Selfish unsplittable flows

What is the price of anarchy when unsplittable demands are routed selfishly in general networks with load-dependent edge delays? Motivated by this question we generalize the model of [14] to the case of weighted congestion games. We show that varying demands of users crucially affect the nature of these games, which are no longer isomorphic to exact potential games, even for very simple instances. Indeed we construct examples where even a single-commodity (weighted) network congestion game may have no pure Nash equilibrium.On the other hand, we study a special family of networks (which we call the l-layered networks) and we prove that any weighted congestion game on such a network with resource delays equal to the congestions, possesses a pure Nash Equilibrium. We also show how to construct one in pseudo-polynomial time. Finally, we give a surprising answer to the question above for such games: The price of anarchy of any weighted ℓ-layered network congestion game with m edges and edge delays equal to the loads, is \(\Theta\left(\frac{\log m}{\log\log m}\right)\).KeywordsNash EquilibriumMixed StrategyLayered NetworkMaximum LatencyDelay FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The complexity of shortest path and dilation bounded interval routing

The minimum broadcast range assignment problem on linear multi-hop wireless networks

Deterministic monotone algorithms for scheduling on related machines

We investigate the power of counting in Group Isomorphism. We first leverage the count-free variant of the Weisfeiler–Leman Version I algorithm for groups [J. Brachter and P. Schweitzer, On the Weisfeiler–Leman dimension of finite groups, in 35th Annual ACM/IEEE Symp. Logic in Computer Science, eds. H. Hermanns, L. Zhang, N. Kobayashi and D. Miller, Saarbrucken, Germany, July 8–11, 2020 (ACM, 2020), pp. 287–300, doi:10.1145/3373718.3394786] in tandem with bounded non-determinism and limited counting to improve the parallel complexity of isomorphism testing for several families of groups. These families include: • Direct products of non-Abelian simple groups. • Coprime extensions, where the normal Hall subgroup is Abelian and the complement is an [Formula: see text]-generated solvable group with solvability class [Formula: see text]. This notably includes instances where the complement is an [Formula: see text]-generated nilpotent group. This problem was previously known to be in [Formula: see text] [Y. Qiao, J. M. N. Sarma and B. Tang, On isomorphism testing of groups with normal Hall subgroups, in Proc. 28th Symp. Theoretical Aspects of Computer Science, Dagstuhl Castle, Leibniz Center for Informatics, 2011), pp. 567–578, doi:10.4230/LIPIcs. STACS.2011.567], and the complexity was recently improved to [Formula: see text] [J. A. Grochow and M. Levet, On the parallel complexity of group isomorphism via Weisfeiler–Leman, in 24th Int. Symp. Fundamentals of Computation Theory, eds. H. Fernau and K. Jansen, Lecture Notes in Computer Science, Vol. 14292, September 18–21, 2023, Trier, Germany (Springer, 2023), pp. 234–247]. • Graphical groups of class 2 and exponent [Formula: see text] [A. H. Mekler, Stability of nilpotent groups of class 2 and prime exponent, J. Symb. Logic 46(4) (1981) 781–788] arising from the CFI and twisted CFI graphs [J.-Y. Cai, M. Fürer and N. Immerman, An optimal lower bound on the number of variables for graph identification, Combinatorica 12(4) (1992) 389–410], respectively. In particular, our work improves upon previous results of Brachter and Schweitzer [On the Weisfeiler–Leman dimension of finite groups, in 35th Annual ACM/IEEE Symp. Logic in Computer Science, eds. H. Hermanns, L. Zhang, N. Kobayashi and D. Miller, Saarbrucken, Germany, July 8–11, 2020 (ACM, 2020), pp. 287–300, doi:10.1145/3373718.3394786]. Notably, each of these families was previously known to be identified by the counting variant of the more powerful Weisfeiler–Leman Version II algorithm. We finally show that the q-ary count-free pebble game is unable to even distinguish Abelian groups. This extends the result of Grochow and Levet (ibid), who established the result in the case of [Formula: see text]. The general theme is that some counting appears necessary to place [Formula: see text] into [Formula: see text].

The correspondence between partial metrics and semivaluations

One of the most widely used solution concepts for strategic games is the concept of Nash equilibrium. A Nash equilibrium is a state in which no player can improve its objective by unilaterally changing its strategy. A Nash equilibrium is called pure if all players choose a pure strategy, and mixed if players choose probability distributions over strategies. Of special interest are fully mixed Nash equilibria where each player chooses each strategy with non-zero probability. Rosenthal [12] introduced a special class of strategic games, now widely known as congestion games. Here, the strategy set of each player is a subset of the power set of given resources. The players share a private objective function, defined as the sum (over their chosen resources) of functions in the number of players sharing this resource. In his seminal work, Rosenthal showed with help of a potential function that congestion games (in sharp contrast to general strategic games) always admit at least one pure Nash equilibrium. An extension to congestion games are weighted congestion games, in which the players have weights and thus different influence on the congestion of the resources. In (weighted) network congestion games the strategy sets of the players correspond to paths in a network. In order to measure the degradation of social welfare due to the selfish behavior of the players, Koutsoupias and Papadimitriou [8] introduced a global objective function, usually coined as social cost. They defined the price of anarchy, also called coordination ratio, as the worst-case ratio between the value of social cost in a Nash equilibrium and that of some social optimum. Thus the coordination ratio measures the extent to which non-cooperation approximates cooperation. As a starting point for studying the coordination ratio, Koutsoupias and Papadimitriou considered a very simple weighted network congestion game, now known as KP-model. Here, the network consists of a single source and a single destination which are connected by parallel links. The load on a link is the total weight of players assigned to this link. Associated with each link is a capacity representing the rate at which the link processes load. Each of the players selfishly routes from the source to the destination by choosing a probability distribution over the links. The private objective function of a player is defined as its expected latency. In the KP-model the social cost is defined as the expected maximum latency on a link, where the expectation is taken over all random choices of the players. In this paper, we give a thorough survey on the most exciting results on finite (weighted) congestion games and on special classes which are related to the KP-model. In particular, we review the findings on the existence and computational complexity of pure Nash equilibria. Furthermore, we discuss results on the price of anarchy. Last but not least, we survey known facts on fully mixed Nash equilibria.

Hybrid commitments and their applications to zero-knowledge proof systems

Inplace run-length 2d compressed search

Elimination of spatial connectives in static spatial logics

A subexponential algorithm for discrete logarithms over hyperelliptic curves of large genus over GF( q)

On the Use of Automata-based Techniques in Symbolic Model Checking: Invited Address

A hierarchical approach to recognition of handwritten Bangla characters

formula omitted] model checking for time Petri nets

A simple polygon P with two distinguished vertices, s and t, is called a street if the two boundary chains from s to t are mutually weakly visible. We present an on-line strategy that walks from s to t, in any unknown street, on a path at most $\sqrt{2}$ times longer than the shortest path. This matches the best lower bound previously known and settles an open problem in the area of competitive path planning. (The result was simultaneously and independently obtained by the first three authors and by the last two authors. Both papers, [C. Icking, R. Klein, and E. Langetepe, Proceedings of the 16th Symposium on Theoretical Aspects in Computer Science, Lecture Notes in Comput. Sci. 1563, Springer-Verlag, Berlin, 1999, pp. 110--120] and [S. Schuierer and I. Semrau, Proceedings of the 16th Symposium on Theoretical Aspects of Computer Science, pp. 121--131], were presented at STACS'99. The present paper contains a joint full version.)