--- res: bibo_abstract: - "We analyze a randomized pursuit-evasion game on graphs. This game is played by two players, a hunter and a rabbit. Let G be any connected, undirected graph with n nodes. The game is played in rounds and in each round both the hunter and the rabbit are located at a node of the graph. Between rounds both the hunter and the rabbit can stay at the current node or move to another node. The hunter is assumed to be restricted to the graph G: in every round, the hunter can move using at most one edge. For the rabbit we investigate two models: in one model the rabbit is restricted to the same graph as the hunter, and in the other model the rabbit is unrestricted, i.e., it can jump to an arbitrary node in every round.\r\n\r\nWe say that the rabbit is caught as soon as hunter and rabbit are located at the same node in a round. The goal of the hunter is to catch the rabbit in as few rounds as possible, whereas the rabbit aims to maximize the number of rounds until it is caught. Given a randomized hunter strategy for G, the escape length for that strategy is the worst case expected number of rounds it takes the hunter to catch the rabbit, where the worst case is with regards to all (possibly randomized) rabbit strategies. Our main result is a hunter strategy for general graphs with an escape length of only O\r\n(n log (diam(G))) against restricted as well as unrestricted rabbits. This bound is close to optimal since Ω(n) is a trivial lower bound on the escape length in both models. Furthermore, we prove that our upper bound is optimal up to constant factors against unrestricted rabbits.@eng" bibo_authorlist: - foaf_Person: foaf_givenName: Micah foaf_name: Adler, Micah foaf_surname: Adler - foaf_Person: foaf_givenName: Harald foaf_name: Räcke, Harald foaf_surname: Räcke - foaf_Person: foaf_givenName: Naveen foaf_name: Sivadasan, Naveen foaf_surname: Sivadasan - foaf_Person: foaf_givenName: Christian foaf_name: Sohler, Christian foaf_surname: Sohler - foaf_Person: foaf_givenName: Berthold foaf_name: Vöcking, Berthold foaf_surname: Vöcking bibo_doi: 10.1007/3-540-45465-9_77 dct_date: 2002^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/0302-9743 - http://id.crossref.org/issn/9783540438649 - http://id.crossref.org/issn/9783540454656 dct_language: eng dct_title: Randomized Pursuit-Evasion in Graphs@ ...