A. Blum, S. Chawla, and A. Kalai. Static Optimality and Dynamic Search-Optimality in Lists and Trees. SODA '02, pages 1-8.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....is as follows. It starts by producing online a fractional solution to the problem, where the fractional solution (at least for the unweighted case) is motivated by similar techniques developed in computational learning theory for online prediction [11, 8] e.g. the WINNOW algorithm) See also [5, 3, 4] for related techniques and additional references. Fractional solutions can often be converted into randomized algorithms, but it is usually impossible to perform this conversion online. In our case, however, this conversion is possible, because of the way the fractional solution evolves in time. ....

S. Chawla, A. Kalai, and A. Blum. Static optimality and dynamic search-optimality in lists and trees. In Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1-8, 2002.

....we can obtain cache oblivious algorithms for the string dictionary problem we have studied here. The details are not straightforward and leave its discussion for later. Finally, there are other forms of self adjusting results that will be of interest: working set theorem [17] dynamic optimality [3, 17], and reference locality [6] SASL allows us to also answer range queries on pairs of strings (S; S 0 ) retrieve all the dictionary words which lexicographically lie between S and S 0 . The algorithm is simple due to the structure of a skip list. The overall performance and impact of SASL in ....

A. Blum, S. Chawla, and A. Kalai. Static optimality and dynamic search-optimality in lists and trees. In ACM-SIAM Symposium on Discrete Algorithms, 2002 (to appear).

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A. Blum, S. Chawla, and A. Kalai. Static Optimality and Dynamic Search-Optimality in Lists and Trees. SODA '02, pages 1-8.

....as well as the best single decision chosen in hindsight, even when there are exponentially many possible decisions. However, the naive application of these algorithms is inefficient for such large problems. For some problems with nice structure, specialized efficient solutions have been developed [10, 16, 17, 6, 3]. We show that a very simple idea, used in Hannan s seminal 1957 paper [9] gives efficient solutions to all of these problems. Essentially, in each period, one chooses the decision that worked best in the past. To guarantee low regret, it is necessary to add randomness. Surprisingly, this simple ....

....The key point here is that step (ii) is executed with probability at most 1=N , so one expects to update only nT times over T accesses. Thus the computational costs and movement costs, which he have thus far ignored, are small. This algorithm has what Blum et al. call strong static optimality [3]. They also presented a follow the perturbed leader type of algorithm for the easier list update problem. Theirs was the original motivation for our work, and they were also unaware of the similarity to Hannan s algorithm. 1.1 Generalization What is important about the above problems is that in ....

Avrim Blum, Shuchi Chawla, and Adam Kalai. Static Optimality and Dynamic Search Optimality in Lists and Trees. In Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '02), 2002.

....to such problems, our algorithms give a generalization of how to do this in terms of optimizing and adding randomness to the space of costs. Of course, following the leader is not a new idea. In fact, FRL was inspired by a similar solution for one particular problem, the list update problem [3]. However, their algorithm does not generalize to other problems with arbitrary feasible sets. The results of this paper lead to several questions. Although, as remarked in the introduction, dynamic optimality is impossible without additional costs, it is possible to be competitive with the best ....

Avrim Blum, Shuchi Chawla, and Adam Kalai. Static Optimality and Dynamic Search Optimality in Lists and Trees. In Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '02), 2002.

....We assume we have some minimization oracle M , that, given a cost vector (direction) c 2 R returns some minimum of c x over x 2 S. In other words, M(c) arg min c x Our basic approach, described below and depicted in Figure 1. 1b, is similar to an algorithm used for list update problem [3]. Follow The Expected Leader FEL( s) On each period j: 1. Choose r 1 ; r 2 ; r s independently from distribution . 2. Use x j : s P s i=1 M(c 1 c 2 c j 1 r i ) We also assume that jc j j 1 1 for all j, and that D is an upper bound on the L 1 diameter of S, ....

Avrim Blum, Shuchi Chawla, and Adam Kalai. Static Optimality and Dynamic Search Optimality in Lists and Trees. In Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '02), 2002.

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