13,675 research outputs found
Lagrangian Relaxation and Partial Cover
Lagrangian relaxation has been used extensively in the design of
approximation algorithms. This paper studies its strengths and limitations when
applied to Partial Cover.Comment: 20 pages, extended abstract appeared in STACS 200
Scheduling Resources for Executing a Partial Set of Jobs
In this paper, we consider the problem of choosing a minimum cost set of
resources for executing a specified set of jobs. Each input job is an interval,
determined by its start-time and end-time. Each resource is also an interval
determined by its start-time and end-time; moreover, every resource has a
capacity and a cost associated with it. We consider two versions of this
problem. In the partial covering version, we are also given as input a number
k, specifying the number of jobs that must be performed. The goal is to choose
k jobs and find a minimum cost set of resources to perform the chosen k jobs
(at any point of time the capacity of the chosen set of resources should be
sufficient to execute the jobs active at that time). We present an O(log
n)-factor approximation algorithm for this problem.
We also consider the prize collecting version, wherein every job also has a
penalty associated with it. The feasible solution consists of a subset of the
jobs, and a set of resources, to perform the chosen subset of jobs. The goal is
to find a feasible solution that minimizes the sum of the costs of the selected
resources and the penalties of the jobs that are not selected. We present a
constant factor approximation algorithm for this problemComment: Full version of paper accepted to FSTTCS'201
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