Games}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.11},
  URN =		{urn:nbn:de:0030-drops-174038},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.11},
  annote =	{Keywords: spatial games, computational complexity, prisoner’s dilemma, dynamical systems}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.22
Simplified Game of Life: Algorithms and Complexity

Authors: Krishnendu Chatterjee, Rasmus Ibsen-Jensen, Ismaël Jecker, and Jakub Svoboda

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
Game of Life is a simple and elegant model to study dynamical system over networks. The model consists of a graph where every vertex has one of two types, namely, dead or alive. A configuration is a mapping of the vertices to the types. An update rule describes how the type of a vertex is updated given the types of its neighbors. In every round, all vertices are updated synchronously, which leads to a configuration update. While in general, Game of Life allows a broad range of update rules, we focus on two simple families of update rules, namely, underpopulation and overpopulation, that model several interesting dynamics studied in the literature. In both settings, a dead vertex requires at least a desired number of live neighbors to become alive. For underpopulation (resp., overpopulation), a live vertex requires at least (resp. at most) a desired number of live neighbors to remain alive. We study the basic computation problems, e.g., configuration reachability, for these two families of rules. For underpopulation rules, we show that these problems can be solved in polynomial time, whereas for overpopulation rules they are PSPACE-complete.
Cite as

Krishnendu Chatterjee, Rasmus Ibsen-Jensen, Ismaël Jecker, and Jakub Svoboda. Simplified Game of Life: Algorithms and Complexity. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 22:1-22:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chatterjee_et_al:LIPIcs.MFCS.2020.22,
  author =	{Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Jecker, Isma\"{e}l and Svoboda, Jakub},
  title =	{{Simplified Game of Life: Algorithms and Complexity}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{22:1--22:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.22},
  URN =		{urn:nbn:de:0030-drops-126903},
  doi =		{10.4230/LIPIcs.MFCS.2020.22},
  annote =	{Keywords: game of life, cellular automata, computational complexity, dynamical systems}
}
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