TY - JOUR

T1 - Randomized competitive algorithms for generalized caching

AU - Bansal, Nikhil

AU - Buchbinder, Niv

AU - Naor, Joseph

PY - 2012

Y1 - 2012

N2 - We consider online algorithms for the generalized caching problem. Here we are given a cache of size k and pages with arbitrary sizes and fetching costs. Given a request sequence of pages, the goal is to minimize the total cost of fetching the pages into the cache. Our main result is an online algorithm with competitive ratio O(log 2 k), which gives the first o(k) competitive algorithm for the problem. We also give improved O(log k)-competitive algorithms for the special cases of the bit model and fault model, improving upon the previous O(log 2 k) guarantees due to Irani [Proceedings of the 29th Annual ACM Symposium on Theory of Computing, 1997, pp. 701- 710]. Our algorithms are based on an extension of the online primal-dual framework introduced by Buchbinder and Naor [Math. Oper. Res., 34 (2009), pp. 270-286] and involve two steps. First, we obtain an O(log k)-competitive fractional algorithm based on solving online an LP formulation strengthened with exponentially many knapsack cover constraints. Second, we design a suitable online rounding procedure to convert this online fractional algorithm into a randomized algorithm. Our techniques provide a unified framework for caching algorithms and are substantially simpler than those previously used.

AB - We consider online algorithms for the generalized caching problem. Here we are given a cache of size k and pages with arbitrary sizes and fetching costs. Given a request sequence of pages, the goal is to minimize the total cost of fetching the pages into the cache. Our main result is an online algorithm with competitive ratio O(log 2 k), which gives the first o(k) competitive algorithm for the problem. We also give improved O(log k)-competitive algorithms for the special cases of the bit model and fault model, improving upon the previous O(log 2 k) guarantees due to Irani [Proceedings of the 29th Annual ACM Symposium on Theory of Computing, 1997, pp. 701- 710]. Our algorithms are based on an extension of the online primal-dual framework introduced by Buchbinder and Naor [Math. Oper. Res., 34 (2009), pp. 270-286] and involve two steps. First, we obtain an O(log k)-competitive fractional algorithm based on solving online an LP formulation strengthened with exponentially many knapsack cover constraints. Second, we design a suitable online rounding procedure to convert this online fractional algorithm into a randomized algorithm. Our techniques provide a unified framework for caching algorithms and are substantially simpler than those previously used.

KW - Competitive analysis

KW - Generalized caching

KW - Paging

KW - Randomization

UR - http://www.scopus.com/inward/record.url?scp=84861601267&partnerID=8YFLogxK

U2 - 10.1137/090779000

DO - 10.1137/090779000

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AN - SCOPUS:84861601267

SN - 0097-5397

VL - 41

SP - 391

EP - 414

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

IS - 2

ER -