137 research outputs found
The K-Server Dual and Loose Competitiveness for Paging
This paper has two results. The first is based on the surprising observation
that the well-known ``least-recently-used'' paging algorithm and the
``balance'' algorithm for weighted caching are linear-programming primal-dual
algorithms. This observation leads to a strategy (called ``Greedy-Dual'') that
generalizes them both and has an optimal performance guarantee for weighted
caching.
For the second result, the paper presents empirical studies of paging
algorithms, documenting that in practice, on ``typical'' cache sizes and
sequences, the performance of paging strategies are much better than their
worst-case analyses in the standard model suggest. The paper then presents
theoretical results that support and explain this. For example: on any input
sequence, with almost all cache sizes, either the performance guarantee of
least-recently-used is O(log k) or the fault rate (in an absolute sense) is
insignificant.
Both of these results are strengthened and generalized in``On-line File
Caching'' (1998).Comment: conference version: "On-Line Caching as Cache Size Varies", SODA
(1991
Online Service with Delay
In this paper, we introduce the online service with delay problem. In this
problem, there are points in a metric space that issue service requests
over time, and a server that serves these requests. The goal is to minimize the
sum of distance traveled by the server and the total delay in serving the
requests. This problem models the fundamental tradeoff between batching
requests to improve locality and reducing delay to improve response time, that
has many applications in operations management, operating systems, logistics,
supply chain management, and scheduling.
Our main result is to show a poly-logarithmic competitive ratio for the
online service with delay problem. This result is obtained by an algorithm that
we call the preemptive service algorithm. The salient feature of this algorithm
is a process called preemptive service, which uses a novel combination of
(recursive) time forwarding and spatial exploration on a metric space. We hope
this technique will be useful for related problems such as reordering buffer
management, online TSP, vehicle routing, etc. We also generalize our results to
servers.Comment: 30 pages, 11 figures, Appeared in 49th ACM Symposium on Theory of
Computing (STOC), 201
Greedy D-Approximation Algorithm for Covering with Arbitrary Constraints and Submodular Cost
This paper describes a simple greedy D-approximation algorithm for any
covering problem whose objective function is submodular and non-decreasing, and
whose feasible region can be expressed as the intersection of arbitrary (closed
upwards) covering constraints, each of which constrains at most D variables of
the problem. (A simple example is Vertex Cover, with D = 2.) The algorithm
generalizes previous approximation algorithms for fundamental covering problems
and online paging and caching problems
An O(log k)-competitive algorithm for generalized caching
In the generalized caching problem, we have a set of pages and a cache of size k. Each page p has a size wpe1 and fetching cost cp for loading the page into the cache. At any point in time, the sum of the sizes of the pages stored in the cache cannot exceed k. The input consists of a sequence of page requests. If a page is not present in the cache at the time it is requested, it has to be loaded into the cache incurring a cost of cp. We give a randomized O(log k)-competitive online algorithm for the generalized caching problem, improving the previous bound of O(log2 k) by Bansal, Buchbinder, and Naor (STOC'08). This improved bound is tight and of the same order as the known bounds for the classic problem with uniform weights and sizes. We use the same LP based techniques as Bansal et al. but provide improved and slightly simplified methods for rounding fractional solutions online
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