Geevarghese Philip

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We study the recently introduced Connected Feedback Vertex Set (CFVS) problem from the view-point of parameterized algorithms. CFVS is the connected variant of the classical Feedback Vertex Set problem and is defined as follows: given a graph G = (V, E) and an integer k, decide whether there exists F ⊆ V , |F | ≤ k, such that G[V \ F ] is a forest and G[F ](More)
We show that the k-Dominating Set problem is fixed parameter tractable (FPT) and has a polynomial kernel for any class of graphs that exclude Ki,j as a subgraph, for any fixed i, j ≥ 1. This strictly includes every class of graphs for which this problem has been previously shown to have FPT algorithms and/or polynomial kernels. In particular, our result(More)
According to the classical Erdős–Pósa theorem, given a positive integer k, every graph G either contains k vertex disjoint cycles or a set of at most O(k log k) vertices that hits all its cycles. Robertson and Seymour [Graph minors. V. Excluding a planar graph. J. Comb. Theory Series B, 41:92–114, 1986] generalized this result in the best possible way. More(More)
We study a general class of problems called F -Deletion problems. In an F -Deletion problem, we are asked whether a subset of at most k vertices can be deleted from a graph G such that the resulting graph does not contain as a minor any graph from the family F of forbidden minors. We obtain a number of algorithmic results on the F -Deletion problem when F(More)
The input to the NP-hard <scp>point line cover</scp> problem (PLC) consists of a set <i>P</i> of <i>n</i> points on the plane and a positive integer <i>k</i>; the question is whether there exists a set of at most <i>k</i> lines that pass through all points in <i>P</i>. By straightforward reduction rules, one can efficiently reduce any input to one with at(More)
Homogeneous team formation is the task of grouping individuals into teams, each of which consists of members who fulfill the same set of prespecified properties. In this theoretical work, we propose, motivate, and analyze a combinatorial model where, given a matrix over a finite alphabet whose rows correspond to individuals and columns correspond to(More)
The standard parameterization of the VERTEX COVER problem (Given an undirected graph G and k ∈ N as input, does G have a vertex cover of size at most k?) has the solution size k as the parameter. The following more challenging parameterization of VERTEX COVER stems from the observation that the size MM of a maximum matching of G lower-bounds the size of any(More)
In this paper we obtain parameterized subexponential-time algorithms for p-Kemeny Aggregation (p-KAGG) — a problem in social choice theory — and for p-One-Sided Crossing Minimization (p-OSCM) – a problem in graph drawing (see the introduction for definitions). These algorithms run in time O∗(2O( √ k log ), where k is the parameter, and significantly improve(More)
The Colorful Motif problem asks if, given a vertex-colored graph G, there exists a subset S of vertices of G such that the graph induced by G on S is connected and contains every color in the graph exactly once. The problem is motivated by applications in computational biology and is also well-studied from the theoretical point of view. In particular, it is(More)
The dominating set problem has been extensively studied in the realm of parameterized complexity. It is one of the most common sources of reductions while proving the parameterized intractability of problems. In this paper, we look at dominating set and its generalization r-dominating set on graphs of bounded diameter in the realm of parameterized(More)