Distributed Chasing of Network Intruders

This paper addresses the graph searching problem in a distributed setting. We describe a distributed protocol that enables searchers with logarithmic size memory to clear any network, in a fully decentralized manner. The search strategy for the network in which the searchers are launched is computed online by the searchers themselves without knowing the topology of the network in advance. It performs in an asynchronous environment, i.e., it implements the necessary synchronization mechanism in a decentralized manner. In every network, our protocol performs a connected strategy using at most k + 1 searchers, where k is the minimum number of searchers required to clear the network in a monotone connected way, computed in the centralized and synchronous setting

[1]  T. D. Parsons,et al.  Pursuit-evasion in a graph , 1978 .

[2]  Nicolas Nisse,et al.  Connected Treewidth and Connected Graph Searching , 2006, LATIN.

[3]  Hans-Anton Rollik,et al.  Automaten in planaren Graphen , 1979, Acta Informatica.

[4]  Michael A. Bender,et al.  The power of team exploration: two robots can learn unlabeled directed graphs , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[5]  Derek G. Corneil,et al.  Complexity of finding embeddings in a k -tree , 1987 .

[6]  Konstantin Skodinis Computing Optimal Linear Layouts of Trees in Linear Time , 2000, ESA.

[7]  Nicola Santoro,et al.  Searching for a black hole in arbitrary networks: optimal mobile agent protocols , 2002, PODC '02.

[8]  Krzysztof Diks,et al.  Tree exploration with little memory , 2002, SODA.

[9]  Christos H. Papadimitriou,et al.  Interval graphs and seatching , 1985, Discret. Math..

[10]  Nicolas Nisse,et al.  Nondeterministic Graph Searching: From Pathwidth to Treewidth , 2005, Algorithmica.

[11]  Lali Barrière,et al.  Searching Is Not Jumping , 2003, WG.

[12]  Andrea S. LaPaugh,et al.  Recontamination does not help to search a graph , 1993, JACM.

[13]  Christos H. Papadimitriou,et al.  Searching and Pebbling , 1986, Theor. Comput. Sci..

[14]  Paola Flocchini,et al.  Decontamination of chordal rings and tori , 2006, Proceedings 20th IEEE International Parallel & Distributed Processing Symposium.

[15]  Nicola Santoro,et al.  Mobile Search for a Black Hole in an Anonymous Ring , 2007, Algorithmica.

[16]  Michael A. Bender,et al.  The power of a pebble: exploring and mapping directed graphs , 1998, STOC '98.

[17]  Reuven Cohen,et al.  Label-guided graph exploration by a finite automaton , 2005, TALG.

[18]  Omer Reingold,et al.  Undirected ST-connectivity in log-space , 2005, STOC '05.

[19]  Andrzej Pelc,et al.  Graph exploration by a finite automaton , 2005, Theor. Comput. Sci..

[20]  Paola Flocchini,et al.  Contiguous search in the hypercube for capturing an intruder , 2005, 19th IEEE International Parallel and Distributed Processing Symposium.

[21]  Fillia Makedon,et al.  On minimizing width in linear layouts , 1989, Discret. Appl. Math..

[22]  Paul D. Seymour,et al.  Monotonicity in Graph Searching , 1991, J. Algorithms.

[23]  James R. Lee,et al.  Improved approximation algorithms for minimum-weight vertex separators , 2005, STOC '05.

[24]  Stephen A. Cook,et al.  Space Lower Bounds for Maze Threadability on Restricted Machines , 1980, SIAM J. Comput..

[25]  Pierre Fraigniaud,et al.  Digraphs Exploration with Little Memory , 2004, STACS.

[26]  Lali Barrière,et al.  Capture of an intruder by mobile agents , 2002, SPAA '02.

[27]  Fedor V. Fomin,et al.  Exact algorithms for treewidth and minimum fill-in ∗ † , 2006 .

[28]  Boting Yang,et al.  Sweeping Graphs with Large Clique Number , 2004, ISAAC.

[29]  Daniel Bienstock,et al.  Graph Searching, Path-Width, Tree-Width and Related Problems (A Survey) , 1989, Reliability Of Computer And Communication Networks.

[30]  Christos H. Papadimitriou,et al.  The complexity of searching a graph , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).