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We show that any randomised Monte Carlo distributed algorithm for the Lovász local lemma requires Omega(log log n) communication rounds, assuming that it finds a correct assignment with high probability. Our result holds even in the special case of d = O(1), where d is the maximum degree of the dependency graph. By prior work, there are distributed(More)
Consider the Ants Nearby Treasure Search (ANTS) problem introduced by Feinerman, Korman, Lotker, and Sereni (PODC 2012), where n mobile agents, initially placed in a single cell of an infinite grid, collaboratively search for an adversarially hidden treasure. In this paper, the model of Feinerman et al. is adapted such that each agent is controlled by an(More)
We are given an unknown binary matrix, where the entries correspond to preferences of users on items. We want to find at least one 1-entry in each row with a minimum number of queries. The number of queries needed heavily depends on the input matrix and a straightforward competitive analysis yields bad results for any online algorithm. Therefore, we analyze(More)
We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (∆+ 1) synchronous communication rounds, where ∆ is the maximum degree of the graph. For ∆ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.
In this paper, we study a variant of the Ants Nearby Treasure Search problem, where n mobile agents, controlled by finite automata, search collaboratively for a treasure hidden by an adversary. In our version of the model, the agents may fail at any time during the execution. We provide a distributed protocol that enables the agents to detect failures and(More)
A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in 2-coloured and weakly 2-coloured graphs. In a weakly 2-coloured graph, both problems admit a local algorithm with the(More)
In the classical game of Cops and Robbers on graphs, the capture time is defined by the least number of moves needed to catch all robbers with the smallest amount of cops that suffice. While the case of one cop and one robber is well understood, it is an open question how long it takes for multiple cops to catch multiple robbers. We show that capturing ` ∈(More)
For the game of Cops and Robbers, it is known that in 1-cop-win graphs, the cop can capture the robber in O(n) time, and that there exist graphs in which this capture time is tight. When k ≥ 2, a simple counting argument shows that in k-cop-win graphs, the capture time is at most O(nk+1), however, no non-trivial lower bounds were previously known; indeed,(More)