We give the rst non-trivial approximation algorithms for the Steiner tree problem and the generalized Steiner network problem on general directed graphs. These problems have several applications inâ€¦ (More)

Let f : 2 â†’ R+ be a monotone submodular set function, and let (X, I) be a matroid. We consider the problem maxSâˆˆI f(S). It is known that the greedy algorithm yields a 1/2approximation [17] for thisâ€¦ (More)

The Multiple Knapsack problem (MKP) is a natural and well known generalization of the single knapsack problem and is defined as follows. We are given a set of n items and m bins (knapsacks) such thatâ€¦ (More)

Let f : 2 â†’ R be a non-decreasing submodular set function, and let (N, I) be a matroid. We consider the problem maxSâˆˆI f(S). It is known that the greedy algorithm yields a 1/2-approximation [9] forâ€¦ (More)

We consider the problem of maximizing a non-negative submodular set function f:2N -> RR+ over a ground set N subject to a variety of packing type constraints including (multiple) matroid constraints,â€¦ (More)

Given an arc-weighted directed graph G = (V, A, /spl lscr/) and a pair of nodes s, t, we seek to find an s-t walk of length at most B that maximizes some given function f of the set of nodes visitedâ€¦ (More)

We study a variant of the maximum coverage problem which we label the maximum coverage problem with group budget constraints (MCG). We are given a collection of sets S = {S1, S2, . . . , Sm} whereâ€¦ (More)

We consider the problem of non-preemptive scheduling to minimize average (weighted) completion time, allowing for release dates, parallel machines, and precedence constraints. Recent work has led toâ€¦ (More)