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A polynomial time algorithm to compute the connected tree-width of a series-parallel graph [article]

Guillaume Mescoff, Christophe Paul, Dimitrios Thilikos
2021 arXiv   pre-print
We design a O(n^2·log n)-time dynamic programming algorithm to compute the connected treewidth of a biconnected series-parallel graphs.  ...  It has been shown that the connected search number of a graph G can be expressed as the connected treewidth, denoted 𝐜𝐭𝐰(G), that is defined as the minimum width of a rooted tree-decomposition ( X,T  ...  In this paper, we design a O(n 2 · log n)-time algorithm to compute the connected treewidth of a biconnected series-parallel graph.  ... 
arXiv:2004.00547v5 fatcat:umotw6wmyrhblnxmcpvqecnqoi

Combinatorial Optimization on Graphs of Bounded Treewidth

H. L. Bodlaender, A. M. C. A. Koster
2007 Computer journal  
There are many graph problems that can be solved in linear or polynomial time with a dynamic programming algorithm when the input graph has bounded treewidth.  ...  Starting from trees and series-parallel graphs, we introduce the concepts of treewidth and tree decompositions, and illustrate the technique with the Weighted Independent Set problem as an example.  ...  This algorithm computes the branchwidth of a planar graph in polynomial time and can also be used to find a branch decomposition of a planar graph of optimal width in polynomial time.  ... 
doi:10.1093/comjnl/bxm037 fatcat:maq7rjwstvfw7jsda7zrn62zha

Partitioning a graph of bounded tree-width to connected subgraphs of almost uniform size

Takehiro Ito, Xiao Zhou, Takao Nishizeki
2006 Journal of Discrete Algorithms  
The algorithms can be extended for partial k-trees, that is, graphs with bounded tree-width.  ...  We deal with three problems to find an (l, u)-partition of a given graph; the minimum partition problem is to find an (l, u)-partition with the minimum number of components; the maximum partition problem  ...  Acknowledgement We thank Takeshi Tokuyama for suggesting us the partition problems.  ... 
doi:10.1016/j.jda.2005.01.005 fatcat:oulsy2g5ofd67gv7ivjnktnjo4

Subject Index

2006 Journal of Discrete Algorithms  
On Multi-threaded Metrical Task Systems, 401 Parallel segment trees An architecture independent study of parallel seg- ment trees, 1 Partial k-tree Partitioning a graph of bounded tree-width to con  ...  bound Partitioning a graph of bounded tree-width to connected subgraphs of almost uniform size, 142 Weighted) Set Cover Exact algorithms and applications for Tree-like Weighted Set Cover, 608 Worst case  ... 
doi:10.1016/s1570-8667(06)00094-3 fatcat:e5in7ez4svbdlcjyzzev4xkzhm

Spanning Distribution Trees of Graphs

Masaki KAWABATA, Takao NISHIZEKI
2014 IEICE transactions on information and systems  
In the paper, we first observe that the problem is NP-complete even for series-parallel graphs, and then give a pseudo-polynomial time algorithm to solve the problem for a given series-parallel graph G  ...  The computation time is bounded by a polynomial in n and D, where n is the number of vertices in G and D is the sum of all demands in G.  ...  Acknowledgements We thank Kouji Imagawa for his comment on the NPcompleteness proof.  ... 
doi:10.1587/transinf.e97.d.406 fatcat:dwg5gc52onbgbgdxsibzpeky5q

Partitioning a Weighted Graph to Connected Subgraphs of Almost Uniform Size [chapter]

Takehiro Ito, Xiao Zhou, Takao Nishizeki
2004 Lecture Notes in Computer Science  
The algorithms can be easily extended for partial k-trees, that is, graphs with bounded tree-width.  ...  We deal with three problems to find an (l, u)-partition of a given graph. The minimum partition problem is to find an (l, u)-partition with the minimum number of components.  ...  Acknowledgments We thank Takeshi Tokuyama for suggesting us the partition problems.  ... 
doi:10.1007/978-3-540-30559-0_31 fatcat:3i7vec7hezh2fl7pavbwi3uble

An algorithm for the Tutte polynomials of graphs of bounded treewidth

Artur Andrzejak
1998 Discrete Mathematics  
We give an algorithm which computes the Tutte polynomial of any graph G of treewidth at most k in time O(n 2+7 I°g2c), where c is twice the number of partitions of a set with 3k + 3 elements and n the  ...  Let k be a fixed, positive integer.  ...  have proved that the Tutte polynomial of a graph of bounded treewidth is polynomial-time computable but never published the result.  ... 
doi:10.1016/s0012-365x(98)00113-7 fatcat:qcabpflmefhc7kdsqlkjhtrmka

Tutte polynomials computable in polynomial time

J.G. Oxley, D.J.A. Welsh
1992 Discrete Mathematics  
We show that for any accessible computable in polynomial time. class of matroids of bounded width. the Tutte polynomial is  ...  Acknowledgement This research was partially supported by a grant from the Louisiana Education Quality Support Fu d through the Board of Regents.  ...  However the general problem of showing that the Tutte polynomial can be computed in polynomial time for graphs of bounded tree width remains open.  ... 
doi:10.1016/0012-365x(92)90289-r fatcat:fksxc6dyuvddfly7gnrsmppcu4

Partitioning a Multi-weighted Graph to Connected Subgraphs of Almost Uniform Size [chapter]

Takehiro Ito, Kazuya Goto, Xiao Zhou, Takao Nishizeki
2006 Lecture Notes in Computer Science  
Our algorithms for series-parallel graphs can be extended for partial k-trees, that is, graphs with bounded tree-width.  ...  The problem of finding such a "uniform" partition is NP-hard for series-parallel graphs, and is strongly NP-hard for general graphs even for q = 1.  ...  Our algorithms for series-parallel graphs can be extended for partial k-trees, that is, graphs with bounded tree-width [1, 2] .  ... 
doi:10.1007/11809678_9 fatcat:o7ze5ebvcjhgfiw6xtscumcfqy

Partitioning a Multi-Weighted Graph to Connected Subgraphs of Almost Uniform Size

T. ITO, K. GOTO, X. ZHOU, T. NISHIZEKI
2007 IEICE transactions on information and systems  
Our algorithms for series-parallel graphs can be extended for partial k-trees, that is, graphs with bounded tree-width.  ...  The problem of finding such a "uniform" partition is NP-hard for series-parallel graphs, and is strongly NP-hard for general graphs even for q = 1.  ...  Our algorithms for series-parallel graphs can be extended for partial k-trees, that is, graphs with bounded tree-width [1, 2] .  ... 
doi:10.1093/ietisy/e90-d.2.449 fatcat:xwdaiidgcveonkvixcgu7ej52q

Page 4773 of Mathematical Reviews Vol. , Issue 90H [page]

1990 Mathematical Reviews  
In this thesis the author gives polynomial-time algorithms for classes of graphs. The graphs under consideration are of bounded tree-width and of bounded path-width.  ...  Let w(G) denote the tree- width of the graph G. An O(n“*+?)-time algorithm is given to decide whether w(G) < w. Afterwards so-called C- and L-properties are defined.  ... 

Partitioning graphs of supply and demand

Takehiro Ito, Xiao Zhou, Takao Nishizeki
2009 Discrete Applied Mathematics  
In this paper, we show that the problem can be solved in pseudo-polynomial time for series-parallel graphs and partial k-trees -that is, graphs with bounded tree-width.  ...  the sum of demands in C , and wishes to maximize the sum of demands in all components with supply vertices.  ...  Conclusions In this paper we first obtained a pseudo-polynomial-time algorithm to compute the maximum fulfillment f (G) of a given series-parallel graph G.  ... 
doi:10.1016/j.dam.2008.08.012 fatcat:y4eddxhbwvdvratff3odnmo72a

Spanning connectivity games [article]

Haris Aziz, Oded Lachish, Mike Paterson, Rahul Savani
2009 arXiv   pre-print
It is also shown that for any reasonable representation of a simple game, a polynomial time algorithm to compute the Shapley-Shubik indices implies a polynomial time algorithm to compute the Banzhaf indices  ...  Among other results, it is proved that Banzhaf indices can be computed in polynomial time for graphs with bounded treewidth.  ...  Haris Aziz would also like to thank the Pakistan National ICT R&D Fund for funding his research.  ... 
arXiv:0906.3643v1 fatcat:o2t453gl5zeq5kfn626wxh6btu

Power Indices in Spanning Connectivity Games [chapter]

Haris Aziz, Oded Lachish, Mike Paterson, Rahul Savani
2009 Lecture Notes in Computer Science  
It is also shown that for any reasonable representation of a simple game, a polynomial time algorithm to compute the Shapley-Shubik indices implies a polynomial time algorithm to compute the Banzhaf indices  ...  Among other results, it is proved that Banzhaf indices can be computed in polynomial time for graphs with bounded treewidth.  ...  Haris Aziz would also like to thank the Pakistan National ICT R&D Fund for funding his research.  ... 
doi:10.1007/978-3-642-02158-9_7 fatcat:5djeltfj4fa7lainyamscfgmby

Algorithms and complexity results for graph-based pursuit evasion

Richard Borie, Craig Tovey, Sven Koenig
2011 Autonomous Robots  
We study when polynomial-time algorithms exist to determine how many robots are needed to clear a given graph (minimum robot problem) and how a given number of robots should move on the graph to clear  ...  The robots cannot clear a graph if the vertex connectivity of some part of the graph exceeds the number of robots.  ...  It adds new material to these conference papers, namely the minimum cost flow method to minimize distance on paths, and a different description of the algorithm to minimize distance on cycles.  ... 
doi:10.1007/s10514-011-9255-y fatcat:cfn7kk4w2nfo3itom3retgeji4
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