# An Articulation Point-Based Approximation Algorithm for Minimum Vertex Cover Problem

VIT University

^{1}01 Jan 2018-pp 281-289

TL;DR: The aim of this paper is to present an approximation algorithm for minimum vertex cover problem (MVCP) based on articulation points/cut vertices and leaf vertices/pendant vertices that assures the near optimal or optimal solution for a given graph and can be solved in polynomial time.

Abstract: The minimum vertex cover problem (MVCP) is a well-known NP complete combinatorial optimization problem. The aim of this paper is to present an approximation algorithm for minimum vertex cover problem (MVCP). The algorithm construction is based on articulation points/cut vertices and leaf vertices/pendant vertices. The proposed algorithm assures the near optimal or optimal solution for a given graph and can be solved in polynomial time. A numerical example is illustrated to describe the proposed algorithm. Comparative results show that the proposed algorithm is very competitive compared with other existing algorithms.

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01 Jan 1990TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.

Abstract: From the Publisher:
The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures. Like the first edition,this text can also be used for self-study by technical professionals since it discusses engineering issues in algorithm design as well as the mathematical aspects.
In its new edition,Introduction to Algorithms continues to provide a comprehensive introduction to the modern study of algorithms. The revision has been updated to reflect changes in the years since the book's original publication. New chapters on the role of algorithms in computing and on probabilistic analysis and randomized algorithms have been included. Sections throughout the book have been rewritten for increased clarity,and material has been added wherever a fuller explanation has seemed useful or new information warrants expanded coverage.
As in the classic first edition,this new edition of Introduction to Algorithms presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers. Further,the algorithms are presented in pseudocode to make the book easily accessible to students from all programming language backgrounds.
Each chapter presents an algorithm,a design technique,an application area,or a related topic. The chapters are not dependent on one another,so the instructor can organize his or her use of the book in the way that best suits the course's needs. Additionally,the new edition offers a 25% increase over the first edition in the number of problems,giving the book 155 problems and over 900 exercises thatreinforcethe concepts the students are learning.

21,651 citations

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TL;DR: A heuristic is proposed that delivers in O(n^3 ) steps a solution for the set covering problem the value of which does not exceed the maximum number of sets covering an element times the optimal value.

Abstract: We propose a heuristic that delivers in $O(n^3 )$ steps a solution for the set covering problem the value of which does not exceed the maximum number of sets covering an element times the optimal value.

503 citations

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TL;DR: Two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, are considered and their significance for several search problems in applied computer science is discussed.

Abstract: The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation (i.e., given a hypergraph $\cal H$, decide if every subset of vertices is contained in or contains some edge of $\cal H$) is shown to be co-NP-complete. A certain subproblem of hypergraph saturation, the saturation of simple hypergraphs (i.e., Sperner families), is shown to be under polynomial transformation equivalent to transversal hypergraph recognition; i.e., given two hypergraphs ${\cal H}_{1}, {\cal H}_{2}$, decide if the sets in ${\cal H}_{2}$ are all the minimal transversals of ${\cal H}_{1}$. The complexity of the search problem related to the recognition of the transversal hypergraph, the computation of the transversal hypergraph, is an open problem. This task needs time exponential in the input size; it is unknown whether an output-polynomial algorithm exists. For several important subcases, for instance if an upper or lower bound is imposed on the edge size or for acyclic hypergraphs, output-polynomial algorithms are presented. Computing or recognizing the minimal transversals of a hypergraph is a frequent problem in practice, which is pointed out by identifying important applications in database theory, Boolean switching theory, logic, and artificial intelligence (AI), particularly in model-based diagnosis.

456 citations

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TL;DR: Several new techniques, as well as generalizations of previous techniques, are introduced including: general folding, struction, tuples, and local amortized analysis in the polynomial-space algorithm for Vertex Cover.

407 citations