TY - GEN

T1 - Randomized competitive algorithms for generalized caching

AU - Bansal, Nikhil

AU - Buchbinder, Niv

AU - Naor, Joseph

PY - 2008

Y1 - 2008

N2 - We consider online algorithms for the generalized caching problem. Here we are given a, cache of size κ 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. We give an online algorithm with competitive ratio O(log2 κ), which is the first algorithm for the problem with competitive ratio sublinear in κ. We also give improved O(log κ)-competitive algorithms for the special cases of the Bit Model and Fault model. In the Bit Model, the fetching cost is proportional to the size of the page and in the Fault model all fetching costs are uniform. Previously, an O(log2 κ)-competitive algorithm due to Irani [14] was known for both of these models. Our algorithms are based on an extension of the primal-dual framework for online algorithms which was developed by Buchbinder and Naor [7], We first generate an O(log κ)-competitive fractional algorithm for the problem. This is done by using a strengthened LP formulation with knapsack-cover constraints, where exponentially many constraints are added upon arrival of a new request. Second, we round online the fractional solution and obtain a randomized online 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 κ 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. We give an online algorithm with competitive ratio O(log2 κ), which is the first algorithm for the problem with competitive ratio sublinear in κ. We also give improved O(log κ)-competitive algorithms for the special cases of the Bit Model and Fault model. In the Bit Model, the fetching cost is proportional to the size of the page and in the Fault model all fetching costs are uniform. Previously, an O(log2 κ)-competitive algorithm due to Irani [14] was known for both of these models. Our algorithms are based on an extension of the primal-dual framework for online algorithms which was developed by Buchbinder and Naor [7], We first generate an O(log κ)-competitive fractional algorithm for the problem. This is done by using a strengthened LP formulation with knapsack-cover constraints, where exponentially many constraints are added upon arrival of a new request. Second, we round online the fractional solution and obtain a randomized online algorithm. Our techniques provide a unified framework for caching algorithms and are substantially simpler than those previously used.

KW - Algorithms

UR - http://www.scopus.com/inward/record.url?scp=57049106945&partnerID=8YFLogxK

U2 - 10.1145/1374376.1374412

DO - 10.1145/1374376.1374412

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:57049106945

SN - 9781605580470

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 235

EP - 244

BT - STOC'08

PB - Association for Computing Machinery

T2 - 40th Annual ACM Symposium on Theory of Computing, STOC 2008

Y2 - 17 May 2008 through 20 May 2008

ER -