Pruning 2-Connected Graphs

Chekuri, Chandra; Korula, Nitish

doi:10.1007/s00453-010-9462-5

Cited by 6 publications

(10 citation statements)

References 29 publications

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“…This facilitates pruning many infrequent candidates, however, it is only useful when the input graph contains few and very frequent subgraphs [17]- [19], [27]. SUBDUE is a branch-andbound technique that mines subgraphs that can be used to compress the original graph.…”

Section: Related Workmentioning

confidence: 99%

BugLoc: Bug Localization in Multi Threaded Application via Graph Mining Approach

Adhiselvam¹,

Kirubakaran²,

Sukumar³

2016

IJCOA

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Detection of software bugs and its occurrences, repudiation and its root cause is a very difficult process in large multi threaded applications. It is a must for a software developer or software organization to identify bugs in their applications and to remove or overcome them. The application should be protected from malfunctioning. Many of the compilers and Integrated Development Environments are effectively identifying errors and bugs in applications while running or compiling, but they fail in detecting actual cause for the bugs in the running applications. The developer has to reframe or recreate the package with the new one without bugs. It is time consuming and effort is wasted in Software Development Life Cycle. There is a possibility to use graph mining techniques in detecting software bugs. But there are many problems in using graph mining techniques. Managing large graph data, processing nodes with links and processing subgraphs are the problems to be faced in graph mining approach. This paper presents a novel algorithm named BugLoc which is capable of detecting bugs from the multi threaded software application. The BugLoc uses object template to store graph data which reduces graph management complexities. It also uses substring analysis method in detecting frequent subgraphs. The BugLoc then analyses frequent subgraphs to detect exact location of the software bugs. The experimental results show that the algorithm is very efficient, accurate and scalable for large graph dataset.

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Section: Related Workmentioning

confidence: 99%

BugLoc: Bug Localization in Multi Threaded Application via Graph Mining Approach

Adhiselvam¹,

Kirubakaran²,

Sukumar³

2016

IJCOA

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“…The best known approximation ratio for the k-MST problem is 2 [11]. Chekuri and Korula [5] presented an O(log 2 n)-approximation for the problem of finding a minimum-cost 2-vertex connected subgraph with at least k terminals. In [1,6], the fault-tolerant version of the Buy-at-Bulk problem was studied, where two edge-disjoint paths are required to be included from every terminal to the root.…”

Section: Previous Work On Fault-tolerant Problemsmentioning

confidence: 99%

“…The density version of the residual problem seeks a subgraph that minimizes the ratio of its cost over the total profit of vertices that are 2-vertex-connected to the root. We then use the O(log n)-approximation algorithm by Chekuri and Korula [5] for this density problem, combined with the greedy method.…”

Section: A Summary Of Our Techniquesmentioning

confidence: 99%

“…The problem of finding a subgraph that minimizes the ratio of its cost over the total profit of vertices that are 2-vertex-connected to the root was studied by Chekuri and Korula [5], who gave an O(log n)-approximation for the problem. We use their algorithm to compute an O(log n)approximation for the density version of our problem, as follows.…”

Section: Algorithm For Vc-ftgs-2mentioning

confidence: 99%

“…Now we have all the ingredients to present the step Cover. We again use the O(log n)approximation algorithm of Chekuri and Korula [5] that was also used in problem of finding a subgraph that minimizes the ratio of its cost over the total profit of vertices that are 2-vertex-connected to the root. Recall that the subgraph induced by opt has cost at most opt and profit at least q /2 (since T contains twin pairs from at least q /2 uncovered groups).…”

Section: How To Implement Step Covermentioning

confidence: 99%

See 2 more Smart Citations

Approximating fault-tolerant group-Steiner problems

Khandekar¹,

Kortsarz

Nutov

2012

Theoretical Computer Science

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In this paper, we initiate the study of designing approximation algorithms for Fault-Tolerant Group-Steiner (FTGS) problems. The motivation is to protect the well-studied group-Steiner networks from edge or vertex failures. In Fault-Tolerant Group-Steiner problems, we are given a graph with edge-(or vertex-) costs, a root vertex, and a collection of subsets of vertices called groups. The objective is to find a minimum-cost subgraph that has two edge-(or vertex-) disjoint paths from each group to the root. We present approximation algorithms and hardness results for several variants of this basic problem, e.g., edge-costs vs. vertex-costs, edge-connectivity vs. vertex-connectivity, and 2-connecting a single vertex vs. two distinct vertices from each group. Main contributions of our paper include the introduction of general structural lemmas on connectivity and a charging scheme that may find more applications in the future. Our algorithmic results are supplemented by inapproximability results, which are tight in some cases.

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2-Node-Connectivity Network Design

Nutov

2021

Approximation and Online Algorithms

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We consider network design problems in which we are given a graph G = (V, E) with edge costs, and seek a min-cost/size 2-nodeconnected subgraph G = (V , E ) that satisfies a prescribed property.-In the Block-Tree Augmentation problem the goal is to augment a tree T by a min-size edge setWe break the natural ratio of 2 for this problem and show that it admits approximation ratio 1.91. This result extends to the related Crossing Family Augmentation problem. -In the 2-Connected Dominating Set problem G should dominate V . We give the first non-trivial approximation algorithm for this problem, with expected ratio Õ(log 4 |V |). -In the 2-Connected Quota Subgraph problem we are given node profits p(v) and G should have profit at least a given quota Q. We show expected ratio Õ(log 2 |V |), almost matching the best known ratio O(log 2 |V |). Our algorithms are very simple, and they combine three main ingredients: 1. A probabilistic spanning tree embedding with distortion Õ(log |V |) results in a variant of the Block-Tree Augmentation problem. 2. An approximation ratio preserving reduction of Block-Tree Augmentation variants to Node Weighted Steiner Tree problems. 3. Using existing approximation algorithms for variants of the Node Weighted Steiner Tree problem.

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Pruning 2-Connected Graphs

Cited by 6 publications

References 29 publications

BugLoc: Bug Localization in Multi Threaded Application via Graph Mining Approach

BugLoc: Bug Localization in Multi Threaded Application via Graph Mining Approach

Approximating fault-tolerant group-Steiner problems

2-Node-Connectivity Network Design

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