Graphs and algorithms
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Rounding algorithms for covering problems
Mathematical Programming: Series A and B
Greedy strikes back: improved facility location algorithms
Journal of Algorithms
Improved Approximation Guarantees for Packing and Covering Integer Programs
SIAM Journal on Computing
Generalized submodular cover problems and applications
Theoretical Computer Science
Analysis of a local search heuristic for facility location problems
Journal of Algorithms
Local search heuristic for k-median and facility location problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A new greedy approach for facility location problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Facility Location with Nonuniform Hard Capacities
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
An approximation algorithm for scheduling two parallel machines with capacity constraints
Discrete Applied Mathematics
Improved Approximation Algorithms for the Uncapacitated Facility Location Problem
SIAM Journal on Computing
Convex Optimization
Improved approximation algorithms for capacitated facility location problems
Mathematical Programming: Series A and B
A Multiexchange Local Search Algorithm for the Capacitated Facility Location Problem
Mathematics of Operations Research
Approximation Algorithms for Metric Facility Location Problems
SIAM Journal on Computing
Covering Problems with Hard Capacities
SIAM Journal on Computing
An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
A unified approach to scheduling on unrelated parallel machines
Journal of the ACM (JACM)
Mechanism design on trust networks
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Energy efficient scheduling via partial shutdown
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
From stars to comets: Improved local search for universal facility location
Operations Research Letters
Note: A comment on scheduling two parallel machines with capacity constraints
Discrete Optimization
Nonclairvoyant sleep management and flow-time scheduling on multiple processors
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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In this paper we consider a generalization of the machine activation problem introduced recently ["Energy efficient scheduling via partial shutdown" by Khuller, Li and Saha (ACM-SIAM 2010 Symp. on Discrete Algorithms)] where the unrelated parallel machine scheduling problem is studied with machine activation cost. This is the standard unrelated parallel machine scheduling problem with a machine dependent activation cost that is incurred, if any job is assigned to the machine. The problem asks for a choice of machines to activate, and a schedule of all jobs on the active machines subject to the makespan constraint. The goal is to minimize the total activation cost. Our main generalization consists of a general activation cost model, where the activation cost for a machine is a non-decreasing function of its load. We develop a greedy algorithm that yields a fractional assignment of jobs, such that at least n − ε jobs are assigned fractionally and the total cost is at most 1 + ln(n/ε) times the optimum. Combining with standard rounding methods yields improved bounds for several machine activation problems. In addition, we study the machine activation problem with d linear constraints (these could model makespan constraints, as well as other types of constraints). Our method yields a schedule with machine activation cost of O(1/ε log n) times the optimum and a constraint violation by a factor of 2d + ε. This result matches our previous bound for the case d = 1. As a by-product, our method also yields a ln n + 1 approximation factor for the non-metric universal facility location problem for which the cost of opening a facility is an arbitrary non-decreasing function of the number of clients assigned to it. This gives an affirmative answer to the open question posed in earlier work on universal facility location.