An annotated bibliography on guaranteed graph searching

Graph searching encompasses a wide variety of combinatorial problems related to the problem of capturing a fugitive residing in a graph using the minimum number of searchers. In this annotated bibliography, we give an elementary classification of problems and results related to graph searching and provide a source of bibliographical references on this field.

[1]  Georg Gottlob,et al.  Hypertree Decompositions: Structure, Algorithms, and Applications , 2005, WG.

[2]  B. Intrigila,et al.  On the Cop Number of a Graph , 1993 .

[3]  János Barát.  Directed Path-width and Monotonicity in Digraph Searching , 2006, Graphs Comb..

[4]  Fedor V. Fomin,et al.  Helicopter Search Problems, Bandwidth and Pathwidth , 1998, Discret. Appl. Math..

[5]  Dimitrios M. Thilikos,et al.  Fugitive-Search Games on Graphs and Related Parameters , 1997, Theor. Comput. Sci..

[6]  Richard Krueger.  Graph searching , 2005 .

[7]  Masafumi Yamashita,et al.  Searching for a Mobile Intruder in a Polygonal Region , 1992, SIAM J. Comput..

[8]  Peter Winkler,et al.  Vertex-to-vertex pursuit in a graph , 1983, Discret. Math..

[9]  Richard P. Anstee,et al.  On bridged graphs and cop-win graphs , 1988, J. Comb. Theory, Ser. B.

[10]  Robin Thomas,et al.  Call routing and the ratcatcher , 1994, Comb..

[11]  J. van Leeuwen,et al.  Theoretical Computer Science , 2003, Lecture Notes in Computer Science.

[12]  Isolde Adler.  Marshals, monotone marshals, and hypertree-width , 2004 .

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

[14]  P. A. Golovach.  Minimal trees of a given search number , 1992 .

[15]  Chuan Yi Tang,et al.  The searchlight guarding problem on weighted split graphs and weighted cographs , 2000, Networks.

[16]  Dimitrios M. Thilikos,et al.  Graph Searching in a Crime Wave , 2009, SIAM J. Discret. Math..

[17]  Boting Yang,et al.  Lower Bounds on Edge Searching , 2007, ESCAPE.

[18]  Robin W. Dawes,et al.  Some Pursuit-Evasion Problems on Grids , 1992, Inf. Process. Lett..

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

[20]  Dimitrios M. Thilikos,et al.  On the monotonicity of games generated by symmetric submodular functions , 2003, Discret. Appl. Math..

[21]  Georg Gottlob,et al.  Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width , 2003, J. Comput. Syst. Sci..

[22]  Martin Grohe,et al.  Constraint solving via fractional edge covers , 2006, SODA 2006.

[23]  Stephan Kreutzer,et al.  DAG-Width and Parity Games , 2006, STACS.

[24]  Gary MacGillivray,et al.  A note on k-cop, l-robber games on graphs , 2006, Discret. Math..

[25]  Henry Meyniel,et al.  On a game of policemen and robber , 1987, Discret. Appl. Math..

[26]  John A. Ellis,et al.  Computing the vertex separation of unicyclic graphs , 2004, Inf. Comput..

[27]  Edward M. Reingold,et al.  The Complexity of Pursuit on a Graph , 1995, Theor. Comput. Sci..

[28]  Norbert Zeh,et al.  Boundary-optimal Triangulation Flooding , 2006, Int. J. Comput. Geom. Appl..

[29]  Giora Slutzki,et al.  An algorithm for searching a polygonal region with a flashlight , 2000, SCG '00.

[30]  Timothy J. Carlson,et al.  An infinitary version of the Graham-Leeb-Rothschild theorem , 1987, J. Comb. Theory, Ser. A.

[31]  Fedor V. Fomin,et al.  Mixed search number and linear-width of interval and split graphs , 2010, Networks.

[32]  Chuan Yi Tang,et al.  Edge and Node Searching Problems on Trees , 1997, COCOON.

[33]  Chuan Yi Tang,et al.  Single Step Searching in Weighted Block Graphs , 1994, Inf. Sci..

[34]  Alain Quilliot,et al.  Some Results about Pursuit Games on Metric Spaces Obtained Through Graph Theory Techniques , 1986, Eur. J. Comb..

[35]  Georg Gottlob,et al.  Hypertree width and related hypergraph invariants , 2007, Eur. J. Comb..

[36]  P. Seymour,et al.  Surveys in combinatorics 1985: Graph minors – a survey , 1985 .

[37]  Paola Flocchini,et al.  Decontamination of hypercubes by mobile agents , 2008 .

[38]  Chuan Yi Tang,et al.  Edge and node searching problems on trees , 2000, Theor. Comput. Sci..

[39]  Nicolas Nisse,et al.  Monotony properties of connected visible graph searching , 2008, Inf. Comput..

[40]  Masafumi Yamashita,et al.  Searching a Polygonal Region from the Boundary , 2001, Int. J. Comput. Geom. Appl..

[41]  Alain Quilliot,et al.  A short note about pursuit games played on a graph with a given genus , 1985, J. Comb. Theory, Ser. B.

[42]  Konstantin Skodinis.  Construction of linear tree-layouts which are optimal with respect to vertex separation in linear time , 2003, J. Algorithms.

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

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

[45]  Martin Aigner,et al.  A game of cops and robbers , 1984, Discret. Appl. Math..

[46]  Masafumi Yamashita,et al.  Searching for Mobile Intruders in a Polygonal Region by a Group of Mobile Searchers , 2001, SCG '97.

[47]  Nicolas Nisse,et al.  Distributed chasing of network intruders , 2008, Theor. Comput. Sci..

[48]  Thomas ANDREAE,et al.  Note on a pursuit game played on graphs , 1984, Discret. Appl. Math..

[49]  Boting Yang,et al.  Digraph Strong Searching: Monotonicity and Complexity , 2007, AAIM.

[50]  Boting Yang,et al.  Directed Searching Digraphs: Monotonicity and Complexity , 2007, TAMC.

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

[52]  Nicolas Nisse,et al.  Graph searching with advice , 2007, Theor. Comput. Sci..

[53]  Fedor V. Fomin.  Note on a Helicopter Search Problem on Graphs , 1999, Discret. Appl. Math..

[54]  Franz-Josef Brandenburg,et al.  Graph Searching and Search Time , 2006, SOFSEM.

[55]  Fedor V. Fomin,et al.  Graph Searching, Elimination Trees, and a Generalization of Bandwidth , 2003, Algorithmica.

[56]  Chuan Yi Tang,et al.  Graph Searching on Some Subclasses of Chordal Graphs , 2000, Algorithmica.

[57]  P. W. Hunter,et al.  Complexity and infinite games on finite graphs , 2007 .

[58]  Peter Winkler,et al.  Gibbs Measures and Dismantlable Graphs , 2000, J. Comb. Theory, Ser. B.

[59]  Matthew K. Franklin,et al.  Eavesdropping games: a graph-theoretic approach to privacy in distributed systems , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

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

[61]  Nicolas Nisse,et al.  Connected graph searching in chordal graphs , 2009, Discret. Appl. Math..

[62]  Hans L. Bodlaender,et al.  A Partial k-Arboretum of Graphs with Bounded Treewidth , 1998, Theor. Comput. Sci..

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

[64]  Boting Yang,et al.  Arc Searching Digraphs Without Jumping , 2007, COCOA.

[65]  Stephan Kreutzer,et al.  Digraph measures: Kelly decompositions, games, and orderings , 2007, SODA '07.

[66]  Dimitrios M. Thilikos,et al.  Algorithms and obstructions for linear-width and related search parameters , 2000, Discret. Appl. Math..

[67]  Robin Thomas,et al.  Graph Searching and a Min-Max Theorem for Tree-Width , 1993, J. Comb. Theory, Ser. B.

[68]  Shmuel Gal,et al.  The theory of search games and rendezvous , 2002, International series in operations research and management science.

[69]  Leonidas J. Guibas,et al.  A Visibility-Based Pursuit-Evasion Problem , 1999, Int. J. Comput. Geom. Appl..

[70]  Richard J. Nowakowski,et al.  A Vertex-To-Vertex Pursuit Game Played with Disjoint Sets of Edges , 1993 .

[71]  Fillia Makedon,et al.  Topological Bandwidth , 1983, CAAP.

[72]  Thomas Andreae,et al.  On a pursuit game played on graphs for which a minor is excluded , 1986, J. Comb. Theory, Ser. B.

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

[74]  P. Gács,et al.  Algorithms , 1992 .

[75]  Chuan Yi Tang,et al.  The summation and bottleneck minimization for single-step searching on weighted graphs , 1993, Inf. Sci..

[76]  Peter Frankl,et al.  On a pursuit game on cayley graphs , 1987, Comb..

[77]  Fedor V. Fomin,et al.  On the Domination Search Number , 2000, Discret. Appl. Math..

[78]  Stewart W. Neufeld.  A Pursuit-Evasion Problem on a Grid , 1996, Inf. Process. Lett..

[79]  Boting Yang.  Strong-mixed searching and pathwidth , 2007, J. Comb. Optim..

[80]  Richard J. Nowakowski,et al.  A Tandem version of the Cops and Robber Game played on products of graphs , 2005, Discuss. Math. Graph Theory.

[81]  Jan Obdrzálek,et al.  DAG-width: connectivity measure for directed graphs , 2006, SODA '06.

[82]  Robin Thomas,et al.  Directed Tree-Width , 2001, J. Comb. Theory, Ser. B.

[83]  Richard J. Nowakowski,et al.  Cops, Robber, and Photo Radar , 2000, Ars Comb..

[84]  Peter Frankl,et al.  Cops and robbers in graphs with large girth and Cayley graphs , 1987, Discret. Appl. Math..

[85]  Jonathan D. H. Smith.  Minimal trees of given search number , 1987, Discret. Math..

[86]  Georg Gottlob,et al.  Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width , 2001, PODS '01.

[87]  Richard J. Nowakowski,et al.  A game of cops and robbers played on products of graphs , 1998, Discret. Math..

[88]  Jitender S. Deogun,et al.  Domination Search on Graphs with Low Dominating-Target-Number , 2005, WG.

[89]  Bernd S. W. Schröder.  The Copnumber of a Graph is Bounded by [3/2 genus ( G )] + 3 , 2001 .

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

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

[92]  Richard J. Nowakowski,et al.  Copnumber Of Graphs With Strong Isometric Dimension Two , 2001, Ars Comb..

[93]  Ivan Hal Sudborough,et al.  The Vertex Separation and Search Number of a Graph , 1994, Inf. Comput..

[94]  Yahya Ould Hamidoune,et al.  On a Pursuit Game on Cayley Digraphs , 1987, Eur. J. Comb..

[95]  Hans L. Bodlaender,et al.  A linear time algorithm for finding tree-decompositions of small treewidth , 1993, STOC.

[96]  Xuehou Tan.  Sweeping simple polygons with the minimum number of chain guards , 2007, Inf. Process. Lett..

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

[98]  Anthony Bonato,et al.  The cop density of a graph , 2007, Contributions Discret. Math..

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

[100]  Robin Thomas,et al.  Quickly excluding a forest , 1991, J. Comb. Theory, Ser. B.

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

[102]  Victor Chepoi,et al.  Bridged Graphs Are Cop-Win Graphs: An Algorithmic Proof , 1997, J. Comb. Theory, Ser. B.

[103]  Chuan Yi Tang,et al.  Solving the Single Step Graph Searching Problem by Solving the Maximum Two-Independent Set Problem , 1991, Inf. Process. Lett..

[104]  Masafumi Yamashita,et al.  The Searchlight Scheduling Problem , 1990, SIAM J. Comput..

[105]  Fabrizio Luccio,et al.  Network decontamination in Presence of Local Immunity , 2007, Int. J. Found. Comput. Sci..

[106]  Masafumi Yamashita,et al.  Searching a polygonal region by a group of stationary k-searchers , 2004, Inf. Process. Lett..

[107]  Masafumi Yamashita,et al.  Searching for a mobile intruder in a corridor: the open edge variant of the polygon search problem , 1995, Int. J. Comput. Geom. Appl..

[108]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[109]  Thomas Schwentick,et al.  Generalized hypertree decompositions: np-hardness and tractable variants , 2007, PODS '07.

[110]  Boting Yang,et al.  Searching Cycle-Disjoint Graphs , 2007, COCOA.

[111]  Petr A. Golovach,et al.  Search problems on 1-skeletons of regular polyhedrons , 2005 .

[112]  Egon Wanke,et al.  Bounded Tree-Width and LOGCFL , 1993, J. Algorithms.

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

[114]  Richard J. Nowakowski,et al.  Cops, Robber and traps. , 2001 .

[115]  Ruay-Shiung Chang.  Single Step Graph Search Problem , 1991, Inf. Process. Lett..

[116]  Ichiro Suzuki,et al.  Optimal Algorithms for a Pursuit-Evasion Problem in Grids , 1989, SIAM J. Discret. Math..

[117]  N. N. Petrov,et al.  Graph Searching Problems with the Counteraction , 2005 .

[118]  Spyros Tragoudas,et al.  Searching a Pseudo 3-Sided Solid Orthoconvex Grid , 1993, Int. J. Found. Comput. Sci..

[119]  Nancy E. Clarke,et al.  Cops, Robber, and Alarms , 2006, Ars Comb..

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

[121]  Nicolas Nisse,et al.  Monotonicity of non-deterministic graph searching , 2008, Theor. Comput. Sci..

[122]  Николай Николаевич Петров,et al.  Задачи поиска на графах правильных многогранников@@@Search problems on graphs of regular polyhedra , 1996 .

[123]  B. Alspach.  SEARCHING AND SWEEPING GRAPHS: A BRIEF SURVEY , 2006 .

[124]  Rolf H. Möhring,et al.  Graph Problems Related to Gate Matrix Layout and PLA Folding , 1990 .

[125]  Paola Flocchini,et al.  Decontaminating Chordal Rings and Tori Using Mobile Agents , 2007, Int. J. Found. Comput. Sci..

[126]  Richard J. Nowakowski.  Search ans Sweep Numbers of Finite Directed Acyclic Graphs , 1993, Discret. Appl. Math..

[127]  François Laviolette,et al.  On cop-win graphs , 2002, Discret. Math..

[128]  Nancy G. Kinnersley,et al.  The Vertex Separation Number of a Graph equals its Path-Width , 1992, Inf. Process. Lett..

[129]  Dimitrios M. Thilikos,et al.  Connected Graph Searching in Outerplanar Graphs , 2005, Electron. Notes Discret. Math..

[130]  Peter Buneman,et al.  Semistructured data , 1997, PODS.

[131]  Petr A. Golovach,et al.  Graph Searching and Interval Completion , 2000, SIAM J. Discret. Math..

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

[133]  Richard J. Nowakowski,et al.  Tandem-win graphs , 2005, Discret. Math..

[134]  Shuichi Ueno,et al.  Mixed Searching and Proper-Path-Width , 1995, Theor. Comput. Sci..

[135]  P. Varaiya,et al.  Differential games , 1971 .

[136]  Dimitrios M. Thilikos,et al.  Computing Small Search Numbers in Linear Time , 2004, IWPEC.

[137]  François Laviolette,et al.  On constructible graphs, infinite bridged graphs and weakly cop-win graphs , 2000, Discret. Math..