A fast and simple randomized parallel algorithm for maximal matching
Information Processing Letters
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A random NC algorithm for depth first search
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
An improved parallel algorithm that computes the BFS numbering of a directed graph
Information Processing Letters
Approximating the tree and tour covers of a graph
Information Processing Letters
An optimal parallel algorithm for maximal matching
Information Processing Letters
A fast and efficient NC algorithm for maximal matching
Information Processing Letters
A threshold of ln n for approximating set cover (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Paradigms for fast parallel approximability
Paradigms for fast parallel approximability
Concurrent threads and optimal parallel minimum spanning trees algorithm
Journal of the ACM (JACM)
Matching is as easy as matrix inversion
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Polynomial Time Approximation Scheme for Connected Vertex Cover in Unit Disk Graph
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Connected Vertex Covers in Dense Graphs
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
PTAS for connected vertex cover in unit disk graphs
Theoretical Computer Science
Connected vertex covers in dense graphs
Theoretical Computer Science
| Hi-index | 0.89 |
The connected vertex cover problem is a variant of the vertex cover problem, in which a vertex cover is additional required to induce a connected subgraph in a given connected graph. The problem is known to be NP-hard and to be at least as hard to approximate as the vertex cover problem is. While several 2-approximation NC algorithms are known for vertex cover, whether unweighted or weighted, no parallel algorithm with guaranteed approximation is known for connected vertex cover. Moreover, converting the existing sequential 2-approximation algorithms for connected vertex cover to parallel ones results in RNC algorithms of rather high complexity at best.In this paper we present a 2-approximation NC (and RNC) algorithm for connected vertex cover (and tree cover). The NC algorithm runs in O(log2 n) time using O(Δ2 (m + n)/log n) processors on an EREW-PRAM, while the RNC algorithm runs in O(log n) expected time using O(m + n) processors on a CRCW-PRAM, when a given graph has n vertices and m edges with maximum vertex degree of Δ.