Multimedia applications require a guaranteed level of service for accessing continuous-media data. To obtain such guarantees, the database server where the data are residing must employ an admission control scheme to ...
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Multimedia applications require a guaranteed level of service for accessing continuous-media data. To obtain such guarantees, the database server where the data are residing must employ an admission control scheme to limit the number of clients that can be served concurrently. We investigate the problem of on-line admission control, where the decision of whether to accept or reject a request must be made without any knowledge about future requests. Employing competitive analysis techniques, we address the problem in its most general form with the following key contributions: (1) We prove a tight upper bound on the competitive ratio of the conventional Work-Conserving (WC) policy, showing that it is within a factor 1+Delta/1-p of the optimal clairvoyant strategy, where Delta is the ratio of the maximum to minimum request length (i.e., time duration), and p is the maximum fraction of the server's bandwidth that a request can demand;(2) we prove a lower bound of Omega(log Delta/1-p) on the competitive ratio of any deterministic or randomized admission control scheme, demonstrating an exponential gap between greedy and optimal on-line solutions;(3) we propose simple deterministic schemes based on the idea of bandwidth prepartitioning that guarantee competitive ratios within a small constant factor of log Delta (i.e., they are provably near-optimal) if p < 1 /[log Delta];and (4) we introduce a novel admission control policy that partitions the server bandwidth based on the expected popularities of different request lengths and experimentally demonstrate its benefits compared to WC. (C) 2002 Elsevier Science (USA).
We present a new technique to prove lower bounds for geometric on-line searching problems. We assume that a target of unknown location is hidden somewhere in a known environment and a searcher is trying to find it. We...
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We present a new technique to prove lower bounds for geometric on-line searching problems. We assume that a target of unknown location is hidden somewhere in a known environment and a searcher is trying to find it. We are interested in lower bounds on the competitive ratio of the search strategy, that is, the ratio of the distance traveled by the searcher to the distance of the target. The technique we present is applicable to a number of problems, such as biased searching on m rays and on-line construction of on-line algorithms. For each problem we prove tight lower bounds. (C) 2001 Elsevier Science B.V. All rights reserved.
The k-server problem was introduced by Manasse et al. (in: Proceedings of the 20th annual ACM symposium on theory of computing, Chicago, Illinois, USA, pp 322-333, 1988), and is one of the most famous and well-studied...
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The k-server problem was introduced by Manasse et al. (in: Proceedings of the 20th annual ACM symposium on theory of computing, Chicago, Illinois, USA, pp 322-333, 1988), and is one of the most famous and well-studied online problems. Koutsoupias and Papadimitriou (J ACM42(5):971-983, 1995) showed that the work function algorithm (WFA) has a competitive ratio of at most 2k - 1 for the k-server problem. In this paper, by proposing a potential function that is different from the one in Koutsoupias and Papadimitriou (1995), we show that the WFA has a competitive ratio of at most n - 1, where n is the number of points in the metric space. When n < 2k, this ratio is less than 2k - 1.
In this paper, we describe a randomized incremental algorithm for computing the upper envelope (i.e., the pointwise maximum) of a set of n triangles in three dimensions, This algorithm is an on-line algorithm. It is s...
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In this paper, we describe a randomized incremental algorithm for computing the upper envelope (i.e., the pointwise maximum) of a set of n triangles in three dimensions, This algorithm is an on-line algorithm. It is structure-sensitive: the expected cost of inserting the n-th triangle is O(log n Sigma(r=1)(n) tau(r)/r(2)) and depends on the expected size tau(r) of an intermediate result for r triangles, Since tau(r) can be Theta(r(2) alpha(r)) in the worst case, this cost is bounded in the worst case by O(n alpha(n) log n), (The expected behaviour is analyzed by averaging over all possible orderings of the input.) The main new characteristics is the use of a two-level history graph. (The history graph is an auxiliary data structure maintained by randomized incremental algorithms.) Our algorithm is fairly simple and appears to be efficient in practice, It extends to surfaces and surface patches of fixed maximum algebraic degree.
We introduce a new model of lookahead for on-line paging algorithms and study several algorithms using this model. A paging algorithm is on-line with strong lookahead l if it sees the present request and a sequence of...
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We introduce a new model of lookahead for on-line paging algorithms and study several algorithms using this model. A paging algorithm is on-line with strong lookahead l if it sees the present request and a sequence of future requests that contains l pairwise distinct pages. We show that strong lookahead has practical as well as theoretical importance and improves the competitive factors of on-line paging algorithms. This is the first model of lookahead having such properties. In addition to lower bounds we present a number of deterministic and randomized on-line paging algorithms with strong lookahead which are optimal or nearly optimal.
In the single machine mean completion time problem with release dates, a set of jobs has to be processed non-preemptively on a single machine. No job can be processed before its release date, and the objective is to d...
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In the single machine mean completion time problem with release dates, a set of jobs has to be processed non-preemptively on a single machine. No job can be processed before its release date, and the objective is to determine a sequence of the jobs on the machine which minimizes the sum of the completion times of all jobs. In this paper, we prove the asymptotic optimality of the shortest processing time among available jobs algorithm, in which at the completion time of any job, the next job to be scheduled is the shortest job among all those released but not yet processed. This algorithm is particularly attractive because it falls in the class of easy to implement and computationally inexpensive on-line algorithms. (C) 2001 Elsevier Science BY. All rights reserved.
We study on-line bandwidth allocation on two parallel links. Motivated by issues of quality of service and fair resource allocation, the goal is to maximize the load of the least loaded link. We analyze several models...
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We study on-line bandwidth allocation on two parallel links. Motivated by issues of quality of service and fair resource allocation, the goal is to maximize the load of the least loaded link. We analyze several models for which we give tight bounds on the competitive ratio. (c) 2005 Elsevier B.V. All rights reserved.
We study a new kind of on-line bin packing, motivated by a problem arising when scheduling jobs on the Grid. In this bin packing problem, the set of items is given at the beginning, and variable-sized bins arrive one ...
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We study a new kind of on-line bin packing, motivated by a problem arising when scheduling jobs on the Grid. In this bin packing problem, the set of items is given at the beginning, and variable-sized bins arrive one by one. We analyze the problem using both the competitive ratio and the relative worst order ratio, observing that the two measures often lead to different conclusions. A closely related problem was introduced by Zhang (Discrete Appl. Math. 72:193-197, 1997). Our main result answers a question posed in that paper in the affirmative: we give an algorithm with a competitive ratio strictly better than 2, for our problem as well as Zhang's problem. For identical bins, the new algorithm has essentially the same performance as FFD (First-Fit-Decreasing).
Finding a maximum matching in a graph is a classical problem. The on-line versions of the problem in which the vertices and/or edges of the graph are given one at a time and an algorithm has to calculate a matching in...
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Finding a maximum matching in a graph is a classical problem. The on-line versions of the problem in which the vertices and/or edges of the graph are given one at a time and an algorithm has to calculate a matching incrementally have been studied for more than two decades. Many variants of the problem are considered in the literature. The pioneering work (Karp, 1990) considers a bipartite graph where the vertices of one part are revealed one at a time together with their incident edges. In this work we consider maximal d-colorable graphs which are exactly the complete d-partite graphs. The vertices arrive one at a time together with their incident edges, or equivalently with their corresponding colors in some given d-coloring of the graph. We present an optimal 2/3-competitive deterministic algorithm for this on-line problem. This problem is closely related to that of minimizing the cost of line terminals in star topology optical network. We consider lightpaths arriving in an on-line fashion on a given star network. Our result implies a tight 10/9-competitive algorithm for finding a wavelength assignment minimizing the cost of line terminals in such a network. (C) 2014 Published by Elsevier B.V.
A new measure, the accommodating function, for the quality of on-line algorithms is presented. The accommodating function, which is a generalization of both the competitive ratio and the competitive ratio on accommoda...
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A new measure, the accommodating function, for the quality of on-line algorithms is presented. The accommodating function, which is a generalization of both the competitive ratio and the competitive ratio on accommodating sequences, measures the quality of an on-line algorithm as a function of the resources that would be sufficient for an optimal off-line algorithm to fully grant all requests. More precisely, if we have some amount of resources n, the function value at alpha is the usual ratio ( still on some fixed amount of resources n), except that input sequences are restricted to those where the optimal off-line algorithm will not obtain a better result by having more than the amount alphan of resources. The accommodating functions for three specific on-line problems are investigated: a variant of bin packing in which the goal is to maximize the number of items put in n bins, the seat reservation problem, and the problem of optimizing total ow time when preemption is allowed. We also show that when trying to distinguish between two algorithms, the decision as to which one performs better cannot necessarily be made from the competitive ratio or the competitive ratio on accommodating sequences alone. For the variant of bin-packing considered, we show that Worst-Fit has a strictly better competitive ratio than First-Fit, while First-Fit has a strictly better competitive ratio on accommodating sequences than Worst-Fit.
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