J. Boyar, K. S. Larsen, and M. N. Nielsen. The accommodating function --- a generalization of the competitive ratio. SIAM Journal of Computation, 31(1):233--258, 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

No context found.

J. Boyar, K. S. Larsen, and M. N. Nielsen. The accommodating function --- a generalization of the competitive ratio. SIAM Journal of Computation, 31(1):233--258, 2001.

No context found.

J. Boyar, K. S. Larsen, and M. N. Nielsen. The Accommodating Function: A Generalization of the Competitive Ratio. SIAM Journal on Computing. To appear. Preliminary version in Sixth International Workshop on Algorithms and Data Structures, volume 1663 of Lecture Notes in Computer Science, pages 74-79. Springer-Verlag, 1999.

....sequences may prefer one algorithm while the competitive ratio measure (on all sequences) prefers the other [5] Supported in part by the Israel Science Foundation, and by a USA Israel BSF grant. Supported in part by the Danish Natural Science Research Council (SNF) In earlier papers [4 6], this competitive ratio on accommodating sequences was called the accommodating ratio. The change is made here for consistency with common practice in the field. II In the Bin Packing problem we are given some bins and the goal is to pack a set of items into these bins. We concentrate on the ....

....sequences seems the more appropriate measure, since it is constant while the competitive ratio (on all sequences) is close to zero, for large values of k, basically due to some sequences which seem very contrived. This demonstrated the usefulness of the more general accommodating function [6] which comprises the competitive ratio as well as the competitive ratio on accommodating sequences (it is a function of the restriction on the request sequences) Here, we consider what happens when the fairness restriction is removed. Thus, for the on line problem Unrestricted Bin Packing (UBP) ....

[Article contains additional citation context not shown here]

J. Boyar, K. S. Larsen, and M. N. Nielsen. The Accommodating Function --- A Generalization of the Competitive Ratio. In Sixth International Workshop on Algorithms and Data Structures, volume 1663 of Lecture Notes in Computer Science, pages 74--79. Springer-Verlag, 1999.

....worse than the competitive ratio on unrestricted sequences for any given problem and sometimes can be much better. For problems where the competitive ratio is a bad measure, it may be useful to compare algorithms by their competitive ratio on accommodating sequences. Specifically, it was shown in [4, 5] that there are (benefit) problems where the competitive ratio tends to zero while the competitive ratio on accommodating sequences is a constant, i.e. independent of the parameters of the problem. Moreover, when we are trying to distinguish between two algorithms, the competitive ratio on ....

....sequences is a constant, i.e. independent of the parameters of the problem. Moreover, when we are trying to distinguish between two algorithms, the competitive ratio on accommodating sequences may prefer one algorithm while the competitive ratio measure (on all sequences) prefers the other [5]. Supported in part by the Israel Science Foundation, and by a USA Israel BSF grant. Supported in part by the Danish Natural Science Research Council (SNF) In earlier papers [4 6] this competitive ratio on accommodating sequences was called the accommodating ratio. The change is made ....

[Article contains additional citation context not shown here]

J. Boyar, K. S. Larsen, and M. N. Nielsen. The Accommodating Function --- A Generalization of the Competitive Ratio. Tech. report 24, Department of Mathematics and Computer Science, University of Southern Denmark, Main Campus: Odense University, 1998. Extended version submitted for journal publication 1999.

....can only be rejected if it cannot fit in any bin at the time when it is given. We refer to the problem as Fair Bin Packing 1 . Notice that the fairness criterion is a part of the problem specification. Thus, even though the optimal off line algorithm knows the whole sequence of requests 1 In [6], where a preliminary version of some of these results was presented, the same problem was referred to as Unit Price Bin Packing. 5 in advance, it must process the requests in the same order as the on line algorithm, and do so fairly. In this problem for a given ff, we only consider sequences ....

Joan Boyar, Kim S. Larsen, and Morten N. Nielsen. The Accommodating Function --- a generalization of the competitive ratio. In Sixth International Workshop on Algorithms and Data Structures, volume 1663 of Lecture Notes in Computer Science, pages 74--79. Springer-Verlag, 1999.

....if there exists a constant b, such that A (I) c Delta OPT(I) Gamma b for all sequences I which could be packed in n bins. The accommodating ratio AR = supfc j A is c accommodatingg: Note that the only difference between the accommodating ratio and the competitive ratio is that 1 In [6] where some of the results from [5] were first presented in a preliminary form, this problem was called Unit Price Bin Packing. 2 with the accommodating ratio, the only sequences considered are those which OPT could have packed in the given n bins. The accommodating function is a generalization ....

....Unrestricted Bin Packing which has a better competitive ratio than any algorithm for Fair Bin Packing. It would be difficult to do the same for the accommodating ratio, since the best upper bound known is 6 7 for both cases. FirstFit s accommodating ratio is known to lie between 5 8 and 7 11 [6], and no algorithm for Fair Bin Packing is known to have a better accommodating ratio. The algorithm Unfair First Fit (UFF) presented below, is shown to have an accommodating ratio which is better than that of First Fit as long as the number of bins is at least 22; the ratio approaches 2 3 as n ....

J. Boyar, K. S. Larsen, and M. N. Nielsen. The Accommodating Function --- A Generalization of the Competitive Ratio. In Sixth International Workshop on Algorithms and Data Structures, volume 1663 of Lecture Notes in Computer Science, pages 74--79. Springer-Verlag, 1999.

....I, define the competitive ratio of algorithm A applied to I to be the income of algorithm A over the optimal income (achieved by the optimal off line algorithm) The competitive ratio of algorithm A is the infimum over all possible sequences of requests. The definition of the accommodating ratio [5, 6] of algorithm A is similar to that of the competitive ratio, except that the only sequences of requests allowed are sequences for which the optimal off line algorithm could accommodate all requests therein. This restriction is used to reflect the assumption that the decision as to how many cars ....

J. Boyar, K.S. Larsen and M.N. Nielsen, The accommodating function --- a generalization of the competitive ratio, in: F. Dehne, A. Gupta, J.-R. Sack, R. Tamassia, eds., Proceedings of the Sixth International Workshop on Algorithms and Data Structures (WADS'99), LNCS 1663 (Springer, Berlin, 1999) 74--79.

....The reason for introducing the accommodating ratio was that it is sometimes a more realistic measure than the competitive ratio. In [1] and [6] it is shown that the accommodating ratio can give dioeerent results from the competitive ratio when trying to distinguish between two algorithms. In [4] a generalization of the accommodating and competitive ratios, the accommodating function is introduced. This paper illustrates that the accommodating ratio has an advantage apart from being an alternative to the competitive ratio. A common technique when constructing a diOEcult proof is to start ....

....denote A s prot cost from servicing I and let OPTn (I) denote the prot cost of an optimal ooe line algorithm from servicing I when the amount n of resources is available. Let k be the amount of resources available to A . We use OPT as a shorthand for OPT k . In compliance with the denition in [4], an input sequence I is called a 1 sequence if, for all n k, OPT(I) OPTn (I) i.e. the amount k of resources is optimal in the sense that adding extra resources does not improve the performance of an optimal ooe line algorithm. For maximization problems, the denition is: Denition 3.1. Let 0 ....

J. Boyar, K. S. Larsen, and M. N. Nielsen. The accommodating function a generalization of the competitive ratio. In Sixth International Workshop on Algorithms and Data Structures, volume 1663 of Lecture Notes in Computer Science, pages 7479. Springer-Verlag, 1999.

....algorithm could have granted all requests, A (I) c Delta OPT(I) Gamma b, where b is a fixed constant for the given problem, and, thus, independent of I. The accommodating ratio AR is defined as AR = supfc j A is c accommodatingg. 2 The accommodating ratio is the accommodating function from [4] evaluated at 1. Consider the Unit Price Bin Packing problem defined above. The value of running the on line algorithm A on the request sequence I is the number of objects from I which A packs in the n bins. Since we are only concerned with the accommodating ratio here, all request sequences ....

Joan Boyar, Kim S. Larsen, and Morten N. Nielsen. The Accommodating Function -- a generalization of the competitive ratio. In Proceedings of the Sixth International Workshop on Algorithms and Data Structures, 1999. To appear.

....to the accommodating ratio. This implies that the truth about the relative performance of the two algorithms cannot be obtained from any of the two measures alone. In fact this shows that in order to really see how two algorithms differ, it is necessary to investigate the accommodating function [4], which is a generalization of the competitive ratio as well as the accommodating ratio. The accommodating function is defined for maximization problems as follows (a similar definition can be given for minimization problems) Consider an on line problem with a fixed amount of resources n. Let ....

....objects of size at most k, the objective is to maximize the total number of objects in these bins. This is a fundamental problem in optimization [6] which has been studied in the off line setting, starting in [8] and its applicability to processor and storage allocation is discussed in [7] In [4], fair algorithms for the on line version of this Unit Price Bin Packing problem were considered. In fair algorithms, an object can only be rejected if it cannot fit in any bin. The optimal off line algorithm, OPT, is also required to be fair. We consider two specific algorithms: First Fit (FF) ....

[Article contains additional citation context not shown here]

Joan Boyar, Kim S. Larsen, and Morten N. Nielsen. The Accommodating Function -- a generalization of the competitive ratio. Tech. report PP-1998-24, Dept. of Math. and Computer Science, University of Southern Denmark, Main Campus: Odense University, 1998.

No context found.

J. Boyar, K. S. Larsen, and M. N. Nielsen. The Accommodating Function: A Generalization of the Competitive Ratio. SIAM Journal on Computing, 31(1):233-- 258, 2001.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC