1

August 2018
Algorithmica: Volume 80 Issue 8, August 2018

**Publisher:** Springer-Verlag

Given an undirected simple graph G, a set of vertices is an r-clique transversal if it has at least one vertex from every r-clique. Such sets generalize vertex covers as a vertex cover is a 2-clique transversal. Perfect graphs are a well-studied class of graphs on which a minimum weight ...

**Keywords**:
Perfect graphs, r-Clique transversal, Linear programming, Odd cycle transversal, Approximation algorithms

2

February 2018
Theory of Computing Systems: Volume 62 Issue 2, February 2018

**Publisher:** Springer-Verlag New York, Inc.

Finding low-cost spanning subgraphs with given degree and connectivity requirements is a fundamental problem in the area of network design. We consider the problem of finding d-regular spanning subgraphs (or d-factors) of minimum weight with connectivity requirements. For the case of k-edge-connectedness, we present approximation algorithms that achieve constant approximation ...

**Keywords**:
Edge-connectivity, Graph factors, Approximation algorithms, Vertex-connectivity

3

September 2015
Discrete Applied Mathematics: Volume 192 Issue C, September 2015

**Publisher:** Elsevier Science Publishers B. V.

For a weighted outerplanar graph, the set of lex short cycles is known to be a minimum cycle basis (Liu and Lu, 2010). In our work, we show that the set of lex short cycles is a minimum cycle basis in weighted partial 2-trees (graphs of treewidth at most two), ...

**Keywords**:
Lex short cycles, Minimum cycle basis, Partial 2-trees

4

May 2015
CIAC 2015: Proceedings of the 9th International Conference on Algorithms and Complexity - Volume 9079

**Publisher:** Springer-Verlag New York, Inc.

Block Sorting is an NP-hard combinatorial optimization problem motivated by applications in Computational Biology and Optical Character Recognition OCR. It has been approximated in P time within a factor of 2 using two different techniques and the complexity of better approximations has been open for close to a decade now. ...

5

April 2015
Theoretical Computer Science: Volume 575 Issue C, April 2015

**Publisher:** Elsevier Science Publishers Ltd.

A spanning tree of an unweighted graph is a minimum average stretch spanning tree if it minimizes the ratio of sum of the distances in the tree between the end vertices of the graph edges and the number of graph edges. For a polygonal 2-tree on n vertices, we present ...

**Keywords**:
Minimum fundamental cycle bases, Minimum average stretch spanning trees, Polygonal 2-trees

6

March 2015
Algorithmica: Volume 71 Issue 3, March 2015

**Publisher:** Springer-Verlag New York, Inc.

A binary matrix $$M$$M has the Consecutive Ones Property (COP) if there exists a permutation of columns that arranges the ones consecutively in all the rows. We consider the parameterized complexity of $$d$$d-COS-R (Consecutive Ones Submatrix by Row deletions) problem [9]: Given a matrix $$M$$M and a positive integer $$d$$d, ...

**Keywords**:
Consecutive ones submatrix, Parameterized complexity, Consecutive ones property

7

October 2014
ACM Transactions on Algorithms (TALG): Volume 11 Issue 2, November 2014

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 18

Downloads (6 Weeks): 8, Downloads (12 Months): 39, Downloads (Overall): 313

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We investigate the parameterized complexity of Vertex Cover parameterized by the difference between the size of the optimal solution and the value of the linear programming (LP) relaxation of the problem. By carefully analyzing the change in the LP value in the branching steps, we argue that combining previously known ...

**Keywords**:
vertex cover, Parameterized algorithms

8

November 2013
Information Processing Letters: Volume 113 Issue 22-24, November, 2013

**Publisher:** Elsevier North-Holland, Inc.

Given a graph G and an odd cycle transversal T, we describe an elegant O^@?(2^|^T^|) algorithm for determining whether G has a smaller odd cycle transversal that is disjoint from T. We believe that our algorithm, based on a reduction to Vertex Cover, is conceptually simpler than the known algorithms ...

**Keywords**:
Graph algorithms, Above guarantee vertex cover, Disjoint compression, Odd cycle transversal, Parameterized complexity

9

September 2013
Theoretical Computer Science: Volume 506, September, 2013

**Publisher:** Elsevier Science Publishers Ltd.

The problem of finding a satisfying assignment that minimizes the number of variables that are set to 1 is NP-complete even for a satisfiable 2-SAT formula. We call this problem min ones 2-sat. It generalizes the well-studied problem of finding the smallest vertex cover of a graph, which can be ...

**Keywords**:
Parameterized complexity, Linear programming relaxation, Vertex cover, Min ones 2 -sat

10

February 2012
WALCOM'12: Proceedings of the 6th international conference on Algorithms and computation

**Publisher:** Springer-Verlag

Vertex cover and odd cycle transversal are minimum cardinality sets of vertices of a graph whose deletion makes the resultant graph 1-colorable and 2-colorable, respectively. As a natural generalization of these well-studied problems, we consider the Graph r-Partization problem of finding a minimum cardinality set of vertices whose deletion makes ...

**Keywords**:
generalized above guarantee vertex cover, odd cycle transversal, r-partization, parameterized complexity, perfect graphs, split graphs

11

August 2011
Theoretical Computer Science: Volume 412 Issue 35, August, 2011

**Publisher:** Elsevier Science Publishers Ltd.

Problems like the directed feedback vertex set problem have much better algorithms in tournaments when compared to general graphs. This motivates us to study a natural generalization of tournaments, named c-tournaments, and see if the structural properties of these graphs are helpful in obtaining similar algorithms. c-tournaments are simple digraphs ...

**Keywords**:
Feedback vertex set, Dominating set, Tournaments, Parameterized complexity, Graph modification

12

February 2011
WALCOM'11: Proceedings of the 5th international conference on WALCOM: algorithms and computation

**Publisher:** Springer-Verlag

The longest path problem is the problem of finding a simple path of maximum length in a graph. Polynomial solutions for this problem are known only for special classes of graphs, while it is NP-hard on general graphs. In this paper we are proposing a O ( n 6 ) ...

**Keywords**:
dynamic programming, complexity, longest path problem, biconvex graphs, polynomial algorithm

13

February 2011
Information Processing Letters: Volume 111 Issue 6, February, 2011

**Publisher:** Elsevier North-Holland, Inc.

We show that the 3-colorability problem can be solved in O(1.296^n) time on any n-vertex graph with minimum degree at least 15. This algorithm is obtained by constructing a dominating set of the graph greedily, enumerating all possible 3-colorings of the dominating set, and then solving the resulting 2-list coloring ...

**Keywords**:
Exact algorithms, 3-coloring, Exponential time algorithms, Graph algorithms, Graph coloring, Design of algorithms

14

January 2011
CATS 2011: Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119

**Publisher:** Australian Computer Society, Inc.

**Bibliometrics**:

Citation Count: 0

Downloads (6 Weeks): 0, Downloads (12 Months): 5, Downloads (Overall): 24

Full text available:

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For a connected graph, a subset of vertices of least size whose deletion increases the number of connected components is the vertex connectivity of the graph. A graph with vertex connectivity k is said to be k-vertex connected . Given a k -vertex connected graph G , vertex connectivity augmentation ...

**Keywords**:
k-trees, connectivity augmentation, 1-connected graphs, 2-connected graphs, connectivity

15

January 2011
CATS '11: Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119

**Publisher:** Australian Computer Society, Inc.

**Bibliometrics**:

Citation Count: 0

Downloads (6 Weeks): 1, Downloads (12 Months): 3, Downloads (Overall): 13

Full text available:

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For a connected graph, a subset of vertices of least size whose deletion increases the number of connected components is the vertex connectivity of the graph. A graph with vertex connectivity k is said to be k-vertex connected . Given a k -vertex connected graph G , vertex connectivity augmentation ...

**Keywords**:
k-trees, connectivity augmentation, 1-connected graphs, 2-connected graphs, connectivity

16

August 2010
MFCS'10: Proceedings of the 35th international conference on Mathematical foundations of computer science

**Publisher:** Springer-Verlag

The problem of finding a satisfying assignment for a 2-SAT formula that minimizes the number of variables that are set to 1 (MIN ONES 2-SAT) is NP-complete. It generalizes the well-studied problem of finding the smallest vertex cover of a graph, which can be modeled using a 2-SAT formula with ...

17

November 2009
Graphs and Combinatorics: Volume 25 Issue 4, November 2009

**Publisher:** Springer-Verlag

Contraction of an edge e merges its end points into a new single vertex, and each neighbor of one of the end points of e is a neighbor of the new vertex. An edge in a k -connected graph is contractible if its contraction does not result in a graph ...

**Keywords**:
Connectivity, Contraction, Contractible edges, Partial *k*-trees

18

November 2009
Discrete Applied Mathematics: Volume 157 Issue 18, November, 2009

**Publisher:** Elsevier Science Publishers B. V.

We consider the following constraint satisfaction problem: Given a set F of subsets of a finite set S of cardinality n, and an assignment of intervals of the discrete set {1,...,n} to each of the subsets, does there exist a bijection f:S->{1,...,n} such that for each element of F, its ...

**Keywords**:
Interval graphs, 0-1 matrices, Consecutive ones property

19

September 2007
Information Processing Letters: Volume 104 Issue 1, September, 2007

**Publisher:** Elsevier North-Holland, Inc.

The intention of this note is to motivate the researchers to study Hadwiger's conjecture for circular arc graphs. Let @h(G) denote the largest clique minor of a graph G, and let @g(G) denote its chromatic number. Hadwiger's conjecture states that @h(G)>

[email protected](G) and is one of the most important and difficult ...

**Keywords**:
Hadwiger's conjecture, Minor, Graph coloring, Circular arc, Combinatorial problems

20

October 2006
Theoretical Computer Science - Computing and combinatorics: Volume 363 Issue 1, 25 October 2006

**Publisher:** Elsevier Science Publishers Ltd.

We present an improved online algorithm for coloring interval graphs with bandwidth. This problem has recently been studied by Adamy and Erlebach and a 195-competitive online strategy has been presented. We improve this by presenting a 10-competitive strategy. To achieve this result, we use variants of an optimal online coloring ...

**Keywords**:
online algorithms, graph coloring, interval graphs