scholarly journals Combinatorial approximation of maximum k-vertex cover in bipartite graphs within ratio 0.7

2018 ◽  
Vol 52 (1) ◽  
pp. 305-314 ◽  
Author(s):  
Vangelis Th. Paschos
Keyword(s):  
Greedy Algorithm ◽  
Vertex Cover ◽  
Bipartite Graphs ◽  
Approximation Ratio ◽  
Combinatorial Algorithm

We propose and analyze a simple purely combinatorial algorithm for max k-vertex cover in bipartite graphs, achieving approximation ratio 0.7. The only combinatorial algorithm currently known until now for this problem is the natural greedy algorithm, that achieves ratio (e − 1)/e = 0.632.

scholarly journals Deterministic Dynamic Matching in O(1) Update Time

Algorithmica ◽  
2019 ◽  
Vol 82 (4) ◽  
pp. 1057-1080 ◽  
Author(s):  
Sayan Bhattacharya ◽  
Deeparnab Chakrabarty ◽  
Monika Henzinger
Keyword(s):  
Computer Science ◽  
Vertex Cover ◽  
Approximation Ratio ◽  
Approximate Algorithm ◽  
Maximum Matching ◽  
Matching Problem ◽  
Dynamic Algorithm ◽  
Dynamic Matching ◽  
Deterministic Dynamic ◽  
Oblivious Adversary

Abstract We consider the problems of maintaining an approximate maximum matching and an approximate minimum vertex cover in a dynamic graph undergoing a sequence of edge insertions/deletions. Starting with the seminal work of Onak and Rubinfeld (in: Proceedings of the ACM symposium on theory of computing (STOC), 2010), this problem has received significant attention in recent years. Very recently, extending the framework of Baswana et al. (in: Proceedings of the IEEE symposium on foundations of computer science (FOCS), 2011) , Solomon (in: Proceedings of the IEEE symposium on foundations of computer science (FOCS), 2016) gave a randomized dynamic algorithm for this problem that has an approximation ratio of 2 and an amortized update time of O(1) with high probability. This algorithm requires the assumption of an oblivious adversary, meaning that the future sequence of edge insertions/deletions in the graph cannot depend in any way on the algorithm’s past output. A natural way to remove the assumption on oblivious adversary is to give a deterministic dynamic algorithm for the same problem in O(1) update time. In this paper, we resolve this question. We present a new deterministic fully dynamic algorithm that maintains a O(1)-approximate minimum vertex cover and maximum fractional matching, with an amortized update time of O(1). Previously, the best deterministic algorithm for this problem was due to Bhattacharya et al. (in: Proceedings of the ACM-SIAM symposium on discrete algorithms (SODA), 2015); it had an approximation ratio of $$(2+\varepsilon )$$(2+ε) and an amortized update time of $$O(\log n/\varepsilon ^2)$$O(logn/ε2). Our result can be generalized to give a fully dynamic $$O(f^3)$$O(f3)-approximate algorithm with $$O(f^2)$$O(f2) amortized update time for the hypergraph vertex cover and fractional hypergraph matching problem, where every hyperedge has at most f vertices.

Koszulness of Vertex Cover Algebras of Bipartite Graphs

2011 ◽  
Vol 39 (7) ◽  
pp. 2249-2259 ◽  
Author(s):  
Giancarlo Rinaldo
Keyword(s):  
Vertex Cover ◽  
Bipartite Graphs

Partial Vertex Cover and Budgeted Maximum Coverage in Bipartite Graphs

2017 ◽  
Vol 31 (3) ◽  
pp. 2172-2184 ◽  
Author(s):  
Bugra Caskurlu ◽  
Vahan Mkrtchyan ◽  
Ojas Parekh ◽  
K. Subramani
Keyword(s):  
Vertex Cover ◽  
Bipartite Graphs ◽  
Maximum Coverage

scholarly journals Purely combinatorial approximation algorithms for maximum k-vertex cover in bipartite graphs

2018 ◽  
Vol 27 ◽  
pp. 26-56
Author(s):  
Édouard Bonnet ◽  
Bruno Escoffier ◽  
Vangelis Th. Paschos ◽  
Georgios Stamoulis
Keyword(s):  
Approximation Algorithms ◽  
Vertex Cover ◽  
Bipartite Graphs
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