Academic Journal
A Linear Fixed Parameter Tractable Algorithm for Connected Pathwidth: A linear fixed parameter tractable algorithm for connected pathwidth
| Τίτλος: | A Linear Fixed Parameter Tractable Algorithm for Connected Pathwidth: A linear fixed parameter tractable algorithm for connected pathwidth |
|---|---|
| Συγγραφείς: | Kanté, Mamadou Moustapha, Paul, Christophe, Thilikos, Dimitrios M. |
| Συνεισφορές: | Mamadou Moustapha Kanté and Christophe Paul and Dimitrios M. Thilikos, Thilikos, Dimitrios, Fabrizio Grandoni, Grzegorz Herman, Peter Sanders |
| Πηγή: | SIAM Journal on Discrete Mathematics. 36:411-435 |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | Society for Industrial & Applied Mathematics (SIAM), 2022. |
| Έτος έκδοσης: | 2022 |
| Θεματικοί όροι: | FOS: Computer and information sciences, parameterized algorithms, [INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS], Pathwidth, G.2.2, 0102 computer and information sciences, 01 natural sciences, Typical sequences, width parameter, Graph theory, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Parameterized algorithms, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), Graph algorithms (graph-theoretic aspects), Computer Science - Data Structures and Algorithms, Cops and Robber games, Data Structures and Algorithms (cs.DS), 05C85, graph decomposition, Width parameter, Graph decompositions, cops and robber game, Graph searching |
| Περιγραφή: | The graph parameter of pathwidth can be seen as a measure of the topological resemblance of a graph to a path. A popular definition of pathwidth is given in terms of node search where we are given a system of tunnels that is contaminated by some infectious substance and we are looking for a search strategy that, at each step, either places a searcher on a vertex or removes a searcher from a vertex and where an edge is cleaned when both endpoints are simultaneously occupied by searchers. It was proved that the minimum number of searchers required for a successful cleaning strategy is equal to the pathwidth of the graph plus one. Two desired characteristics for a cleaning strategy is to be monotone (no recontamination occurs) and connected (clean territories always remain connected). Under these two demands, the number of searchers is equivalent to a variant of pathwidth called {\em connected pathwidth}. We prove that connected pathwidth is fixed parameter tractable, in particular we design a $2^{O(k^2)}\cdot n$ time algorithm that checks whether the connected pathwidth of $G$ is at most $k.$ This resolves an open question by [Dereniowski, Osula, and Rz{ą}{ż}ewski, Finding small-width connected path-decompositions in polynomial time. Theor. Comput. Sci., 794:85-100, 2019]. For our algorithm, we enrich the typical sequence technique that is able to deal with the connectivity demand. Typical sequences have been introduced in [Bodlaender and Kloks. Efficient and constructive algorithms for the pathwidth and treewidth of graphs. J. Algorithms, 21(2):358-402, 1996] for the design of linear parameterized algorithms for treewidth and pathwidth. The proposed extension is based on an encoding of the connectivity property that is quite versatile and may be adapted so to deliver linear parameterized algorithms for the connected variants of other width parameters as well. |
| Τύπος εγγράφου: | Article Conference object |
| Περιγραφή αρχείου: | application/xml; application/pdf |
| Γλώσσα: | English |
| ISSN: | 1095-7146 0895-4801 |
| DOI: | 10.1137/20m1369361 |
| DOI: | 10.48550/arxiv.2004.11937 |
| DOI: | 10.4230/lipics.esa.2020.64 |
| Σύνδεσμος πρόσβασης: | https://drops.dagstuhl.de/opus/volltexte/2020/12930/pdf/LIPIcs-ESA-2020-64.pdf http://arxiv.org/abs/2004.11937 https://zbmath.org/7489476 https://doi.org/10.1137/20m1369361 https://arxiv.org/abs/2004.11937 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.64 https://hal.science/hal-03002761v1 https://hal.science/hal-03002761v1/document https://doi.org/10.4230/lipics.esa.2020.64 |
| Rights: | CC BY arXiv Non-Exclusive Distribution |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....5b0c4e7a82a7a1baa0093efa7c2c9b6f |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 10957146 08954801 |
|---|---|
| DOI: | 10.1137/20m1369361 |