We formulate clustering aggregation as a special instance of Maximum-Weight Independent Set (MWIS) problem. For a given dataset, an attributed graph is constructed from the union of the input clusterings generated by different underlying clustering algorithms with different parameters. The vertices, which represent the distinct clusters, are weighted by an internal index measuring both cohesion...

Given an ensemble of distinct, low-level segmentations of an image, our goal is to identify visually “meaningful” segments in the ensemble. Knowledge about any specific objects and surfaces present in the image is not available. The selection of image regions occupied by objects is formalized as the maximum-weight independent set (MWIS) problem. MWIS is the heaviest subset of mutually non-adjac...

We show that the maximum independent set problem (MIS) on an n-vertex graph can be solved in 1.1996n time and polynomial space, which even is faster than Robson’s 1.2109n-time exponential-space algorithm published in 1986. We also obtain improved algorithms for MIS in graphs with maximum degree 6 and 7, which run in time of 1.1893n and 1.1970n, respectively. Our algorithms are obtained by using...

In this paper, we consider two geometric optimization problems: Rectangle Coloring problem (RCOL) and Maximum Independent Set of Rectangles (MISR). In RCOL, we are given a collection of n rectangles in the plane where overlapping rectangles need to be colored differently, and the goal is to find a coloring that minimizes the number of colors. Let q be the maximum clique size of the instance, i....

We present a simple distributed ∆-approximation algorithm for maximum weight independent set (MaxIS) in the CONGEST model which completes in O(MIS(G) · logW ) rounds, where ∆ is the maximum degree, MIS(G) is the number of rounds needed to compute a maximal independent set (MIS) on G, and W is the maximum weight of a node. Plugging in the best known algorithm for MIS gives a randomized solution ...

A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space. Given an input graph G without cycles of length 4, 5, and 6, we cha...