Allocation of bandwidth and storage

Abstract We consider two allocation problems in this paper, namely, allocation of bandwidth and storage. In these problems, we face a number of independent requests, respectively, for reservation of bandwidth of a communication channel of fixed capacity and for storage of items into a space of fixed size. In both problems, a request is characterized by: (i) its required period of allocation; (ii) its required bandwidth (item width, respectively)and (iii)the profit of accepting the request. The problem is to decide which requests to accept so as to maximize the total profit. These problems in general are NP-hard. In this paper we provide polynomial-time algorithms for solving various special cases, and develop polynomial-time approximation algorithms for very general NP-hard cases with good performance guarantees.

[1]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[2]  John Michael Robson,et al.  Bounds for Some Functions Concerning Dynamic Storage Allocation , 1974, JACM.

[3]  Chak-Kuen Wong,et al.  Approximate Algorithms for Some Generalized Knapsack Problems , 1976, Theor. Comput. Sci..

[4]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[5]  Maciej Slusarek.  An Off-Line Storage Allocation Algorithm , 1987, Inf. Process. Lett..

[6]  Janelle J. Harms,et al.  Performance Modeling of a Channel Reservation Service , 1995, Comput. Networks ISDN Syst..

[7]  Reuven Bar-Yehuda,et al.  A unified approach to approximating resource allocation and scheduling , 2001, JACM.

[8]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[9]  Esther M. Arkin,et al.  Scheduling jobs with fixed start and end times , 1987, Discret. Appl. Math..

[10]  G. Nemhauser,et al.  Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms , 1977 .

[11]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[12]  Ran Canetti,et al.  Bandwidth Allocation with Preemption , 1999, SIAM J. Comput..

[13]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[14]  Jr. E. G. Coffman.  An Introduction to Combinatorial Models of Dynamic Storage Allocation , 1983 .

[15]  Cynthia A. Phillips,et al.  Off-line admission control for general scheduling problems , 2000, SODA '00.

[16]  A. Frieze,et al.  Approximation algorithms for the m-dimensional 0–1 knapsack problem: Worst-case and probabilistic analyses , 1984 .

[17]  Ran Canetti,et al.  Bandwidth allocation with preemption , 1995, STOC '95.

[18]  Jordan Gergov,et al.  Algorithms for compile-time memory optimization , 1999, SODA '99.

[19]  George L. Nemhauser,et al.  Note--On "Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms" , 1979 .