S. Irani, N. Reingold, D. Sleator and J. Westbrook. "Randomized Competitive Algorithms for the List Update Problem". In Proceedings of the 2nd ACM Symposium on Discrete Algorithms, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....is how often items can be requested repeatedly. Next we consider randomized on line algorithms and give two lower bounds. The proofs appear in the appendix. None of the randomized on line algorithms that have been presented so far for the standard list update problem uses paid exchanges, see e.g. [2, 35]. We show that such algorithms cannot be better than d competitive in the setting with delayed action. action and suppose that A does not use paid exchanges. If A is c competitive against any oblivious d. This lower bound holds for both types of adversaries. If a randomized on line algorithm ....

N. Reingold, J. Westbrook, and D.D. Sleator. Randomized competitive algorithms for the list update problem. Algorithmica, 11:15--32, 1994.

....relative of the deterministic MHD family. Algorithm RMHD: Upon a request for an item x currently at the ith position, randomly choose a position from the set f1; ig and move x to that position. The family of algorithms counter(s; S) CTR(s; S) due to Reingold, Westbrook and Sleator [18] is a sophisticated generalization of algorithm BIT. Let s be a positive integer and S, a nonempty subset of f0; 1; s Gamma 1g. Algorithm CTR(s; S) For each item x on the list maintain a mod s counter c(x) initially set randomly, independently and uniformly to a number in f0; 1; ....

....1 (mod s) and then if c(x) 2 S move x to the front. Thus, CTR(2; f1g) is BIT. Reingold et al. prove that CTR(7; f0; 2; 4g) is 85=49 competitive ( 1:735) From this family we have tested algorithm CTR(7; f0; 2; 4g) The family of algorithms random reset(s; D) RST(s; D) due to Reingold et al. [18] is a variation on the counter algorithms. Let s be a positive integer and D, a probability distribution on the set S = f0; 1; s Gamma 1g such that for i 2 S,D(i) is the probability of i. Algorithm RST(s; D) For each item x on the list maintain a counter c(x) initially set randomly a ....

N. Reingold, J. Westbrook, and D. Sleator. Randomized competitive algorithms for the list update problem. 11:15--32, 1994.

....MTF can be used to devise a very simple and successful (text) compression algorithm (see e.g. 7, 9, 10] Soon after its discovery, algorithm TIMESTAMP was also shown to play an important role. Continuing Albers work, Albers, von Stengel and Werchner [3] combined TIMESTAMP and algorithm BIT [17, 13] in a 1=5 4=5 probability mixture and showed that the resulting randomized algorithm (called COMB) is 8=5 competitive against an oblivious adversary. So far this is the best known randomized upper bound that leaves a small gap to the best known lower bound of 3=2 [22] Another work due to Albers ....

S. Irani, N. Reingold, J. Westbrook, and D.D. Sleator. Randomized competitive algorithms for the list update problem. pages 251--260, 1991.

....in two respects for online list update. First and most obviously, it may lead to better lower bounds on OPT(oe) to plug into (1) second, it might reveal structural properties that turn out to be useful in devising better online algorithms. Properties of OPT have already been studied in the past [14, 15, 2, 3]. The size of an OLUP instance on n items and m requests is Theta(log(n) Delta m) But we can assume m n. Therefore, an algorithm is still polynomial if its runtime is polynomial in n. The currently best algorithm for OLUP runs in O(2 n n m) 14] It is based on a straightforward dynamic ....

N. Reingold, J. Westbrook, and D. D. Sleator (1994), Randomized competitive algorithms for the list update problem. Algorithmica 11, 15--32.

....data structures [4] Requests to items in an unsorted linear list must be served by accessing the requested item. We assume the partial cost model where accessing the ith item in the list incurs a cost of i Gamma 1 units. This is simpler to analyze than the original full cost model [12] where that cost is i. The goal is to keep access costs small by rearranging the items in the list. After an item has been requested, it may be moved free of charge closer to the front of the list. This is called a free exchange. Any other exchange of two consecutive items in the list incurs cost ....

....for all request sequences oe. The competitive ratio c in this inequality is the standard yardstick for measuring the performance of the online algorithm. The well known moveto front rule MTF, for example, which moves each item to the front of the list after it has been requested, is 2 competitive [12, 13]. This is also the best possible competitiveness for any deterministic online algorithm for the list update problem [12] Another deterministic algorithm that is also 2 competitive is TIMESTAMP due to Albers [1] which moves the requested item x in front of all items which have been requested at ....

[Article contains additional citation context not shown here]

N. Reingold, J. Westbrook, and D. D. Sleator (1994), Randomized competitive algorithms for the list update problem. Algorithmica 11, 15--32.

....[4] Requests to items in an unsorted linear list must be served while maintaining the list so that access costs remain small. We assume the partial cost model where accessing the ith item in the list incurs a cost of i Gamma 1 units. This is simpler to analyze than the original full cost model [14] where that cost is i. After an item has been requested, it may be moved free of charge closer to the front of the list. This is called a free exchange. Any other exchange of two consecutive items in the list incurs cost one and is called a paid exchange. An online algorithm must serve the ....

....all request sequences oe. The competitive ratio c in this inequality is the standard yardstick for measuring the performance of the online algorithm. The well known moveto front rule MTF , for example, which moves each item to the front of the list after it has been requested, is 2 competitive [14, 15]. This is also the best possible competitiveness for any deterministic online algorithm for the list update problem [10] 1 Institute for Theoretical Computer Science, ETH Zurich, 8092 Zurich, Switzerland. Email: ambuehl inf.ethz.ch, gaertner inf.ethz.ch 2 Mathematics Department, London ....

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N. Reingold, J. Westbrook, and D. D. Sleator (1994), Randomized competitive algorithms for the list update problem, Algorithmica 11, 15--32.

....[4] Requests to items in an unsorted linear list must be served while maintaining the list so that access costs remain small. We assume the partial cost model where accessing the ith item in the list incurs a cost of i 1 units. This is simpler to analyze than the original full cost model [14] where that cost is i. After an item has been requested, it may be moved free of charge closer to the front of the list. This is called a free exchange. Any other exchange of two consecutive items in the list incurs cost one and is called a paid exchange. An online algorithm must serve the ....

....for all request sequences . The competitive ratio c in this inequality is the standard yardstick for measuring the performance of the online algorithm. The well known moveto front rule MTF , for example, which moves each item to the front of the list after it has been requested, is 2 competitive [14, 15]. This is also the best possible competitiveness for any deterministic online algorithm for the list update problem [10] 1 Institute for Theoretical Computer Science, ETH Z urich, 8092 Z urich, Switzerland. Email: ambuehl inf.ethz.ch, gaertner inf.ethz.ch 2 Mathematics Department, London ....

[Article contains additional citation context not shown here]

N. Reingold, J. Westbrook, and D. D. Sleator (1994), Randomized competitive algorithms for the list update problem, Algorithmica 11, 15-32.

....which build on it. Our understanding of the usefulness of randomization in this problem is particularly bad. Thus any progress towards understanding this problem would be of great bene t. A barely random algorithm is one which is a distribution over a constant number of deterministic strategies [15]. Barely random algorithms are desirable in that they conserve random bits. Neither of the algorithms of Bartal et al. or Seiden are barely random. In fact, both of these algorithms potentially make a random choice for each job scheduled. Further, both algorithms use nm) variables, and use a ....

Reingold, N., Westbrook, J., and Sleator, D. Randomized competitive algorithms for the list update problem. Algorithmica 11, 1 (Jan 1994), 15-32.

....relative of the deterministic MHD family. Algorithm RMHD: Upon a request for an item x currently at the ith position, randomly choose a position from the set f1; ig and move x to that position. The family of algorithms counter(s; S) CTR(s; S) due to Reingold, Westbrook and Sleator [18] is a sophisticated generalization of algorithm BIT. Let s be a positive integer and S, a nonempty subset of f0; 1; s 1g. Algorithm CTR(s; S) For each item x on the list maintain a mod s counter c(x) initially set randomly, independently and uniformly to a number in f0; 1; s ....

....1 (mod s) and then if c(x) 2 S move x to the front. Thus, CTR(2; f1g) is BIT. Reingold et al. prove that CTR(7; f0; 2; 4g) is 85=49 competitive ( 1:735) From this family we have tested algorithm CTR(7; f0; 2; 4g) The family of algorithms random reset(s; D) RST(s; D) due to Reingold et al. [18] is a variation on the counter algorithms. Let s be a positive integer and D, a probability distribution on the set S = f0; 1; s 1g such that for i 2 S,D(i) is the probability of i. Algorithm RST(s; D) For each item x on the list maintain a counter c(x) initially set randomly a number ....

N. Reingold, J. Westbrook, and D. Sleator. Randomized competitive algorithms for the list update problem. Algorithmica, 11:15-32, 1994.

....MTF can be used to devise a very simple and successful (text) compression algorithm (see e.g. 7, 9, 10] Soon after its discovery, algorithm TIMESTAMP was also shown to play an important role. Continuing Albers work, Albers, von Stengel and Werchner [3] combined TIMESTAMP and algorithm BIT [17, 13] in a 1=5 4=5 probability mixture and showed that the resulting randomized algorithm (called COMB) is 8=5 competitive against an oblivious adversary. So far this is the best known randomized upper bound, leaving a small gap to the best known lower bound of 3=2 [22] Another work due to Albers and ....

S. Irani, N. Reingold, J. Westbrook, and D.D. Sleator. Randomized competitive algorithms for the list update problem. In Proceedings of the 2nd ACM-SIAM Symposium on Discrete Algorithms, pages 251-260, 1991.

....randomized online algorithms problem against oblivious adversaries [17] An oblivious adversary has to construct the entire request sequence in advance and is not allowed to see the random choices made by an online algorithm. Many randomized online algorithms for list update have been proposed [1,7,35,36,49]. We present the two most important algorithms. Reingold et al. 49] gave a very simple algorithm, called Bit. Bit: Each item in the list maintains a bit that is complemented whenever the item is accessed. If an access causes a bit to change to 1, then the requested item is moved to the front of ....

....oblivious adversary has to construct the entire request sequence in advance and is not allowed to see the random choices made by an online algorithm. Many randomized online algorithms for list update have been proposed [1,7,35,36,49] We present the two most important algorithms. Reingold et al. [49] gave a very simple algorithm, called Bit. Bit: Each item in the list maintains a bit that is complemented whenever the item is accessed. If an access causes a bit to change to 1, then the requested item is moved to the front of the list. Otherwise the list remains unchanged. The bits of the ....

[Article contains additional citation context not shown here]

N. Reingold, J. Westbrook and D.D. Sleator. Randomized competitive algorithms for the list update problem. Algorithmica, 11:15--32, 1994.

....for all request sequences oe, E[CA (oe) c Delta COPT (oe) a; where the expectation is taken over the random choices made by A. Irani [2] has exhibited the first randomized on line algorithm for the list update problem; the SPLIT algorithm she proposed is 31 16 competitive. Reingold et al. [4] have given a family of COUNTER and RANDOM RESet al..gorithms that achieve a competitive ratio of p 3 1:73. This has been the best upper bound known so far for randomized list update algorithms. The best lower bound known is due to Teia [6] He shows that no randomized on line algorithm for the ....

....makes use of the fact that the decision whether a given request is processed using Step (a) or (b) does not depend on previous requests (see the analysis after Claim 3) In the simplified TIMESTAMP algorithm we can reduce the number of random bits using a technique presented by Reingold et 11 al. [4]. For each item in the list we maintain a mod i counter, where i is a positive integer. These counters are initialized independently and uniformly at random to a value in f0; 1; i Gamma 1g. Furthermore, we choose a non empty subset I of f0; 1; i Gamma 1g. At a request to item x, ....

N. Reingold, J. Westbrook and D.D. Sleator. Randomized competitive algorithms for the list update problem. Algorithmica, 11(1):15--32, 1994.

....which build on it. Our understanding of the usefulness of randomization in this problem is particularly bad. Thus any progress towards understanding this problem would be of great bene t. A barely random algorithm is one which is a distribution over a constant number of deterministic strategies [14]. Barely random algorithms are desirable in that they conserve random bits. Neither of the algorithms of Bartal et al. or Seiden are barely random. In fact, both of these algorithms potentially make a random choice for each job scheduled. Further, both algorithms use nm) variables, and use a ....

Reingold, N., Westbrook, J., and Sleator, D. Randomized competitive algorithms for the list update problem. Algorithmica 11, 1 (Jan 1994), 15-32.

....of 0 or 1 to the items uniformly at random from all the possible 2 n assignements. Every time a request is made to an item x, the bit that is assoicated with x b(x) is flipped and if the bit is flipped from 0 to 1, the item is moved to the first of the list. The following theorem was proved in [IRSW91]. Theorem 24.5 BIT is 1.75 competitive. 24 4 Lecture 24: April 29 Proof: To prove the theorem, we first prove a lemma. Lemma 24.6 For every item x and every t, just after the t th request b(x) is 0 or 1 with equal probability. The value is independent of x s position in the list and independent ....

S. Irani, N. Reingold, D. Sleator and J. Westbrook. Randomized Competitive Algorithms for the List Update Problem. In Proc. 2nd ACM-SIAM Symposium on Discrete Algorithms, pages 251--260, January 1991. 24-8 Lecture 24: April 29

....requested items within the list. Keywords. On line algorithms, analysis of algorithms, competitive analysis, linear lists, list update. 1. Description of the algorithm The list update problem is one of the first on line problems that have been studied with respect to competitiveness (see [5] and references) The problem is to maintain an unsorted list of items so that access costs are kept small. An initial list of items is given. A sequence of requests must be served in that order. A request specifies an item in the list. The request is served by accessing the item, incurring a cost ....

....be better than 1.5 competitive [7] We will combine two on line algorithms for the list update problem that store with each item some information about past requests. Both algorithms use only free exchanges. The first is the 1. 75 competitive BIT algorithm due to Reingold, Westbrook, and Sleator [5]. The algorithm maintains a bit for each item in the list. Initially, the bit is set at random to 0 or 1 with equal probability so that the bits of the items are pairwise independent. Algorithm BIT. Each time an item is requested, its bit is complemented. When the value of the bit changes to 1, ....

[Article contains additional citation context not shown here]

N. Reingold, J. Westbrook, and D. D. Sleator, Randomized competitive algorithms for the list update problem, Algorithmica 11 (1994) 15--32.

....et al. in [BDBK 90] The first to apply randomization in the list accessing problem was Irani in [Ira91] where she invented the SPLIT algorithm that attains a competitive ratio of 31 16 = 1.9375, independent of the length of the list. Subsequently, Reingold, Westbrook, and Sleator [RWS94] presented two families of randomized algorithms: COUNTER(s;S) and RANDOMRESET (s; D) The COUNTER(s;S) algorithm associates a counter with each element. Each counter is initialized to some integer from 0 to s uniformly at random, and is decremented by 1 each time the associated element is ....

....for the standard list accessing problem. The history of lower bounds against oblivious adversaries, on the other hand, started with the work by Raghavan and Karp, who proved a lower bound of 9 8 for any randomized algorithm. Then, using a similar technique, Reingold, Westbrook, and Sleator [RWS94] and independently Chrobak and Larmore (reported in [Ira91] were able to improve the bound to approximately 1.27. The best lower bound to date was obtained in 1993 [Tei93] when Teia proved that no randomized algorithm can be better than ( 3 2 Gamma 5 l 5 ) competitive against an oblivious ....

[Article contains additional citation context not shown here]

N. Reingold, J. Westbrook, and D.D. Sleator. Randomized competitive algorithms for the list update problem. Algorithmica, 11:15--32, 1994.

....are called off line. For example, linear programming has traditionally been viewed as an off line optimization problem. On the other hand, there are problems, such as paging [ST85, BIRS91, FKL 88, KRS88, MS89] circuit routing [AAP93, RU94, BFL96] and list accessing [GMS79, ST85, Ira91, IRWS, RWS94, Alb95] where the natural assumption is that the input is given one piece at a time, and the output has to be produced in the same manner. These problems are called on line. Off line algorithms for these problems are not acceptable, and serve only as a basis for comparison. 2.1.2 ....

S. Irani, N. Reingold, J. Westbrook, and D.D. Sleator. Randomized competitive algorithms for the list update problem. In Proceedings of the 2nd Annual ACMSIAM Symposium on Discrete Algorithms, pages 251--260.

....single edge problems. Thus strongly competitive strategies for a single edge are generalized to a tree. Our algorithms are strongly competitive for specific applications and networks and also illustrate these two useful techniques. Our randomized algorithm for file allocation is barely random [20]; i.e. it uses a bounded number of random bits, independent of the number of requests. A random choice is made only at the initialization of the algorithm, after which it runs deterministically. 1.1. Problem description. We study three variants of distributed data management: replication [1, 7, ....

<F3.752e+05> N. Reingold, J. Westbrook, and D. D.<F3.887e+05> Sleator,<F3.732e+05> Randomized competitive algorithms for the list update<F3.887e+05> problem, Algorithmica, 11 (1994), pp. 15--32.

....into single edge problems. Thus strongly competitive strategies for a single edge is generalized to a tree. Our algorithms are strongly competitive for specific applications and networks, and also illustrate these two useful techniques. Our randomized algorithm for file allocation is barely random [20], i.e. it uses a bounded number of random bits, independent of the number of requests. A random choice is made only at the initialization of the algorithm, after which it runs deterministically. 1.1. Problem Description. We study three variants of distributed data management: replication [1, ....

N. Reingold, J. Westbrook, and D. D. Sleator, Randomized Competitive Algorithms for The List Update Problem, Algorithmica, 11 (1994), pp. 15--32.

....Using free exchanges, the algorithm can lower the cost on subsequent requests. At any time two adjacent items in the list may be exchanged at a cost of 1. These exchanges are called paid exchanges. The cost model defined above is called the standard model. Manasse et al. 53] and Reingold et al. [61] introduced the P d cost model. In the P d model there are no free exchanges and each paid exchange costs d. In this survey, we will present results both for the standard and the P d model. However, unless otherwise stated, we will always assume the standard cost model. We are interested in ....

....2 The proof shows that the lower bound is actually 2 Gamma 2 n 1 , where n is the number of items in the list. Thus, the upper bound given by Irani on the competitive ratio of the Move To Front rule is tight. Next we consider list update algorithms for other cost models. Reingold et al. [61] gave a lower bound on the competitiveness achieved by deterministic on line algorithms. Theorem 6. Let A be a deterministic on line algorithm for the list update problem in the P d model. If A is c competitive, then c 3. Below we will give a family of deterministic algorithms for the P d ....

[Article contains additional citation context not shown here]

N. Reingold, J. Westbrook, and D.D. Sleator. Randomized competitive algorithms for the list update problem. Algorithmica, 11:15--32, 1994.

No context found.

S. Irani, N. Reingold, D. Sleator and J. Westbrook. "Randomized Competitive Algorithms for the List Update Problem". In Proceedings of the 2nd ACM Symposium on Discrete Algorithms, 1991.

No context found.

N. Reingold, J. Westbrook, D. Sleator, "Randomized competitive algorithms for the list update problem", Algorithmica, 11, pp. 15--32, 1994.

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N. Reingold, J. Westbrook, D. Sleator, Randomized competitive algorithms for the list update problem, Algorithmica 11 (1) (1994) 15-32.

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N. Reingold, J. Westbrook and D.D. Sleator. Randomized competitive algorithms for the list update problem. Algorithmica, 11(1):15--32, 1994.

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N. Reingold, J. Westbrook, D. Sleator, "Randomized competitive algorithms for the list update problem", Algorithmica, 11, pp. 15--32, 1994.

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