Murali Krishna Enduri

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.

Dynamics of dengue disease with human and vector mobility

Dengue is a vector borne disease transmitted to humans by Aedes aegypti mosquitoes carrying virus of different serotypes. Dengue exhibits complex spatial and temporal dynamics, influenced by various biological, human and environmental factors. In this work, we study the dengue spread for a single serotype (DENV-1) including statistical models of human mobility with exponential step length distribution, by using reaction-diffusion equations and Stochastic Cellular Automata (SCA) approach. We analyze the spatial and temporal spreading of the disease using parameters from field studies. We choose mosquito density data from Ahmedabad city as a proxy for climate data in our SCA model. We find an interesting result that although human mobility makes the infection spread faster, there is an apparent early suppression of the epidemic compared to immobile humans. The disease extinction time is lesser when human mobility is included.

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 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

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

t=0

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

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

Dynamics of Dengue with human and vector mobility

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

Estimation of reproduction number and non stationary spectral analysis of Dengue epidemic

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