The combinatorics of pivoting for the maximum weight clique

Swaps, Diversification, and the Combinatorics of Pivoting for the Maximum Weight Clique

Lower bounds on the signed (total) $k$-domination number

Let $G$ be a graph with vertex set $V(G)$. For any integer $kge 1$, a signed (total) $k$-dominating functionis a function $f: V(G) rightarrow { -1, 1}$ satisfying $sum_{xin N[v]}f(x)ge k$ ($sum_{xin N(v)}f(x)ge k$)for every $vin V(G)$, where $N(v)$ is the neighborhood of $v$ and $N[v]=N(v)cup{v}$. The minimum of the values$sum_{vin V(G)}f(v)$, taken over all signed (total) $k$-dominating functi...

A Complementary Pivoting Approach to the Maximum Weight Clique Problem

Given an undirected graph with positive weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (i.e., a clique) having largest total weight. The problem is known to be NP -hard, even to approximate. Motivated by a recent quadratic programming formulation, which generalizes an earlier remarkable result of Motzkin and Straus, in this pa...

Complete pivoting strategy for the $IUL$ preconditioner obtained from Backward Factored APproximate INVerse process

‎In this paper‎, ‎we use a complete pivoting strategy to compute the IUL preconditioner obtained as the by-product of the Backward Factored APproximate INVerse process‎. ‎This pivoting is based on the complete pivoting strategy of the Backward IJK version of Gaussian Elimination process‎. ‎There is a parameter $alpha$ to control the complete pivoting process‎. ‎We have studied the effect of dif...

Hierarchical matching of panoramic images

When matching regions from “similar” images, one typically has the problem of missing counterparts due to local or even global variations of segmentation fineness. Matching segmentation hierarchies, however, not only increases the chances of finding counterparts, but also allows us to exploit the manifold constraints coming from the topological relations between the regions in a hierarchy. In t...