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Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
An improved coating pan apparatus and spray arm assembly are disclosed for providing facilitated maintenance and cleaning of sensitive spray nozzles. The spray arm assembly includes means for varyingExpand
Approximation algorithms for directed Steiner problems
We obtain the first non-trivial approximation algorithms for the Steiner Tree problem and the Generalized Steiner Tree problem in general directed graphs. Essentially no approximation algorithms wereExpand
Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
The generalized assignment problem (GAP) is a special case of the problem, and although the reduction requires |N| to be exponential in the original problem size, it is able to interpret the recent (1 i¾? 1/e)-approximation for GAP by Fleischer et al.[10] in the framework. Expand
A recursive greedy algorithm for walks in directed graphs
  • C. Chekuri, Martin Pál
  • Mathematics, Computer Science
  • 46th Annual IEEE Symposium on Foundations of…
  • 23 October 2005
An O(log OPT) approximation is obtained for a generalization of the orienteering problem in which the profit for visiting each node may vary arbitrarily with time and the implications for the approximability of several basic optimization problems are interesting. Expand
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
A polynomial time approximation scheme (PTAS) for MKP, which appears to be the strongest special case of GAP that is not APX-hard, and a PTAS-preserving reduction from an arbitrary instance of MKP to an instance with distinct sizes and profits. Expand
A PTAS for the multiple knapsack problem
The main result of this paper is a polynomial time approximation scheme for MKP, which helps demarcate the boundary at which instances of GAP become APX-hard. Expand
Dependent Randomized Rounding via Exchange Properties of Combinatorial Structures
A new {\em swap rounding} technique which can be applied in a variety of settings including matroids and matroid intersection, while providing Chernoff-type concentration bounds for linear and sub modular functions of the rounded solution is described. Expand
Approximation techniques for average completion time scheduling
It is shown that a preemptive one-machine relaxation is a powerful tool for designing parallel machine scheduling algorithms that simultaneously produce good approximations and have small running times, and a general theorem relating the value of one- machine relaxations to that of the schedules obtained for the original m-machine problems is proved. Expand
Submodular function maximization via the multilinear relaxation and contention resolution schemes
A broadly applicable framework for maximizing linear and submodular functions subject to independence constraints is developed and it is shown that contention resolution schemes are an effective way to round a fractional solution, even when f is non-monotone. Expand
Approximation schemes for minimizing average weighted completion time with release dates
This work presents the first known polynomial time approximation schemes for several variants of the problem of scheduling n jobs with release dates on m machines so as to minimize their average weighted completion time. Expand