Tree-width, path-width, and cutwidth
Ephraim Korach,Nir Solel +1 more
94
TL;DR: It is proved that c ( G )=O(tw( G )· Δ ( G)·log n ), and if ({ X i : i ∈ I }, T =( I, A )) is a tree decomposition of G with tree-width≤ k then c (G )≤( k +1)·δ ( G ), and pw( G)=O (log n)· c ( T ).
read more
About: This article is published in Discrete Applied Mathematics. The article was published on 06 May 1993. and is currently open access.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
An Efficient Curing Policy for Epidemics on Graphs
TL;DR: If the budget of curing resources available at each time is $\Omega (W)$, then the expected time until the extinction of the epidemic is of order $O(n/r)$ , which is within a constant factor from optimal, as well as sublinear in the number of nodes.
Cutwidth I: a linear time fixed parameter algorithm
TL;DR: This paper provides a linear time algorithm that for any input graph G, answers whether G has cutwidth at most k and, in the case of a positive answer, outputs the corresponding linear layout.
109
Cutwidth II: Algorithms for partial w-trees of bounded degree
TL;DR: This work shows how to construct an algorithm that, in n^O^(^w^^^2^d^) steps, computes the cutwidth of any partial w-tree with vertices of degree bounded by a fixed constant d.
69
•Book
Exponential Time Algorithms: Structures, Measures, and Bounds
Serge Gaspers
- 11 Feb 2010
TL;DR: This book studies exponential time algorithms for NP-hard problems, to design algorithms for combinatorially hard problems that execute provably faster than a brute-force enumeration of all candidate solutions.
An efficient curing policy for epidemics on graphs
Kimon Drakopoulos,Asuman Ozdaglar,John N. Tsitsiklis +2 more
- 01 Dec 2014
TL;DR: In this article, an implementable dynamic policy for the rapid containment of a contagious process modeled as an SIS epidemic is presented, and for graphs with low CutWidth (sublinear) rapid containment defined as achieving sublinear expected extinction time for the epidemic is feasible with sublinear budget.
49
References
Graph minors. II: Algorithmic aspects of tree-width
Neil Robertson,Paul Seymour +1 more
TL;DR: An invariant of graphs called the tree-width is introduced, and used to obtain a polynomially bounded algorithm to test if a graph has a subgraph contractible to H, where H is any fixed planar graph.
1.9K
Complexity of finding embeddings in a k -tree
TL;DR: This work determines the complexity status of two problems related to finding the smallest number k such that a given graph is a partial k-tree and presents an algorithm with polynomially bounded (but exponential in k) worst case time complexity.
1.4K
Graph minors. I. Excluding a forest
Neil Robertson,Paul Seymour +1 more
TL;DR: It is proved that there is a numberk such that every graph with no minor isomorphic toH has path-width≆k, and this implies that ifP is any property of graphs such that some forest does not have propertyP, then the set of minor-minimal graphs without propertyP is finite.
716
Graph minors. IV. Tree-width and well-quasi-ordering
Neil Robertson,Paul Seymour +1 more
TL;DR: A strengthening of Kruskal's result-Wagner's conjecture is true for all sequences in which G1 is planar, and the results of this paper will be needed for that proof.
209
Min cut is NP-complete for edge weighted trees
TL;DR: The Min Cut Linear Arrangement Problem is NP-complete for trees with polynomial size edge weights and this is used to show the NP-completeness of Search Number, Vertex Separation, Progressive Black/White Pebble Demand, and Topological Bandwidth for planar graphs with maximum vertex degree 3.
173