Filters








9,471 Hits in 4.9 sec

The Complexity of Packing Edge-Disjoint Paths [article]

Jan Dreier, Janosch Fuchs, Tim A. Hartmann, Philipp Kuinke, Peter Rossmanith, Bjoern Tauer, Hung-Lung Wang
2019 arXiv   pre-print
We introduce and study the complexity of Path Packing. Given a graph G and a list of paths, the task is to embed the paths edge-disjoint in G.  ...  Packing paths of length two is polynomial time solvable, while packing paths of length three is NP-hard.  ...  Since packing edge-disjoint and vertex-disjoint triangles is NP-hard for planar graphs, the parameterized complexity is studied [7] .  ... 
arXiv:1910.00440v1 fatcat:wm2hcglaqngalbldsc57ljg6cu

The Complexity of Packing Edge-Disjoint Paths

Jan Dreier, Janosch Fuchs, Tim A. Hartmann, Philipp Kuinke, Peter Rossmanith, Bjoern Tauer, Hung-Lung Wang, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation  
We introduce and study the complexity of Path Packing. Given a graph G and a list of paths, the task is to embed the paths edge-disjoint in G.  ...  Finally, even the spacial case Exact Path Packing where the paths have to cover every edge in G exactly once is already NP-hard for two paths on 4-regular graphs.  ...  Since packing edge-disjoint and vertex-disjoint triangles is NP-hard for planar graphs, the parameterized complexity is studied [7] .  ... 
doi:10.4230/lipics.ipec.2019.10 dblp:conf/iwpec/DreierFHKRTW19 fatcat:usj4jariyncldcolhvejshtku4

Kernelization of Cycle Packing with Relaxed Disjointness Constraints

Akanksha Agrawal, Daniel Lokshtanov, Diptapriyo Majumdar, Amer E. Mouawad, Saket Saurabh
2018 SIAM Journal on Discrete Mathematics  
While the Pairwise Disjoint Cycle Packing problem admits a polynomial kernel for all t ≥ 1, the kernelization complexity of Almost Disjoint Cycle Packing reveals an interesting spectrum of upper and lower  ...  A key result in the field of kernelization, a subfield of parameterized complexity, states that the classic Disjoint Cycle Packing problem, i.e. finding k vertex disjoint cycles in a given graph G, admits  ...  As we shall see, the kernelization complexity landscape for Almost Disjoint Cycle Packing is much more diverse than that of Pairwise Disjoint Cycle Packing.  ... 
doi:10.1137/17m1136614 fatcat:2bb622lgo5fy3i7ooe3at4ybse

Packing (2^k+1-1)-order perfect binary trees into (k+1)-connected graph [article]

Jia Zhao, Jianfeng Guan, Changqiao Xu, Hongke Zhang
2013 arXiv   pre-print
We prove that in G' the largest number of vertex-disjoint subgraphs isomorphic to T_k is equal to the smallest number of vertices that cover all subgraphs isomorphic to T_k.  ...  Packing problem is to find in G the largest number of independent subgraphs each of which is isomorphic to H. Let U⊂V. If the graph G-U has no subgraph isomorphic to H, U is a cover of G.  ...  A key process in the algorithm is to detect the blocks of a connected graph. The T 1 packing algorithm has complexity of O(n 2 ) and the T 2 packing algorithm has complexity of O(n 4 ).  ... 
arXiv:1309.3825v1 fatcat:qb6uyasudvdblbxafhk3pw3ede

Edge-disjoint odd cycles in 4-edge-connected graphs

Ken-ichi Kawarabayashi, Yusuke Kobayashi
2016 Journal of combinatorial theory. Series B (Print)  
We show that, for any ε > 0, if k = O((log log log n) 1/2−ε ), then the edge-disjoint k odd cycle packing in G can be solved in polynomial time of n. ACM Subject Classification G.2.2 Graph Theory  ...  Finding edge-disjoint odd cycles is one of the most important problems in graph theory, graph algorithm and combinatorial optimization.  ...  As we have already seen before, the edge-disjoint k odd cycle packing is a generalization of the k edge-disjoint paths problem.  ... 
doi:10.1016/j.jctb.2015.12.002 fatcat:ur67y2kfrvfulf4rnh7yorekqy

Edge-packing of graphs and network reliability

Charles J. Colbourn
1988 Discrete Mathematics  
Edge-packings of graphs An edge-packing of a multigraph G is a collection of edge-disjoint subgraphs of G.  ...  The three problems of most interest to us here are edgepackings by spanning trees, by s, t-paths, and by s, t-cuts. We first review the use of edge-packings in the reliability context.  ...  Acknowledgements Thanks to University of Auckland and University of Toronto for hospitality while this paper was written, and to NSERC Canada for financial support.  ... 
doi:10.1016/0012-365x(88)90193-8 fatcat:lx7uhfhnx5bfnoolloblbbyhwm

Edge-Packings of Graphs and Network Reliability [chapter]

Charles J. Colbourn
1988 Annals of Discrete Mathematics  
Edge-packings of graphs An edge-packing of a multigraph G is a collection of edge-disjoint subgraphs of G.  ...  The three problems of most interest to us here are edgepackings by spanning trees, by s, t-paths, and by s, t-cuts. We first review the use of edge-packings in the reliability context.  ...  Acknowledgements Thanks to University of Auckland and University of Toronto for hospitality while this paper was written, and to NSERC Canada for financial support.  ... 
doi:10.1016/s0167-5060(08)70770-2 fatcat:gejugmxtiffv5i6ac5bosrjr5i

Edge-disjoint packings of graphs

Derek G. Corneil, Shigeru Masuyama, S. Louis Hakimi
1994 Discrete Applied Mathematics  
In this paper we study two types of edge-disjoint packings of graphs.  ...  We show that if G has at most two edges then the induced edge-disjoint G packing problem belongs to P, whereas for all other graphs G the problem is NP-complete.  ...  The rest of this section deals with edge-disjoint induced packing problems; we show that we can determine the complexity status of all remaining such problems.  ... 
doi:10.1016/0166-218x(92)00153-d fatcat:xjlp5zevqfb5dkq4d62it7f6ja

Parameterized Complexity of $$(A,\ell )$$-Path Packing [chapter]

Rémy Belmonte, Tesshu Hanaka, Masaaki Kanzaki, Masashi Kiyomi, Yasuaki Kobayashi, Yusuke Kobayashi, Michael Lampis, Hirotaka Ono, Yota Otachi
2020 Lecture Notes in Computer Science  
Given a graph G = (V, E), A ⊆ V , and integers k and , the (A, )-Path Packing problem asks to find k vertex-disjoint paths of length that have endpoints in A and internal points in V \ A.  ...  We study the parameterized complexity of this problem with parameters |A|, , k, treewidth, pathwidth, and their combinations. We present sharp complexity contrasts with respect to these parameters.  ...  Given G and A, A-Path Packing is the problem of finding the maximum number of vertex-disjoint A-paths in G.  ... 
doi:10.1007/978-3-030-48966-3_4 fatcat:g5va7c7tt5fm5ltbvsjmdmfdqu

The P k Partition Problem and Related Problems in Bipartite Graphs [chapter]

Jérôme Monnot, Sophie Toulouse
2007 Lecture Notes in Computer Science  
More precisely, we prove that the problem consisting of deciding if a graph of nk vertices has n vertex disjoint simple paths {P1, · · · , Pn} such that each path Pi has k vertices is NP-complete, even  ...  In this paper, we continue the investigation proposed in [15] about the approximability of P k partition problems, but focusing here on their complexity.  ...  In other words, we want to know if there exists n vertex disjoint simple paths of length k in G.  ... 
doi:10.1007/978-3-540-69507-3_36 fatcat:x3qfgf2hifaddkfx7gzn2u53lu

Distributed Connectivity Decomposition [article]

Keren Censor-Hillel, Mohsen Ghaffari, Fabian Kuhn
2013 arXiv   pre-print
(II) A decomposition of each undirected graph with edge-connectivity λ into (fractionally) edge-disjoint weighted spanning trees with total weight λ-1/2(1-ε), in O(D+√(nλ)) rounds.  ...  We also show round complexity lower bounds of Ω̃(D+√(n/k)) and Ω̃(D+√(n/λ)) for the above two decompositions, using techniques of [Das Sarma et al., STOC'11].  ...  λ ′ edge-disjoint spanning trees-which we call a spanning tree packing of size λ ′ -then for each pair of vertices we get λ ′ edge-disjoint paths, one through each tree.  ... 
arXiv:1311.5317v1 fatcat:74qs7lgzmff6tmnzcgopksmel4

An Algorithm for Packing Connectors

J. Keijsper
1998 Journal of combinatorial theory. Series B (Print)  
As a corollary, we obtain an O( (n; m) + nm) time algorithm for nding a maximum number of S{T connectors, where (n; m) denotes the complexity of nding a maximum number of edge disjoint spanning trees in  ...  On the other hand, if G is bipartite with colour classes S and T, then an S{T connector is an edge cover of G (a set of edges covering all vertices).  ...  Here, (x; y) denotes the complexity of nding the maximum number of edge-disjoint spanning trees in a graph on x vertices and y edges.  ... 
doi:10.1006/jctb.1998.1863 fatcat:isgqcnpkojblncqgqnxhldniay

Parameterized Complexity of (A,ℓ)-Path Packing [article]

Rémy Belmonte, Tesshu Hanaka, Masaaki Kanzaki, Masashi Kiyomi, Yasuaki Kobayashi, Yusuke Kobayashi, Michael Lampis, Hirotaka Ono, Yota Otachi
2020 arXiv   pre-print
Given a graph G = (V,E), A ⊆ V, and integers k and ℓ, the (A,ℓ)-Path Packing problem asks to find k vertex-disjoint paths of length ℓ that have endpoints in A and internal points in V ∖ A.  ...  We study the parameterized complexity of this problem with parameters |A|, ℓ, k, treewidth, pathwidth, and their combinations. We present sharp complexity contrasts with respect to these parameters.  ...  Given G and A, A-Path Packing is the problem of finding the maximum number of vertex-disjoint A-paths in G.  ... 
arXiv:2008.03448v1 fatcat:qqhkwar3xjex3hvckwytlduske

Distributed connectivity decomposition

Keren Censor-Hillel, Mohsen Ghaffari, Fabian Kuhn
2014 Proceedings of the 2014 ACM symposium on Principles of distributed computing - PODC '14  
A distributed O(log n)-approximation of vertex connectivity with round complexity of O(D + √ n).  ...  with total weight λ−1 We also show round complexity lower bounds ofΩ(D + n k ) andΩ(D + n λ ) for the above two decompositions, using techniques of [Das Sarma et al., STOC'11].  ...  λ edge-disjoint spanning trees-which we call a spanning tree packing of size λ -then for each pair of vertices we get λ edge-disjoint paths, one through each tree.  ... 
doi:10.1145/2611462.2611491 dblp:conf/podc/Censor-HillelGK14 fatcat:dpytrsr765gurdxrj24mfek44i

Counting Paths and Packings in Halves [article]

Andreas Björklund and Thore Husfeldt and Petteri Kaski and Mikko Koivisto
2009 arXiv   pre-print
It is shown that one can count k-edge paths in an n-vertex graph and m-set k-packings on an n-element universe, respectively, in time n k/2 and n mk/2, up to a factor polynomial in n, k, and m; in polynomial  ...  These are implications of a more general result: given two set families on an n-element universe, one can count the disjoint pairs of sets in the Cartesian product of the two families with (n ℓ) basic  ...  This research was supported in part by the Academy of Finland, Grants 117499 (P.K.) and 125637 (M.K.).  ... 
arXiv:0904.3093v1 fatcat:asuyur4l45d2tpsekdyx5cp2yy
« Previous Showing results 1 — 15 out of 9,471 results