Both learning and inference tasks on Bayesian networks are NP-hard in general. Bounded tree-width Bayesian networks have recently received a lot of attention as a way to circumvent this complexity issue; however, while inference on bounded tree-width networks is tractable, the learning problem remains NP-hard even for tree-width 2. In this paper, we propose bounded vertex cover number Bayesian ...

Exact Inference problem in Belief Networks has been well studied in the literature and has various application areas. In this thesis, a polynomial time transformation from Vertex Cover Problem to Exact Inference problem in Belief Networks is proposed and proved. To understand and see the development of the transformation, some well-known transformations about Vertex Cover Problem and Exact Infe...

We use mobile guards on the vertices of a graph to defend it against an infinite sequence of attacks on its edges. A guard on an incident vertex moves across the attacked edge to defend it; other guards may also move to neighboring vertices. We prove upper and lower bounds on the minimum number of guards needed for this eternal vertex cover problem and characterize the graphs for which the uppe...

Assuming the AND-distillation conjecture, the Pathwidth problem of determining whether a given graphG has pathwidth at most k admits no polynomial kernelization with respect to k. The present work studies the existence of polynomial kernels for Pathwidth with respect to other, structural, parameters. Our main result is that, unless NP ⊆ coNP/poly, Pathwidth admits no polynomial kernelization ev...

This paper examines the complexity of several geometric problems due to un bounded dimension The problems considered are i minimum cover of points by unit cubes ii minimum cover of points by unit balls and iii minimum number of lines to hit a set of balls Each of these problems is proven not to have a poly nomial approximation scheme unless P NP Speci c lower bounds on the error ratios attainab...

Capacitated Domination generalizes the classic Dominating Set problem by specifying for each vertex a required demand and an available capacity for covering demand in its closed neighborhood. The objective is to find a minimum-sized set of vertices that can cover all of the graph’s demand without exceeding any of the capacities. In this paper we look specifically at domination with hard-capacit...

We deene a class of integer programs with constraints that involve up to three variables each. A generic constraint in such integer program is of the form ax + by z + c, where the variable z appears only in that constraint. For such binary integer programs it is possible to derive half integral superoptimal solutions in polynomial time. The scheme is also applicable with few modiications to non...

Recently, there has been increasing interest and progress in improvising the approximation algorithm for well-known NP-Complete problems, particularly the approximation algorithm for the Vertex-Cover problem. Here we have proposed a polynomial time efficient algorithm for vertex-cover problem for more approximate to the optimal solution, which lead to the worst time complexity Θ(V ) and space c...

A rigorous runtime analysis of evolutionary multi-objective optimization for the classical vertex cover problem in the context of parameterized complexity analysis has been presented by Kratsch and Neumann [11]. In this paper, we extend the analysis to the weighted vertex cover problem and provide a fixed parameter evolutionary algorithm with respect to OPT , where OPT is the cost of the the op...

Article history: Received 22 February 2016 Available online 23 April 2017 Given a directed graph D = (V, E) with n vertices and a permutation π : V → V on its vertices, we say that π has a drop at a vertex u ∈ V is (u, π(u)) is an edge of D. Letting 〈 D k 〉 denote the number of permutations on V with precisely k drops, we can define the binomial drop polynomial BD(x) = ∑ k 〈 D k 〉( x+k n ) . In...