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A New Bound for the 2-Edge Connected Subgraph Problem [chapter]

Robert Carr, R. Ravi
1998 Lecture Notes in Computer Science
A lower bound for the minimum cost 2-edge connected subgraph is obtained by solving the fractional linear programming relaxation for this problem, which coincides with the subtour relaxation of the traveling  ...  Given a complete graph with non-negative costs on the edges, the 2-Edge Connected Subgraph Problem consists in nding the minimum cost spanning 2-edge connected subgraph (where multiedges are allowed in  ...  Introduction The 2-Edge Connected Subgraph Problem is a fundamental problem in Survivable Network Design.  ...

New Algorithms for Edge Induced König-Egerváry Subgraph Based on Gallai-Edmonds Decomposition

Qilong Feng, Guanlan Tan, Senmin Zhu, Bin Fu, Jianxin Wang, Michael Wagner
2018 International Symposium on Algorithms and Computation
Using 2|E|/3 as a lower bound, we define the Edge Induced König Subgraph above lower bound problem, and give a kernel of at most 30k edges for the problem.  ...  We obtain a new structural property of König-Egerváry subgraph: every graph G = (V, E) has an edge induced König-Egerváry subgraph with at least 2|E|/3 edges.  ...  By using 2m/3 as a lower bound, we propose a variant of the Edge Induced König Subgraph problem, called Edge Induced König Subgraph above lower bound problem, and give a kernel of at most 30k edges for  ...

Minimum survivable graphs with bounded distance increase

Selma Djelloul, Mekkia Kouider
2003 Discrete Mathematics & Theoretical Computer Science
We give upper and lower bounds on the minimum number of edges of a k-self-repairing graph for prescribed k and n, where n is the order of the graph.  ...  We prove that the problem of finding, in a k-self-repairing graph, a spanning k-self-repairing subgraph of minimum size is NP-Hard.  ...  When the property dealing with is 2-connectivity, the problem is known as the 2-connected Steiner subgraph problem.  ...

Page 4866 of Mathematical Reviews Vol. , Issue 89I [page]

1989 Mathematical Reviews
The authors present new lower and upper bounds for ap (the node covering number), fo (the node independence number), a, (the edge covering number), (the edge independence number) and the number of edges  ...  89i:05155 tation problem is stated as follows: how many edges are needed for augmenting G to make it a K-edge connected graph?  ...

A Constant Factor Approximation for Minimum λ-Edge-Connected k-Subgraph with Metric Costs

2011 SIAM Journal on Discrete Mathematics
The only previously known results on this problem [12, 4] show that the (k, 2)-subgraph problem has an O(log 2 n)-approximation (even for 2-node-connectivity) and that the (k, λ)-subgraph problem in general  ...  For larger values of λ, i.e. finding minimum cost λ-edge-connected spanning subgraphs, the problem is APX-hard.  ...  These lower bounds were used earlier in [6] for the problem of minimum cost subset k-node-connected subgraph.  ...

Survivable Network Design with Degree or Order Constraints

Lap Chi Lau, Joseph (Seffi) Naor, Mohammad R. Salavatipour, Mohit Singh
2009 SIAM journal on computing (Print)
Jain [22] gave a 2-approximation algorithm for the edge-  ...  We give a polylogarithmic approximation for the (k, 2)-subgraph problem.  ...  We also thank Chandra Chekuri and Nitish Korula for pointing out an error in the proof of Theorem 5.1 in the extended abstract version of this paper.  ...

On the Advice Complexity of Online Edge- and Node-Deletion Problems [chapter]

Peter Rossmanith
2018 Lecture Notes in Computer Science
For node-deletion problems we characterize the advice complexity exactly for all cases and for edge-deletion problems at least for the case of a single forbidden induced subgraph.  ...  We consider a model of online graph modification problems where the input graph is read piecewise in an adversarial order and the algorithm has to modify the graph by deleting vertices or edges in order  ...  I would like to thank Walter Unger, Janosch Fuchs, Ling-Ju Hung, and Li-Hsuan Chen for stimulating discussions about the proof of Lemma 3 and an anonymous referee for insightful feedback.  ...

Survivable network design with degree or order constraints

Lap Chi Lau, Joseph (Seffi) Naor, Mohammad R. Salavatipour, Mohit Singh
2007 Proceedings of the thirty-ninth annual ACM symposium on Theory of computing - STOC '07
Jain [22] gave a 2-approximation algorithm for the edge-  ...  We give a polylogarithmic approximation for the (k, 2)-subgraph problem.  ...  We also thank Chandra Chekuri and Nitish Korula for pointing out an error in the proof of Theorem 5.1 in the extended abstract version of this paper.  ...

Parallel Planar Subgraph Isomorphism and Vertex Connectivity [article]

Lukas Gianinazzi, Torsten Hoefler
2020 arXiv   pre-print
By using a connection to certain separating cycles, our subgraph isomorphism algorithm can decide the vertex connectivity of a planar graph (with high probability) in asymptotically near-linear work and  ...  We present the first parallel fixed-parameter algorithm for subgraph isomorphism in planar graphs, bounded-genus graphs, and, more generally, all minor-closed graphs of locally bounded treewidth.  ...  As for the decision problem, we observe that only k edges introduce a new vertex to the mapping.  ...

Distributed verification and hardness of distributed approximation

Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, Roger Wattenhofer
2011 Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11
We study the verification problem in distributed networks, stated as follows. Let H be a subgraph of a network G where each vertex of G knows which edges incident on it are in H.  ...  as connectivity, spanning connected subgraph, and s − t cut verification.  ...  In red: the new edges (u p i , u p i+1 ), in green, the new paths/nodes connecting u l i to u p i·d p−l +1 . (a).  ...

Distributed Verification and Hardness of Distributed Approximation

Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, Roger Wattenhofer
2012 SIAM journal on computing (Print)
We study the verification problem in distributed networks, stated as follows. Let H be a subgraph of a network G where each vertex of G knows which edges incident on it are in H.  ...  as connectivity, spanning connected subgraph, and s − t cut verification.  ...  In red: the new edges (u p i , u p i+1 ), in green, the new paths/nodes connecting u l i to u p i·d p−l +1 . (a).  ...

Approximation Schemes for Minimum 2-Connected Spanning Subgraphs in Weighted Planar Graphs [chapter]

André Berger, Artur Czumaj, Michelangelo Grigni, Hairong Zhao
2005 Lecture Notes in Computer Science
We first give a PTAS for the problem of finding minimum-weight 2-edge-connected spanning subgraphs where duplicate edges are allowed.  ...  Then we present a new greedy spanner construction for edge-weighted planar graphs, which augments any connected subgraph A of a weighted planar graph G to a (1 + ε)-spanner of G with total weight bounded  ...  Let ε > 0, and let G be a weighted planar graph with n vertices. There is an algorithm running in time n O(log n·log(1/ε)/ε) that outputs a {1,2}-VCSS H of G such that w(H) ≤ (1 + ε) · OPT.  ...

Subexponential parameterized algorithms for degree-constrained subgraph problems on planar graphs

Ignasi Sau, Dimitrios M. Thilikos
2010 Journal of Discrete Algorithms
We present subexponential parameterized algorithms on planar graphs for a family of problems of the following shape: given a graph, find a connected (induced) subgraph with bounded maximum degree and with  ...  These techniques can be applied to a more general family of problems that deal with finding connected subgraphs under certain degree constraints.  ...  Acknowledgement We would like to thank the anonymous referees for helpful comments that improved the presentation of the article.  ...

On locating cubic subgraphs in bounded-degree connected bipartite graphs

Iain A Stewart
1997 Discrete Mathematics
We show that the problem of deciding whether a connected bipartite graph of degree at most 4 has a cubic subgraph is NP-complete.  ...  Consequently, the problem of deciding whether a given graph has a cubic subgraph remains NP-complete when restricted to the class of planar graphs (of degree at most 7) and also to the class of (connected  ...  The problem of deciding whether a given connected bipartite graph of degree at most 4 has a cubic subgraph is complete for NP via projection translations.  ...

Local Access to Sparse Connected Subgraphs Via Edge Sampling [article]

Rogers Epstein
2020 arXiv   pre-print
We contribute an approach to the problem of locally computing sparse connected subgraphs of dense graphs.  ...  This is the first algorithm to work on general graphs and allow for a tradeoff between its probe complexity and the number of edges in the resulting subgraph.  ...  For graphs with degree upper bound ∆, one can construct a subgraph with O(n 1+1/k ) edges using O(∆ 4 n 2/3 ) probes per edge. 2.  ...
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