Artur Czumaj

Artur Czumaj
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Artur Czumaj

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Computer Science - Distributed; Parallel; and Cluster Computing (4)
Computer Science - Data Structures and Algorithms (4)
Computer Science - Computer Science and Game Theory (2)
Computer Science - Discrete Mathematics (1)

Publications Authored By Artur Czumaj

We study two fundamental communication primitives: broadcasting and leader election in the classical model of multi-hop radio networks with unknown topology and without collision detection mechanisms. It has been known for almost 20 years that in undirected networks with n nodes and diameter D, randomized broadcasting requires Omega(D log n/D + log^2 n) rounds in expectation, assuming that uninformed nodes are not allowed to communicate (until they are informed). Only very recently, Haeupler and Wajc (PODC'2016) showed that this bound can be slightly improved for the model with spontaneous transmissions, providing an O(D log n loglog n / log D + log^O(1) n)-time broadcasting algorithm. Read More

We present a new, distributed method to compute approximate Nash equilibria in bimatrix games. In contrast to previous approaches that analyze the two payoff matrices at the same time (for example, by solving a single LP that combines the two players payoffs), our algorithm first solves two independent LPs, each of which is derived from one of the two payoff matrices, and then compute approximate Nash equilibria using only limited communication between the players. Our method has several applications for improved bounds for efficient computations of approximate Nash equilibria in bimatrix games. Read More

In this paper we improve the deterministic complexity of two fundamental communication primitives in the classical model of ad-hoc radio networks with unknown topology: broadcasting and wake-up. We consider an unknown radio network, in which all nodes have no prior knowledge about network topology, and know only the size of the network $n$, the maximum in-degree of any node $\Delta$, and the eccentricity of the network $D$. For such networks, we first give an algorithm for wake-up, in both directed and undirected networks, based on the existence of small universal synchronizers. Read More

The beep model is a very weak communications model in which devices in a network can communicate only via beeps and silence. As a result of its weak assumptions, it has broad applicability to many different implementations of communications networks. This comes at the cost of a restrictive environment for algorithm design. Read More

We present two optimal randomized leader election algorithms for multi-hop radio networks, which run in expected time asymptotically equal to the time required to broadcast one message to the entire network. We first observe that, under certain assumptions, a simulation approach of Bar-Yehuda, Golreich and Itai (1991) can be used to obtain an algorithm that for directed and undirected networks elects a leader in $O(D \log\frac{n}{D} + \log^2 n)$ expected time, where $n$ is the number of the nodes and $D$ is the eccentricity or the diameter of the network. We then extend this approach and present a second algorithm, which operates on undirected multi-hop radio networks with collision detection and elects a leader in $O(D + \log n)$ expected run-time. Read More

We study the problem of recognizing the cluster structure of a graph in the framework of property testing in the bounded degree model. Given a parameter $\varepsilon$, a $d$-bounded degree graph is defined to be $(k, \phi)$-clusterable, if it can be partitioned into no more than $k$ parts, such that the (inner) conductance of the induced subgraph on each part is at least $\phi$ and the (outer) conductance of each part is at most $c_{d,k}\varepsilon^4\phi^2$, where $c_{d,k}$ depends only on $d,k$. Our main result is a sublinear algorithm with the running time $\widetilde{O}(\sqrt{n}\cdot\mathrm{poly}(\phi,k,1/\varepsilon))$ that takes as input a graph with maximum degree bounded by $d$, parameters $k$, $\phi$, $\varepsilon$, and with probability at least $\frac23$, accepts the graph if it is $(k,\phi)$-clusterable and rejects the graph if it is $\varepsilon$-far from $(k, \phi^*)$-clusterable for $\phi^* = c'_{d,k}\frac{\phi^2 \varepsilon^4}{\log n}$, where $c'_{d,k}$ depends only on $d,k$. Read More

The $\varepsilon$-well-supported Nash equilibrium is a strong notion of approximation of a Nash equilibrium, where no player has an incentive greater than $\varepsilon$ to deviate from any of the pure strategies that she uses in her mixed strategy. The smallest constant $\varepsilon$ currently known for which there is a polynomial-time algorithm that computes an $\varepsilon$-well-supported Nash equilibrium in bimatrix games is slightly below $2/3$. In this paper we study this problem for symmetric bimatrix games and we provide a polynomial-time algorithm that gives a $(1/2+\delta)$-well-supported Nash equilibrium, for an arbitrarily small positive constant $\delta$. Read More

We initiate the study of property testing in arbitrary planar graphs. We prove that bipartiteness can be tested in constant time: for every planar graph $G$ and $\epsilon>0$, we can distinguish in constant time between the case that $G$ is bipartite and the case that $G$ is $\epsilon$-far from bipartite. The previous bound for this class of graphs was $\tilde{O}(\sqrt{n})$, where $n$ is the number of vertices, and the constant-time testability was only known for planar graphs with bounded degree. Read More

We present sublinear-time (randomized) algorithms for finding simple cycles of length at least $k\geq 3$ and tree-minors in bounded-degree graphs. The complexity of these algorithms is related to the distance of the graph from being $C_k$-minor-free (resp., free from having the corresponding tree-minor). Read More

Let P be a set of n points in the Euclidean plane and let O be the origin point in the plane. In the k-tour cover problem (called frequently the capacitated vehicle routing problem), the goal is to minimize the total length of tours that cover all points in P, such that each tour starts and ends in O and covers at most k points from P. The k-tour cover problem is known to be NP-hard. Read More