We present a simple algorithm for the maximum independent set problem in an n-vertex graph with degree bounded by 4, which runs in O∗(1.1446n) time and improves all previous algorithms for this problem. The algorithm is analyzed by using the “Measure and Conquer” method. We use some good reduction and branching rules with a new idea on setting weights to obtain the improved time bound without i...

Based on serological data from prevalence studies of rubella, mumps and hepatitis A, this paper describes a flexible local maximum likelihood method for the estimation of the rate at which susceptible individuals acquire infection at different ages. In contrast to parametric models used before in the literature, the local polynomial likelihood method allows one to model this age-dependent force...

Let G be a graph of order n and let q (G) be the largest eigenvalue of the signless Laplacian of G. Let Sn,k be the graph obtained by joining each vertex of a complete graph of order k to each vertex of an independent set of order n − k; and let S n,k be the graph obtained by adding an edge to Sn,k. It is shown that if k ≥ 2, n ≥ 400k2, and G is a graph of order n, with no cycle of length 2k + ...

In this note, we consider several polynomial optimization formulations of the maximum independent set problem and use Lasserre hierarchy with these different formulations. We demonstrate using computational experiments that choice formulation may have a significant impact on resulting bounds. also provide theoretical justifications for observed behavior.