A Note on Approximating the 2-Catalog Segmentation Problem

We present a $.73$-approximation algorithm for a disjoint $2$-Catalog Segmentation and $.63$-approximation algorithm for the joint version of the problem. Previously best known results are $.65$ and $.56$, respectively. The results are based on semidefinite programming and a subtle rounding method. Citation Working Paper, Department of Management Sciences, Henry, B. Tippie College of Business, The … Read more

A New Trust Region Technique for the Maximum Weight Clique Problem

A new simple generalization of the Motzkin-Straus theorem for the maximum weight clique problem is formulated and directly proved. Within this framework a new trust region heuristic is developed. In contrast to usual trust region methods, it regards not only the global optimum of a quadratic objective over a sphere, but also a set of … Read more

Anti-matroids

We introduce an anti-matroid as a family $\cal F$ of subsets of a ground set $E$ for which there exists an assignment of weights to the elements of $E$ such that the greedy algorithm to compute a maximal set (with respect to inclusion) in $\cal F$ of minimum weight finds, instead, the unique maximal set … Read more

Near-optimal solutions to large scale facility location problems

We investigate the solution of large scale instances of the capacitated and uncapacitated facility location problems. Let n be the number of customers and m the number of potential facility sites. For the uncapacitated case we solved instances of size m x n=3000 x 3000; for the capacitated case the largest instances were 1000 x … Read more