Approximation bounds for Black Hole Search problems

Ralf Klasing (1, 2) , Euripides Markou (3) , Tomasz Radzik (4) , Fabiano Sarracco (5)

1 CEPAGE - Algorithmics for computationally intensive applications over wide scale distributed platforms
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique
3 DI NKUA - Department of Informatics and Telecomunications [Kapodistrian Univ]
4 DCS - Department of Computer Science
5 DIS - Dipartimento di Informatica e Sistemistica "Antonio Ruberti"

A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node without leaving any trace. The Black Hole Search is the task of locating all black holes in a network, through the exploration of its nodes by a set of mobile agents. In this paper we consider the problem of designing the fastest Black Hole Search, given the map of the network, the starting node and a subset of nodes of the network initially known to be safe. We study the version of this problem that assumes that there is at most one black hole in the network and there are two agents, which move in synchronized steps. We prove that this problem is not polynomial-time approximable within any constant factor less than 389/388 (unless PTIME=NPTIME). We give a 6-approximation algorithm, thus improving on the 9.3-approximation algorithm from [3]. We also prove APX-hardness for a restricted version of the problem, in which only the starting node is initially known to be safe.

Domaines: Réseaux et télécommunications [cs.NI]

Ralf Klasing, Euripides Markou, Tomasz Radzik, Fabiano Sarracco. Approximation bounds for Black Hole Search problems. [Research Report] RR-6185, INRIA. 2007. ⟨inria-00145157v2⟩