Journal ArticleDOI
An improved algorithm for the planar 3-cut problem
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This paper presents an O ( n log n ) algorithm for finding a minimum 3-cut in planar graphs and improves the best previously known algorithm for the problem by an O( n logn) factor.About:
This article is published in Journal of Algorithms.The article was published on 1991-01-02. It has received 20 citations till now. The article focuses on the topics: Planar graph & Line graph.read more
Citations
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Proceedings ArticleDOI
Finding k-cuts within twice the optimal
Huzur Saran,Vijay V. Vazirani +1 more
TL;DR: Two simple approximation algorithms are presented for the minimum k-cut problem, requiring a total of only n-1 maximum flow computations for finding a set of near-optimal k-cuts.
Journal ArticleDOI
The Critical Node Detection Problem in networks: A survey.
TL;DR: This survey reviews, classify and discusses several recent advances and results obtained for each variant, including theoretical complexity, exact solving algorithms, approximation schemes and heuristic approaches, and proves new complexity results and induce some solving algorithms through relationships established between different variants.
Proceedings ArticleDOI
The Minimum k-way Cut of Bounded Size is Fixed-Parameter Tractable
TL;DR: This work considers the minimum-k-way cut problem for unweighted undirected graphs with a size bound on the number of cut edges allowed, and shows that this problem is fixed-parameter tractable (FPT) with the standard parameterization in terms of the solution size $s$.
Journal ArticleDOI
A Deterministic Algorithm for Finding All Minimum $k$-Way Cuts
TL;DR: The algorithm is a divide-and-conquer method based on a procedure that reduces an instance of the minimum $k$-way cut problem to $O(n^{2k-5})$ instances of theminimum $(\lfloor (k+\sqrt{k})/2\rfloor+1)$- way cut problem, and can be implemented to run in time.
Book ChapterDOI
Parallel Algorithms for Series Parallel Graphs
TL;DR: With the same time and processor resources, a tree-decomposition of width at most two can be built of a given series parallel graph, and hence, very efficient parallel algorithms can be found for a large number of graph problems on series parallel graphs, including many well known problems, e.g., all problems that can be stated in monadic second order logic.
References
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Journal ArticleDOI
Efficient Planarity Testing
TL;DR: An efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane is described, which used depth-first search and has time and space bounds.
Journal ArticleDOI
Applications of a Planar Separator Theorem
TL;DR: Any n-vertex planar graph has the property that it can be divided into components of roughly equal size by removing only O(√n) vertices, and this separator theorem in combination with a divide-and-conquer strategy leads to many new complexity results for planar graphs problems.
Journal ArticleDOI
Arboricity and subgraph listing algorithms
Norishige Chiba,Takao Nishizeki +1 more
TL;DR: A new simple strategy into edge-searching of a graph, which is useful to the various subgraph listing problems, is introduced, and an upper bound on $a(G)$ is established for a graph $G:a (G) \leqq \lceil (2m + n)^{1/2} \rceil $, where n is the number of vertices in G.
Journal ArticleDOI
Finding a Minimum Circuit in a Graph
Alon Itai,Michael Rodeh +1 more
TL;DR: Results of Bloniarz, Fisher and Meyer are used to obtain an algorithm with $O(n^2 \log n)$ average behavior, and three methods for finding a triangle in a graph are given.
Proceedings ArticleDOI
Finding a minimum circuit in a graph
Alon Itai,Michael Rodeh +1 more
TL;DR: Finding minimum circuits in graphs and digraphs is discussed and an algorithm to find an almost minimum circuit is presented and an alternative method is to reduce the problem of finding a minimum circuit to that of finding an auxiliary graph.