A leapfrog strategy for pursuit-evasion in a polygonal environment, Int. J. Comput. Geometry Appl, vol.25, issue.2, pp.77-100, 2015. ,
Non-deterministic graph searching in trees, Theoretical Computer Science, vol.580, pp.101-121, 2015. ,
DOI : 10.1016/j.tcs.2015.02.038
URL : https://hal.archives-ouvertes.fr/hal-01132032
Arc Searching Digraphs Without Jumping, Proc. of first int. conf. on Combinatorial Optimization and Applications (COCOA), pp.354-365, 2007. ,
DOI : 10.1007/978-3-540-73556-4_37
Directed tree-width examples, Journal of Combinatorial Theory, Series B, vol.97, issue.5, pp.718-725, 2007. ,
DOI : 10.1016/j.jctb.2006.12.006
URL : https://doi.org/10.1016/j.jctb.2006.12.006
DAG-width is PSPACE-complete, Theoretical Computer Science, vol.655, issue.59, pp.78-8965, 2004. ,
DOI : 10.1016/j.tcs.2016.09.011
Directed Path-width and Monotonicity in Digraph Searching, Graphs and Combinatorics, vol.22, issue.2, pp.161-172, 2006. ,
DOI : 10.1007/s00373-005-0627-y
Brief Announcement: Distributed Exclusive and Perpetual Tree Searching, Proc. of 26th International Symposium on Distributed Computing (DISC), pp.403-404, 2012. ,
DOI : 10.1007/978-3-642-33651-5_29
URL : https://hal.archives-ouvertes.fr/hal-00741982
Exclusive graph searching The dag-width of directed graphs, Algorithmica J. Comb. Theory, Ser. B, vol.77, issue.1024, pp.942-969900, 2012. ,
Distributed graph searching with a sense of direction, Distributed Computing, pp.155-170, 2015. ,
DOI : 10.1007/11753728_58
URL : https://link.springer.com/content/pdf/10.1007%2Fs00446-014-0236-1.pdf
Approximation of pathwidth of outerplanar graphs, J. Algorithms, vol.43, issue.2, pp.190-200, 2002. ,
Connected graph searching, Inf. Comput, vol.219, pp.1-16, 2012. ,
Capture of an intruder by mobile agents, Proc. of the 14th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA), pp.200-209, 2002. ,
Brushing without capacity restrictions, Discrete Applied Mathematics, vol.170, pp.33-45, 2014. ,
(meta) kernelization, 50th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp.629-638, 2009. ,
Distributed chasing of network intruders, Theoretical Computer Science, vol.399, issue.1-2, pp.12-37, 2008. ,
DOI : 10.1016/j.tcs.2008.02.004
URL : https://hal.archives-ouvertes.fr/hal-01310347
Searching is not jumping, Proc. of 29th International Workshop on Graph-Theoretic Concepts in Computer Science (WG), pp.34-45, 2003. ,
Contraction obstructions for connected graph searching Graph searching and search time [Bie91] Daniel Bienstock. Graph searching, path-width, tree-width and related problems (A survey), 32nd Conference on Current Trends Proc. of Reliability Of Computer And Communication Networks of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp.27-47, 1991. ,
DOI : 10.1016/j.dam.2015.07.036
URL : http://arxiv.org/pdf/1410.8756
Efficient and constructive algorithms for the pathwidth and treewidth of graphs, J. Algorithms, vol.21, issue.2, pp.358-402, 1996. ,
Capturing an evader in polygonal environments with obstacles: The full visibility case, BLS99] Andreas Brandstädt, pp.1176-1189, 1999. ,
DOI : 10.1287/mnsc.17.11.712
The pathwidth and treewidth of cographs, SIAM J. Discrete Math, vol.6, issue.2, pp.181-188, 1993. ,
Efficient self-stabilizing graph searching in tree networks, Proc. of 12th Int. Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), pp.111-125, 2010. ,
The game of Cops and Robber on Graphs, 2011. ,
DOI : 10.1090/stml/061
A partial k -arboretum of graphs with bounded treewidth, Theor. Comput. Sci, vol.209, issue.12, pp.1-45, 1998. ,
An intuitive approach to speleotopology, Southwestern Cavers, vol.6, pp.72-78, 1967. ,
Lost in a Cave: applying graph theory to cave exploration. Greyhound press, 2012. ,
Quickly excluding a forest, BS91] Daniel Bienstock and Paul D. Seymour. Monotonicity in graph searching, pp.274-283, 1991. ,
DOI : 10.1016/0095-8956(91)90068-U
URL : https://doi.org/10.1016/0095-8956(91)90068-u
, J. Algorithms, vol.12, issue.2, pp.239-245, 1991.
Computing small search numbers in linear time, Proc. of First Int. Workshop on Parameterized and Exact Computation (IWPEC), pp.37-48, 2004. ,
Algorithms and complexity results for graph-based pursuit evasion, Autonomous Robots, vol.18, issue.5, pp.317-332, 2011. ,
DOI : 10.1109/TRA.2002.804040
Tradeoffs in process strategy games with application in the WDM reconfiguration problem, Theoretical Computer Science, vol.412, issue.35, pp.4675-4687, 2011. ,
DOI : 10.1016/j.tcs.2011.05.002
A tie-break model for graph search, Michal Pilipczuk, and Saket Saurabh. Parameterized Algorithms, pp.89-100, 2015. ,
Search and pursuit-evasion in mobile robotics, Autonomous Robots, vol.21, issue.1, pp.299-316, 2011. ,
DOI : 10.1109/ROBOT.2005.1570598
Reconfiguration of the Routing in WDM Networks with Two Classes of Services, Conference on Optical Network Design and Modeling (ONDM), 2009. ,
URL : https://hal.archives-ouvertes.fr/inria-00423453
A Distributed Algorithm for Computing the Node Search Number in Trees, Algorithmica, vol.47, issue.1, pp.158-190, 2012. ,
DOI : 10.1016/S0196-6774(02)00225-0
URL : https://hal.archives-ouvertes.fr/inria-00587819
Pathwidth of outerplanar graphs The treewidth and pathwidth of hypercubes Monadic second-order evaluations on tree-decomposable graphs, Journal of Graph Theory Discrete Mathematics Theor. Comput. Sci, vol.55, issue.1091&2, pp.27-41359, 1993. ,
A note on Integer Linear Programming formulations for linear ordering problems on graphs Research report, Inria ; I3S [CS11] David Coudert and Jean-Sébastien Sereni. Characterization of graphs and digraphs with small process numbers On minimum cost edge searching Three-fastsearchable graphs, Der09] Dariusz Dereniowski. Maximum vertex occupation time and inert fugitive: Recontamination does help, pp.1-3, 2009. ,
Approximate search strategies for weighted trees, Theoretical Computer Science, vol.463, pp.96-113, 2012. ,
DOI : 10.1016/j.tcs.2012.07.006
From Pathwidth to Connected Pathwidth, SIAM Journal on Discrete Mathematics, vol.26, issue.4, pp.1709-1732, 2012. ,
DOI : 10.1137/110826424
URL : https://hal.archives-ouvertes.fr/hal-00573616
Network Decontamination with Temporal Immunity by Cellular Automata, Proc. of 9th Int. Conference on Cellular Automata for Research and Industry (ACRI), pp.287-299, 2010. ,
DOI : 10.1145/42267.42268
The bidimensionality theory and its algorithmic applications Graph Theory, 4th Edition, volume 173 of Graduate texts in mathematics Exact and approximate solutions for the gate matrix layout problem, Die12] Reinhard DiestelDJS16] Yassine Daadaa, Asif Jamshed, and Mudassir Shabbir. Network decontamination with a single agent. Graphs and CombinatoricsDKL87] Narsingh Deo, pp.292-302559, 1987. ,
Fugitive-search games on graphs and related parameters, Theoretical Computer Science, vol.172, issue.1-2, pp.233-254, 1997. ,
DOI : 10.1016/S0304-3975(96)00177-6
URL : https://doi.org/10.1016/s0304-3975(96)00177-6
The complexity of minimum-length path decompositions, Journal of Computer and System Sciences, vol.81, issue.8, pp.1715-1747, 2015. ,
DOI : 10.1016/j.jcss.2015.06.011
URL : http://arxiv.org/pdf/1302.2788
A unified approach for gathering and exclusive searching on rings under weak assumptions . Distributed Computing, DOR18] Dariusz Dereniowski, Dorota Osula, and Pawé l Rzazewski. Finding small-width connected path decompositions in polynomial time. CoRR, pp.17-48, 2017. ,
Computing on rings by oblivious robots: A unified approach for different tasks, DU16] Dariusz Dereniowski and Dorota Urbanska. Distributed searching of partial grids. CoRR, abs, pp.1055-1096, 1458. ,
On the Fast Searching Problem, Proc. of 4th Int. Conference on Algorithmic Aspects in Information and Management (AAIM), pp.143-154, 2008. ,
DOI : 10.1007/978-3-540-68880-8_15
D-width and cops and robbers ,
Computing the vertex separation of unicyclic graphs, Inf. Comput, vol.192, issue.2, pp.123-161, 2004. ,
Graph separation and search number, 1987. ,
DOI : 10.1006/inco.1994.1064
URL : https://doi.org/10.1006/inco.1994.1064
The Vertex Separation and Search Number of a Graph, Information and Computation, vol.113, issue.1, pp.50-79, 1994. ,
DOI : 10.1006/inco.1994.1064
Nondeterministic graph searching: From pathwidth to treewidth, Algorithmica, vol.53, issue.3, pp.358-373, 2009. ,
Graph searching and interval completion, SIAM J. Discrete Math, vol.13, issue.4, pp.454-464, 2000. ,
DECONTAMINATING CHORDAL RINGS AND TORI USING MOBILE AGENTS, International Journal of Foundations of Computer Science, vol.27, issue.03, pp.547-563, 2007. ,
DOI : 10.1016/S1389-1286(00)00136-5
Decontamination of hypercubes by mobile agents, Networks, vol.3341, issue.3, pp.167-178, 2008. ,
DOI : 10.1007/3-540-45071-8_39
URL : http://www.site.uottawa.ca/~flocchin/Papers/Networks07.pdf
Mixed search number and linear-width of interval and split graphs, Networks, vol.56, issue.3, pp.207-214, 2010. ,
Graph searching , elimination trees, and a generalization of bandwidth, Algorithmica, vol.41, issue.2, pp.73-87, 2005. ,
Oracle size, Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing , PODC '06, pp.179-187, 2006. ,
DOI : 10.1145/1146381.1146410
URL : https://hal.archives-ouvertes.fr/hal-00339854
On search, decision, and the efficiency of polynomial-time algorithms, J. Comput. Syst. Sci, vol.49, issue.3, pp.769-779, 1994. ,
Network decontamination under <mml:math altimg="si60.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi>m</mml:mi></mml:math>-immunity, Proc. of the Int. Conference on Communications in Computing (CIC), pp.114-129, 2005. ,
DOI : 10.1016/j.dam.2015.07.020
Excluded grid minors and efficient polynomial-time approximation schemes, J. ACM, vol.6510, issue.2, pp.1-1044, 2018. ,
Tree Decontamination with Temporary Immunity, Proc. of 19th Int. Symposium on Algorithms and Computation (ISAAC), pp.330-341, 2008. ,
DOI : 10.1007/BFb0055153
URL : http://www.comp.mq.edu.au/~bmans/BMans/Papers/FMS_ISAAC08.pdf
Monotony properties of connected visible graph searching, Information and Computation, vol.206, issue.12, pp.1383-1393, 2008. ,
DOI : 10.1016/j.ic.2008.09.002
URL : https://hal.archives-ouvertes.fr/hal-00421416
Decontamination of Arbitrary Networks using a Team of Mobile Agents with Limited Visibility, 6th IEEE/ACIS International Conference on Computer and Information Science (ICIS 2007), pp.469-474, 2007. ,
DOI : 10.1109/ICIS.2007.87
Helicopter search problems, bandwidth and pathwidth, Discrete Applied Mathematics, vol.85, issue.1, pp.59-70, 1998. ,
Note on a helicopter search problem on graphs, Discrete Applied Mathematics, vol.95, issue.1-3, pp.241-249, 1999. ,
Searching expenditure and interval graphs Distributed security algorithms by mobile agents, Distributed Computing and Networking, 8th International Conference, ICDCN, pp.97-104, 2004. ,
An annotated bibliography on guaranteed graph searching, Theor. Comput. Sci, vol.399, issue.3, pp.236-245, 2008. ,
Connected graph searching in outerplanar graphs, Electronic Notes in Discrete Mathematics, vol.22, pp.213-216, 2005. ,
Are there any good digraph width measures?, Journal of Combinatorial Theory, Series B, vol.116, pp.250-286, 2016. ,
DOI : 10.1016/j.jctb.2015.09.001
URL : http://arxiv.org/pdf/1004.1485
Edge search number of cographs, Discrete Applied Mathematics, vol.160, issue.6, pp.734-743, 2012. ,
DOI : 10.1016/j.dam.2011.04.020
URL : https://doi.org/10.1016/j.dam.2011.04.020
Lifosearch: A min-max theorem and a searching game for cycle-rank and treedepth A visibility-based pursuit-evasion problem, Discrete Applied Mathematics Int. J. Comput. Geometry Appl, vol.160, issue.945, pp.2089-2097471, 1999. ,
Equivalence of two formalizations of a search problem on a graph, pp.13-19, 1989. ,
A topological invariant in pursuit problems, Differ. Equ, vol.25, pp.657-661, 1989. ,
Digraph measures: Kelly decompositions , games, and orderings [HM08] Pinar Heggernes and Rodica Mihai Mixed search number of permutation graphs Workshop on Frontiers in Algorithmics FAW The cost of monotonicity in distributed graph searching Capturing an intruder in product networks, Proc. of Second Annual Int Distributed ComputingISZ08] Navid Imani, Hamid Sarbazi-Azad, and Albert Y. Zomaya. Intruder capturing in mesh and torus networks, pp.233-248206, 1993. ,
Directed Tree-Width, Journal of Combinatorial Theory, Series B, vol.82, issue.1, pp.138-154, 2001. ,
DOI : 10.1006/jctb.2000.2031
URL : https://doi.org/10.1006/jctb.2000.2031
The vertex separation number of a graph equals its pathwidth, Inform. Process. Lett, 1992. ,
DOI : 10.1016/0020-0190(92)90234-m
Approximation algorithms for digraph width parameters, Kirousis and Christos H. Papadimitriou. Interval graphs and searching. Discrete Mathematics, pp.365-376138, 1985. ,
DOI : 10.1016/j.tcs.2014.10.009
URL : http://arxiv.org/pdf/1107.4824
Searching and pebbling, Theor. Comput. Sci, vol.47, issue.3, pp.205-218, 1986. ,
Game brush number, Discrete Applied Mathematics, vol.207, pp.1-14, 2016. ,
Pursuit Evasion on Polyhedral Surfaces, Algorithmica, vol.21, issue.1???2, pp.730-747, 2015. ,
DOI : 10.1137/0221051
Recontamination does not help to search a graph Network decontamination with local immunization Contiguous search problem in sierpinski graphs, Proc. of 20th Int. Parallel and Distributed Processing Symposium (IPDPS). IEEE, 2006. [Luc09] Flaminia L. Luccio, pp.224-245186, 1993. ,
Linear Ordering Based MIP Formulations for the Vertex Separation or Pathwidth Problem, Proc. of 28th Int. Workshop on Combinatorial Algorithms (IWOCA), pp.327-340, 2018. ,
DOI : 10.1016/j.dam.2007.08.045
The complexity of searching a graph [MM09] Rodica Mihai and Morten Mjelde. A self-stabilizing algorithm for graph searching in trees Monotonicity of non-deterministic graph searching, Proc. of 11th Int. Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS)MNP08] Margaret-Ellen Messinger, Richard J. Nowakowski, and Pawel Pralat. Cleaning a network with brushes, pp.18-44, 1988. ,
DOI : 10.1109/sfcs.1981.46
Exclusive graph searching vs. pathwidth Min cut is np-complete for edge weighted trees, MT09] Rodica Mihai and Ioan Todinca, pp.243-260209, 1988. ,
URL : https://hal.archives-ouvertes.fr/hal-00980877
, Proc. of Third International Workshop on Frontiers in Algorithmics, pp.181-195
Recognizing digraphs of Kelly-width 2, Discrete Applied Mathematics, vol.158, issue.7, pp.741-746, 2010. ,
DOI : 10.1016/j.dam.2009.09.018
Connected graph searching in chordal graphs Algorithmic complexity: Between Structure and Knowledge How Pursuit-evasion Games help. 2014. HabilitationàHabilitation`Habilitationà Diriger des Recherches Graph searching with advice On the monotonicity of process number, Eur. J. Comb. Discrete Applied Mathematics Theor. Comput. Sci. Discrete Applied Mathematics, vol.29, issue.210, pp.760-7762603, 2008. ,
Pursuit-evasion in a graph, International Conference on Theory and applications of graphs, pp.426-441, 1978. ,
DOI : 10.1007/BFb0070400
The search number of a connected graph, 9th Southeastern Conf. on Combinatorics, Graph Theory, and Computing, Congress. Numer., XXI, pp.549-554, 1978. ,
A problem of pursuit in the absence of information on the pursued Edge and node searching problems on trees, Differ. Uravn. Theor. Comput . Sci, vol.18, issue.2402, pp.1345-1352429, 1982. ,
Integer programming models and algorithms for the graph decontamination problem with mobile agents Graph searching on some subclasses of chordal graphs [PY07] Sheng-Lung Peng and Yi-Chuan Yang. On the treewidth and pathwidth of biconvex bipartite graphs, PTK + 00] Sheng-Lung Peng, Proc. of 4th Int. on Theory and Applications of Models of ComputationRS83] Neil Robertson and Paul D. Seymour. Graph minors. I. excluding a forest, pp.611-19395, 2000. ,
Graph minors. IV. tree-width and well-quasi-ordering Graph minors XIII. the disjoint paths problem Graph minors. XX. wagner's conjecture Searching for a visible, lazy fugitive D-width: A more natural measure for directed tree width Capturing an intruder in the pyramid Construction of linear tree-layouts which are optimal with respect to vertex separation in linear time, Saf05] Mohammad Ali Safari 30th International Symposium on Mathematical Foundations of Computer Science (MFCS)SIS06] Pooya Shareghi, Navid Imani, Proc. of First Int. Computer Science Symposium in Russia on Computer Science -Theory and Applications (CSR), pp.39-61227, 1983. ,
Graph searching and a min-max theorem for tree-width, J. Comb. Theory, Ser. B, vol.58, issue.1, pp.22-33, 1993. ,
Pathwidth of Circular-Arc Graphs, 33rd International Workshop on Graph-Theoretic Concepts in Computer Science (WG), pp.258-269 ,
DOI : 10.1007/978-3-540-74839-7_25
URL : https://hal.archives-ouvertes.fr/hal-00462302
,
Lower bounds on fast searching Fast searching games on graphs Algorithms and obstructions for linear-width and related search parameters, Proc. of 4th Int. Workshop on Parameterized and Exact Computation Proc. of 20th Int. Symposium on Algorithms and Computation, pp.324-335, 2000. ,
Mixed searching and proper-path-width, Theoretical Computer Science, vol.137, issue.2, pp.253-268, 1995. ,
DOI : 10.1016/0304-3975(94)00160-K
Inapproximability of treewidth and related problems, J. Artif. Intell. Res, vol.49, pp.569-600, 2014. ,
The fast search number of a Cartesian product of graphs, Discrete Applied Mathematics, vol.224, pp.106-119, 2017. ,
DOI : 10.1016/j.dam.2017.03.003
Fast Searching on Complete k-partite Graphs, Proc. of 10th Int. Conference on Combinatorial Optimization and Applications (COCOA), volume 10043 of Lecture Notes in Computer Science, pp.159-174, 2016. ,
DOI : 10.1016/j.tcs.2010.12.065
Strong-mixed searching and pathwidth, Journal of Combinatorial Optimization, vol.137, issue.35, pp.47-59, 2007. ,
DOI : 10.1007/s10878-006-9013-9
Fast edge searching and fast searching on graphs, Theoretical Computer Science, vol.412, issue.12-14, pp.12-141208, 2011. ,
DOI : 10.1016/j.tcs.2010.12.065
Fast???mixed searching and related problems on graphs, Theoretical Computer Science, vol.507, pp.100-113, 2013. ,
DOI : 10.1016/j.tcs.2013.04.015
Directed Searching Digraphs: Monotonicity and Complexity, Proc. of 4th International Conference Theory and Applications of Models of Computation (TAMC), pp.136-147, 2007. ,
DOI : 10.1007/978-3-540-72504-6_12
Monotonicity of strong searching on digraphs, Journal of Combinatorial Optimization, vol.35, issue.4, pp.411-425, 2007. ,
DOI : 10.1007/s10878-007-9042-z
Digraph searching, directed vertex separation and directed pathwidth, Discrete Applied Mathematics, vol.156, issue.10, pp.1822-1837, 2008. ,
DOI : 10.1016/j.dam.2007.08.045
Monotonicity in digraph search problems, Theoretical Computer Science, vol.407, issue.1-3, pp.532-544, 2008. ,
DOI : 10.1016/j.tcs.2008.08.025
On the Monotonicity of Weak Searching, Proc. of 14th Annual Int. Conference on Computing and Combinatorics (COCOON), pp.52-61, 2008. ,
DOI : 10.1007/978-3-540-69733-6_6
Standard directed search strategies and their applications, Journal of Combinatorial Optimization, vol.4, issue.4, pp.378-399, 2009. ,
DOI : 10.1007/978-3-540-30551-4_77
Sweeping graphs with large clique number, Discrete Mathematics, vol.309, issue.18, pp.5770-5780, 2009. ,
DOI : 10.1016/j.disc.2008.05.033
Searching Cycle-Disjoint Graphs, Proc of first int. Conference on Combinatorial Optimization and Applications (COCOA), pp.32-43, 2007. ,
DOI : 10.1007/978-3-540-73556-4_6