I. Vinod Reddy

Logspace and FPT Algorithms for Graph Isomorphism for Subclasses of Bounded Tree-Width Graphs

We give a deterministic logspace algorithm for the graph isomorphism problem for graphs with bounded tree-depth. We also show that the graph isomorphism problem is fixed parameter tractable for a related parameterized graph class where the graph parameter is the length of the longest cycle.

On the Parallel Parameterized Complexity of the Graph Isomorphism Problem

In this paper, we study the parallel and the space complexity of the graph isomorphism problem (\(\mathsf {GI}\)) for several parameterizations.

On Structural Parameterizations of Happy Coloring, Empire Coloring and Boxicity

Distance parameters are extensively used to design efficient algorithms for many hard graph problems. They measure how far a graph is from belonging to some class of graphs. If a problem is tractable on a class of graphs Open image in new window , then distances to Open image in new window provide interesting parameterizations to that problem. For example, the parameter vertex cover measures the closeness of a graph to an edgeless graph. Many hard problems are tractable on graphs of small vertex cover. However, the parameter vertex cover is very restrictive in the sense that the class of graphs with bounded vertex cover is small. This significantly limits its usefulness in practical applications. In general, it is desirable to find tractable results for parameters such that the class of graphs with the parameter bounded should be as large as possible. In this spirit, we consider the parameter distance to threshold graphs, which are graphs that are both split graphs and cographs. It is a natural choice of an intermediate parameter between vertex cover and clique-width. In this paper, we give parameterized algorithms for some hard graph problems parameterized by the distance to threshold graphs. We show that Happy Coloring and Empire Coloring problems are fixed-parameter tractable when parameterized by the distance to threshold graphs. We also present an approximation algorithm to compute the Boxicity of a graph parameterized by the distance to threshold graphs.

Parameterized algorithms for conflict-free colorings of graphs

In this paper, we study the conflict-free coloring of graphs induced by neighborhoods. A coloring of a graph is conflict-free if every vertex has a uniquely colored vertex in its neighborhood. The conflict-free coloring problem is to color the vertices of a graph using the minimum number of colors such that the coloring is conflict-free. We consider both closed neighborhoods, where the neighborhood of a vertex includes itself, and open neighborhoods, where a vertex does not included in its neighborhood. We study the parameterized complexity of conflict-free closed neighborhood coloring and conflict-free open neighborhood coloring problems. We show that both problems are fixed-parameter tractable (FPT) when parameterized by the cluster vertex deletion number of the input graph. This generalizes the result of Gargano et al.(2015) that conflict-free coloring is fixed-parameter tractable parameterized by the vertex cover number. Also, we show that both problems admit an additive constant approximation algorithm when parameterized by the distance to threshold graphs. We also study the complexity of the problem on special graph classes. We show that both problems can be solved in polynomial time on cographs. For split graphs, we give a polynomial time algorithm for closed neighborhood conflict-free coloring problem, whereas we show that open neighborhood conflict-free coloring is NP-complete. We show that interval graphs can be conflict-free colored using at most four colors.

On NC algorithms for problems on bounded rank-width graphs

Abstract In this paper, we show that for a fixed k, there is an NC algorithm that separates the graphs of rank-width at most k from those with rank-width at least 3 k + 1 .

On Structural Parameterizations of Firefighting

The Firefighting problem is defined as follows. At time

The Parameterized Complexity of Happy Colorings

t=0

Polynomial-Time Algorithm for Isomorphism of Graphs with Clique-Width at Most Three

, a fire breaks out at a vertex of a graph. At each time step

Does Diversity of Papers Affect Their Citations? Evidence from American Physical Society Journals

t \geq 0

Polynomial-time algorithm for isomorphism of graphs with clique-width at most three

, a firefighter permanently defends (protects) an unburned vertex, and the fire then spread to all undefended neighbors from the vertices on fire. This process stops when the fire cannot spread anymore. The goal is to find a sequence of vertices for the firefighter that maximizes the number of saved (non burned) vertices. The Firefighting problem turns out to be NP-hard even when restricted to bipartite graphs or trees of maximum degree three. We study the parameterized complexity of the Firefighting problem for various structural parameterizations. All our parameters measure the distance to a graph class (in terms of vertex deletion) on which the firefighting problem admits a polynomial time algorithm. Specifically, for a graph class