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Let T = (V, E) be an undirected tree, in which each edge is associated with a non-negative cost, and let {s1, t1}, . . . , {sk, tk} be a collection of k distinct pairs of vertices. Given a requirement parameter t ≤ k, the partial multicut on a tree problem asks to find a minimum cost set of edges whose removal from T disconnects at least t out of these k(More)
We consider a variety of vehicle routing problems. The input to a problem consists of a graph G = (N, E) and edge lengths l(e) e ∈ E. Customers located at the vertices have to be visited by a set of vehicles. Two important parameters are k the number of vehicles, and λ the longest distance traveled by a vehicle. We consider two types of problems: (1) Given(More)
We consider the offline and online versions of a bin packing problem called bin packing with conflicts. Given a set of items V = {1, 2, . . . , n} with sizes s1, s2 . . . , sn ∈ [0, 1] and a conflict graph G = (V, E), the goal is to find a partition of the items into independent sets of G, where the total size of each independent set is at most one, so that(More)
We give a 7.18-approximation algorithm for the minimum latency problem that uses only O(n logn) calls to the prize-collecting Steiner tree (PCST) subroutine of Goemans and Williamson. This improves the previous best algorithms in both performance guarantee and running time. A previous algorithm of Goemans and Kleinberg for the minimum latency problem(More)
We continue the study of bin packing with splittable items and cardinality constraints. In this problem, a set of n items must be packed into as few bins as possible. Items may be split, but each bin may contain at most k (parts of) items, where k is some given parameter. Complicating the problem further is the fact that items may be larger than 1, which is(More)
T problem of group ranking, also known as rank aggregation, has been studied in contexts varying from sports, to multicriteria decision making, to machine learning, to ranking Web pages, and to behavioral issues. The dynamics of the group aggregation of individual decisions has been a subject of central importance in decision theory. We present here a new(More)