@article{14820, abstract = {We consider a natural problem dealing with weighted packet selection across a rechargeable link, which e.g., finds applications in cryptocurrency networks. The capacity of a link (u, v) is determined by how many nodes u and v allocate for this link. Specifically, the input is a finite ordered sequence of packets that arrive in both directions along a link. Given (u, v) and a packet of weight x going from u to v, node u can either accept or reject the packet. If u accepts the packet, the capacity on link (u, v) decreases by x. Correspondingly, v's capacity on increases by x. If a node rejects the packet, this will entail a cost affinely linear in the weight of the packet. A link is “rechargeable” in the sense that the total capacity of the link has to remain constant, but the allocation of capacity at the ends of the link can depend arbitrarily on the nodes' decisions. The goal is to minimise the sum of the capacity injected into the link and the cost of rejecting packets. We show that the problem is NP-hard, but can be approximated efficiently with a ratio of (1+E) . (1+3) for some arbitrary E>0.}, author = {Schmid, Stefan and Svoboda, Jakub and Yeo, Michelle X}, issn = {0304-3975}, journal = {Theoretical Computer Science}, keywords = {General Computer Science, Theoretical Computer Science}, publisher = {Elsevier}, title = {{Weighted packet selection for rechargeable links in cryptocurrency networks: Complexity and approximation}}, doi = {10.1016/j.tcs.2023.114353}, volume = {989}, year = {2024}, } @inproceedings{12676, abstract = {Turn-based stochastic games (aka simple stochastic games) are two-player zero-sum games played on directed graphs with probabilistic transitions. The goal of player-max is to maximize the probability to reach a target state against the adversarial player-min. These games lie in NP ∩ coNP and are among the rare combinatorial problems that belong to this complexity class for which the existence of polynomial-time algorithm is a major open question. While randomized sub-exponential time algorithm exists, all known deterministic algorithms require exponential time in the worst-case. An important open question has been whether faster algorithms can be obtained parametrized by the treewidth of the game graph. Even deterministic sub-exponential time algorithm for constant treewidth turn-based stochastic games has remain elusive. In this work our main result is a deterministic algorithm to solve turn-based stochastic games that, given a game with n states, treewidth at most t, and the bit-complexity of the probabilistic transition function log D, has running time O ((tn2 log D)t log n). In particular, our algorithm is quasi-polynomial time for games with constant or poly-logarithmic treewidth.}, author = {Chatterjee, Krishnendu and Meggendorfer, Tobias and Saona Urmeneta, Raimundo J and Svoboda, Jakub}, booktitle = {Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms}, isbn = {9781611977554}, location = {Florence, Italy}, pages = {4590--4605}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Faster algorithm for turn-based stochastic games with bounded treewidth}}, doi = {10.1137/1.9781611977554.ch173}, year = {2023}, } @article{12787, abstract = {Populations evolve in spatially heterogeneous environments. While a certain trait might bring a fitness advantage in some patch of the environment, a different trait might be advantageous in another patch. Here, we study the Moran birth–death process with two types of individuals in a population stretched across two patches of size N, each patch favouring one of the two types. We show that the long-term fate of such populations crucially depends on the migration rate μ between the patches. To classify the possible fates, we use the distinction between polynomial (short) and exponential (long) timescales. We show that when μ is high then one of the two types fixates on the whole population after a number of steps that is only polynomial in N. By contrast, when μ is low then each type holds majority in the patch where it is favoured for a number of steps that is at least exponential in N. Moreover, we precisely identify the threshold migration rate μ⋆ that separates those two scenarios, thereby exactly delineating the situations that support long-term coexistence of the two types. We also discuss the case of various cycle graphs and we present computer simulations that perfectly match our analytical results.}, author = {Svoboda, Jakub and Tkadlec, Josef and Kaveh, Kamran and Chatterjee, Krishnendu}, issn = {1471-2946}, journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, number = {2271}, publisher = {The Royal Society}, title = {{Coexistence times in the Moran process with environmental heterogeneity}}, doi = {10.1098/rspa.2022.0685}, volume = {479}, year = {2023}, } @inproceedings{13238, abstract = {We consider a natural problem dealing with weighted packet selection across a rechargeable link, which e.g., finds applications in cryptocurrency networks. The capacity of a link (u, v) is determined by how much nodes u and v allocate for this link. Specifically, the input is a finite ordered sequence of packets that arrive in both directions along a link. Given (u, v) and a packet of weight x going from u to v, node u can either accept or reject the packet. If u accepts the packet, the capacity on link (u, v) decreases by x. Correspondingly, v’s capacity on (u, v) increases by x. If a node rejects the packet, this will entail a cost affinely linear in the weight of the packet. A link is “rechargeable” in the sense that the total capacity of the link has to remain constant, but the allocation of capacity at the ends of the link can depend arbitrarily on the nodes’ decisions. The goal is to minimise the sum of the capacity injected into the link and the cost of rejecting packets. We show that the problem is NP-hard, but can be approximated efficiently with a ratio of (1+ε)⋅(1+3–√) for some arbitrary ε>0. .}, author = {Schmid, Stefan and Svoboda, Jakub and Yeo, Michelle X}, booktitle = {SIROCCO 2023: Structural Information and Communication Complexity }, isbn = {9783031327322}, issn = {1611-3349}, location = {Alcala de Henares, Spain}, pages = {576--594}, publisher = {Springer Nature}, title = {{Weighted packet selection for rechargeable links in cryptocurrency networks: Complexity and approximation}}, doi = {10.1007/978-3-031-32733-9_26}, volume = {13892}, year = {2023}, } @inproceedings{14736, abstract = {Payment channel networks (PCNs) are a promising technology to improve the scalability of cryptocurrencies. PCNs, however, face the challenge that the frequent usage of certain routes may deplete channels in one direction, and hence prevent further transactions. In order to reap the full potential of PCNs, recharging and rebalancing mechanisms are required to provision channels, as well as an admission control logic to decide which transactions to reject in case capacity is insufficient. This paper presents a formal model of this optimisation problem. In particular, we consider an online algorithms perspective, where transactions arrive over time in an unpredictable manner. Our main contributions are competitive online algorithms which come with provable guarantees over time. We empirically evaluate our algorithms on randomly generated transactions to compare the average performance of our algorithms to our theoretical bounds. We also show how this model and approach differs from related problems in classic communication networks.}, author = {Bastankhah, Mahsa and Chatterjee, Krishnendu and Maddah-Ali, Mohammad Ali and Schmid, Stefan and Svoboda, Jakub and Yeo, Michelle X}, booktitle = {27th International Conference on Financial Cryptography and Data Security}, isbn = {9783031477539}, issn = {1611-3349}, location = {Bol, Brac, Croatia}, pages = {309--325}, publisher = {Springer Nature}, title = {{R2: Boosting liquidity in payment channel networks with online admission control}}, doi = {10.1007/978-3-031-47754-6_18}, volume = {13950}, year = {2023}, } @inproceedings{14456, abstract = {In this paper, we present novel algorithms that efficiently compute a shortest reconfiguration sequence between two given dominating sets in trees and interval graphs under the TOKEN SLIDING model. In this problem, a graph is provided along with its two dominating sets, which can be imagined as tokens placed on vertices. The objective is to find a shortest sequence of dominating sets that transforms one set into the other, with each set in the sequence resulting from sliding a single token in the previous set. While identifying any sequence has been well studied, our work presents the first polynomial algorithms for this optimization variant in the context of dominating sets.}, author = {Křišťan, Jan Matyáš and Svoboda, Jakub}, booktitle = {24th International Symposium on Fundamentals of Computation Theory}, isbn = {9783031435867}, issn = {1611-3349}, location = {Trier, Germany}, pages = {333--347}, publisher = {Springer Nature}, title = {{Shortest dominating set reconfiguration under token sliding}}, doi = {10.1007/978-3-031-43587-4_24}, volume = {14292}, year = {2023}, } @inproceedings{12101, 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.}, author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Jecker, Ismael R and Svoboda, Jakub}, booktitle = {42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, isbn = {9783959772617}, issn = {1868-8969}, location = {Madras, India}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Complexity of spatial games}}, doi = {10.4230/LIPIcs.FSTTCS.2022.11}, volume = {250}, year = {2022}, } @article{10731, abstract = {Motivated by COVID-19, we develop and analyze a simple stochastic model for the spread of disease in human population. We track how the number of infected and critically ill people develops over time in order to estimate the demand that is imposed on the hospital system. To keep this demand under control, we consider a class of simple policies for slowing down and reopening society and we compare their efficiency in mitigating the spread of the virus from several different points of view. We find that in order to avoid overwhelming of the hospital system, a policy must impose a harsh lockdown or it must react swiftly (or both). While reacting swiftly is universally beneficial, being harsh pays off only when the country is patient about reopening and when the neighboring countries coordinate their mitigation efforts. Our work highlights the importance of acting decisively when closing down and the importance of patience and coordination between neighboring countries when reopening.}, author = {Svoboda, Jakub and Tkadlec, Josef and Pavlogiannis, Andreas and Chatterjee, Krishnendu and Nowak, Martin A.}, issn = {2045-2322}, journal = {Scientific Reports}, number = {1}, publisher = {Springer Nature}, title = {{Infection dynamics of COVID-19 virus under lockdown and reopening}}, doi = {10.1038/s41598-022-05333-5}, volume = {12}, year = {2022}, } @article{12257, abstract = {Structural balance theory is an established framework for studying social relationships of friendship and enmity. These relationships are modeled by a signed network whose energy potential measures the level of imbalance, while stochastic dynamics drives the network toward a state of minimum energy that captures social balance. It is known that this energy landscape has local minima that can trap socially aware dynamics, preventing it from reaching balance. Here we first study the robustness and attractor properties of these local minima. We show that a stochastic process can reach them from an abundance of initial states and that some local minima cannot be escaped by mild perturbations of the network. Motivated by these anomalies, we introduce best-edge dynamics (BED), a new plausible stochastic process. We prove that BED always reaches balance and that it does so fast in various interesting settings.}, author = {Chatterjee, Krishnendu and Svoboda, Jakub and Zikelic, Dorde and Pavlogiannis, Andreas and Tkadlec, Josef}, issn = {2470-0053}, journal = {Physical Review E}, number = {3}, publisher = {American Physical Society}, title = {{Social balance on networks: Local minima and best-edge dynamics}}, doi = {10.1103/physreve.106.034321}, volume = {106}, year = {2022}, } @inproceedings{8533, 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.}, author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Jecker, Ismael R and Svoboda, Jakub}, booktitle = {45th International Symposium on Mathematical Foundations of Computer Science}, isbn = {9783959771597}, issn = {18688969}, location = {Prague, Czech Republic}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Simplified game of life: Algorithms and complexity}}, doi = {10.4230/LIPIcs.MFCS.2020.22}, volume = {170}, year = {2020}, }