On the relationship between the biconnectivity augmentation and travelling salesman problems
Greg N. Frederickson,Joseph JaJa +1 more
TLDR
An approximation algorithm similar to Christofides' algorithm for the traveling salesman problem is shown to possess the same worst-case bound of 3 2 when applied to the biconnectivity augmentation problem.About:
This article is published in Theoretical Computer Science.The article was published on 1982-08-01 and is currently open access. It has received 109 citations till now. The article focuses on the topics: Bottleneck traveling salesman problem & Christofides algorithm.read more
Citations
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BookDOI
Complexity and Approximation
Giorgio Ausiello,Alberto Marchetti-Spaccamela,Pierluigi Crescenzi,Giorgio Gambosi,Marco Protasi,Viggo Kann +5 more
Journal ArticleDOI
The traveling salesman problem on a graph and some related integer polyhedra
TL;DR: Some facet inducing inequalities of the convex hull of the solutions to the Graphical Traveling Salesman Problem are given and the so-called comb inequalities of Grötschel and Padberg are generalized.
Journal ArticleDOI
Biconnectivity approximations and graph carvings
Samir Khuller,Uzi Vishkin +1 more
TL;DR: This work considers the problem of finding a better approximation to the smallest 2-connected subgraph, by an efficient algorithm, and shows that approximating the optimal solution to within an additive constant is NP-hard as well.
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Design of Survivable Networks: A survey
Hervé Kerivin,A. Ridha Mahjoub +1 more
TL;DR: This paper attempts to survey some of the models and the optimization methods used for solving survivable network models, and particularly cutting plane based algorithms.
Proceedings ArticleDOI
Biconnectivity approximations and graph carvings
Samir Khuller,Uzi Vishkin +1 more
TL;DR: This work considers the problem of finding an approximation to the smallest 2-connected subgraph, by an efficient algorithm, and shows that an approximation factor of 2 is possible in polynomial time for finding a k-edge connected spanning subgraph.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Reducibility Among Combinatorial Problems.
TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
Proceedings ArticleDOI
The complexity of theorem-proving procedures
TL;DR: It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology.