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Memoryless Algorithms for the Generalized k-server Problem on Uniform Metrics
[article]

2020
*
arXiv
*
pre-print

We consider

arXiv:2007.08669v1
fatcat:zbgfp6xdvjg6zlckwbau6eybfq
*the**generalized**k*-*server**problem*on uniform metrics. We study*the*power of*memoryless**algorithms**and*show tight bounds of Θ(*k*!) on their competitive ratio. ... This improves*the*≈ 2^2^*k*doubly-exponential bound of Chiplunkar*and*Vishwanathan*for**the*more*general*setting of uniform metrics with different*weights*. ...*Memoryless**Algorithms**for**Generalized**k*-*server*: Recently Chiplunkar*and*Vishnawathan [11] studied*randomized**memoryless**algorithms*in*weighted*uniform metrics. ...##
###
On Randomized Memoryless Algorithms for the Weighted K-Server Problem

2013
*
2013 IEEE 54th Annual Symposium on Foundations of Computer Science
*

*The*

*weighted*

*k*-

*server*

*problem*is a

*generalization*of

*the*

*k*-

*server*

*problem*in which

*the*cost of moving a

*server*of

*weight*β_i through a distance d is β_i· d. ...

*The*above result has two important implications. Firstly this yields an α_

*k*-competitive

*memoryless*

*algorithm*

*for*

*the*

*weighted*

*k*-

*server*

*problem*on uniform spaces. ... Acknowledgment

*The*authors would like to thank Nikhil Bansal

*for*pointing them to some important work on

*the*

*weighted*

*k*-

*server*

*problem*. ...

##
###
A lower bound on the competitivity of memoryless algorithms for a generalization of the CNN problem

2006
*
Theoretical Computer Science
*

This

doi:10.1016/j.tcs.2006.01.047
fatcat:mpkecyfgcvgldih63qjzkoplme
*generalizes*in several aspects*the*lower bounds obtained by Koutsoupias*and*Taylor [*The*CNN*Problem**and*other*k*-*server*variants, Theoret. Comput. ... Sci. 324 (2004) 347-359]*for**the*original*problem*.*The*proof consists in*the*analysis of carefully selected*random*walks, which appear naturally in*the*framework of*memoryless**algorithms*. ... Acknowledgments*The*author would like to thank Miklos Santha*for*bringing to his attention this*problem**and**for*all his advice. ...##
###
The -server problem

2009
*
Computer Science Review
*

*The*

*k*-

*server*conjecture, which was posed more that two decades ago when

*the*

*problem*was first studied within

*the*competitive analysis framework, is still open

*and*has been a major driving force

*for*

*the*... Supported in part by IST-2008-215270 (FRONTS). 1 Although

*for*deterministic

*algorithms*

*the*configurations can be inferred from C0

*and*

*the*sequence of requests r,

*randomized*

*algorithms*are based on all ...

*For*

*the*

*weighted*paging

*problem*(equivalent to

*the*

*k*-

*server*

*problem*on stars where

*the*requests are at

*the*end of leaves), Irani [Ira97] established

*the*

*randomized*

*k*-

*server*conjecture

*for*

*the*

*weighted*...

##
###
The weighted 2-server problem

2004
*
Theoretical Computer Science
*

*For*arbitrary metric spaces, in contrast with

*the*non-

*weighted*case, we prove that there is no

*memoryless*

*randomized*

*algorithm*with ÿnite competitive ratio. ... We consider a

*generalization*of

*the*2-

*server*

*problem*in which

*servers*have di erent costs. ... Acknowledgements We would like to thank

*the*anonymous referees

*for*pointing out some mistakes

*and*

*for*insightful comments that helped us improve

*the*presentation. ...

##
###
An Optimal On-Line Algorithm for K Servers on Trees

1991
*
SIAM journal on computing (Print)
*

We investigate

doi:10.1137/0220008
fatcat:4jd3f4rgcngj5n66qypio5sgmu
*the**k*-*server**problem*when*the*metric space is a tree.*For*this case we present an on-line*k*-competitive*algorithm**for**k**servers*.*The*competitiveness ratio*k*is optimal. ...*The**algorithm*is*memoryless*, in*the*sense that it does not use any information from*the*past. ... Allan Borodin pointed out to us that our potential function can be espressed by*the*formula we currently use in*the*paper.*The*same formula was used in 3]. ...##
###
Random walks on weighted graphs and applications to on-line algorithms

1993
*
Journal of the ACM
*

We study

doi:10.1145/174130.174131
fatcat:eww5qvq3a5eszgtgpolhiurmym
*the*design*and*analysis of*randomized*on-line*algorithms*. We show that this*problem*is closely related to*the*synthesis of*random*walks on graphs with positive real costs on their edges. ... We develop a theory*for**the*synthesis of such w alks,*and*employ it to design competitive on-line*algorithms*. ... Acknowledgements We thank Allan Borodin*and*Gil Strang*for*their helpful comments*and*suggestions. ...##
###
The CNN Problem and Other k-Server Variants
[chapter]

2000
*
Lecture Notes in Computer Science
*

In particular, no

doi:10.1007/3-540-46541-3_48
fatcat:57qxfstqnvh3xpqjrpsoz7nyle
*memoryless**randomized**algorithm*can be competitive. ...*The*CNN*problem*contains as special cases two important*problems*:*the*BRIDGE*problem*, also known as*the*cow-path*problem*,*and**the**weighted*2-*server**problem*in which*the*2*servers*may have di erent speeds ... Acknowledgements We thank*the*anonymous referees*for*their helpful, in-depth comments. ...##
###
The CNN problem and other k-server variants

2004
*
Theoretical Computer Science
*

In particular, no

doi:10.1016/j.tcs.2004.06.002
fatcat:pthcfaqq3jhp3f55mws6dgncyq
*memoryless**randomized**algorithm*can be competitive. ...*The*CNN*problem*contains as special cases two important*problems*:*the*BRIDGE*problem*, also known as*the*cow-path*problem*,*and**the**weighted*2-*server**problem*in which*the*2*servers*may have di erent speeds ... Acknowledgements We thank*the*anonymous referees*for*their helpful, in-depth comments. ...##
###
Random walks on weighted graphs, and applications to on-line algorithms

1990
*
Proceedings of the twenty-second annual ACM symposium on Theory of computing - STOC '90
*

We study

doi:10.1145/100216.100266
dblp:conf/stoc/CoppersmithDRS90
fatcat:sumfy2hprzbyjmc2qobtfzpz5m
*the*design*and*analysis of*randomized*on-line*algorithms*. We show that this*problem*is closely related to*the*synthesis of*random*walks on graphs with positive real costs on their edges. ... We develop a theory*for**the*synthesis of such walks,*and*employ it to design competitive on-line*algorithms*. ... Acknowledgements We thank Allan Borodin*and*Gil Strang*for*their helpful comments*and*suggestions. ...##
###
On-Line Load Balancing in a Hierarchical Server Topology

2001
*
SIAM journal on computing (Print)
*

We also show a lower bound of 3

doi:10.1137/s0097539798346135
fatcat:62jdjgj2lfb3zlhlhjjqfz7bqy
*for**the*unweighted integral model when temporary jobs are allowed. We*generalize**the**problem**and*consider hierarchies in which*the**servers*form a tree. ... We show a lower bound of e*for**the*unweighted case (both integral*and*fractional). This bound is valid even with respect to*randomized**algorithms*. ... Note that*the*assignment*generated*by a uniform*memoryless**algorithm*is independent of both*the*number of*servers**and**the*order of jobs in*the*input. ...##
###
The server problem and on-line games
[chapter]

1992
*
DIMACS Series in Discrete Mathematics and Theoretical Computer Science
*

*The*

*General*Work Function

*Algorithm*. In Section 2.3 we introduced

*for*

*the*

*k*-

*server*

*problem*.

*The*concept

*generalizes*naturally to a wide collection of on-line

*problems*. ... Lemma 2. 3 3 If M is a metric space,

*and*if M embeds isometrically in M ,

*and*if there is a c-competitive

*algorithm*

*for*

*the*

*k*-

*server*

*problem*in M , then there is a c-competitive

*algorithm*

*for*

*the*

*k*-

*server*...

##
###
The Randomized Competitive Ratio of Weighted k-server is at least Exponential
[article]

2021
*
arXiv
*
pre-print

*The*

*weighted*

*k*-

*server*

*problem*is a natural

*generalization*of

*the*

*k*-

*server*

*problem*in which

*the*cost incurred in moving a

*server*is

*the*distance traveled times

*the*

*weight*of

*the*

*server*. ... In this article, we make significant progress towards understanding

*the*

*randomized*competitive ratio of

*weighted*

*k*-

*server*on uniform metrics. ... It is, in fact, a

*randomized*

*memoryless*

*algorithm*

*generalizing*

*the*

*algorithm*by Chrobak

*and*Sgall [7]

*for*

*k*= 2,

*and*it achieves

*the*competitive ratio against a stronger form of adversary called adaptive ...

##
###
Design of On-Line Algorithms Using Hitting Times

1999
*
SIAM journal on computing (Print)
*

Besides providing new insight into

doi:10.1137/s0097539798335511
fatcat:ke2weubvivdqfdyb54qpvzn6eu
*random*walks on*weighted*graphs, we show how these identities give us a way of designing competitive*randomized*on-line*algorithms**for*certain well-known*problems*. ...*Random*walks are well known*for*playing a crucial role in*the*design of*randomized*off-line as well as on-line*algorithms*. ...*The*author would also like to thank Mike Saks (*the*no-longer-anonymous referee)*for*a careful reading*and*constructive criticism of*the*manuscript. ...##
###
Page 1283 of Mathematical Reviews Vol. , Issue 2001B
[page]

2001
*
Mathematical Reviews
*

Then we give a ve competitive

*algorithm**for**the*(6,3)-*server**problem*on*the*real line. Our*algorithm*is simple*and**memoryless*. ... We consider a more*general**problem*called*the*(*k*,/)-*server**problem*, in which a request is served using / out of*k*available*servers*. ...
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