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On the k-server conjecture

1994
*
Proceedings of the twenty-sixth annual ACM symposium on Theory of computing - STOC '94
*

Manasse et al. [1988]

doi:10.1145/195058.195245
fatcat:hoy6zia6crgm3hh2l7d5v7guz4
*conjectured*that*the*competitive ratio for*the**k*-*server*problem is exactly*k*(it is trivially at least*k*); previously*the*best-known upper bound was exponential in*k*. ... We prove that*the*work function algorithm for*the**k*-*server*problem has a competitive ratio at most 2k -1. ... In Manasse et al. [1988] , it was shown that no*on*-line algorithm can have a competitive ratio less that*k*and*the*following*conjecture*was posed:*CONJECTURE*1.1 (*THE**k*-*SERVER**CONJECTURE*), For elley metric ...##
###
On the k-server conjecture

1995
*
Journal of the ACM
*

Manasse et al. [1988]

doi:10.1145/210118.210128
fatcat:tgvoujbj75cylk33k2gdfs27dm
*conjectured*that*the*competitive ratio for*the**k*-*server*problem is exactly*k*(it is trivially at least*k*); previously*the*best-known upper bound was exponential in*k*. ... We prove that*the*work function algorithm for*the**k*-*server*problem has a competitive ratio at most 2k -1. ... In Manasse et al. [1988] , it was shown that no*on*-line algorithm can have a competitive ratio less that*k*and*the*following*conjecture*was posed:*CONJECTURE*1.1 (*THE**k*-*SERVER**CONJECTURE*), For elley metric ...##
###
On the Monotonicity of Work Function in k-Server Conjecture
[article]

2008
*
arXiv
*
pre-print

This paper presents a mistake in work function algorithm of

arXiv:0808.3197v1
fatcat:t77ghadiljemthdgqduypvdjqy
*k*-*server**conjecture*. That is,*the*monotonicity of*the*work function is not always true. ... Introduction*The**k*-*server**conjecture*has not been proved. A lot of literature deal with*the**k*-*server**conjecture*[3] [2] [4] [1] and references therein. ... We still think WFA would be*k*-competitive. d(a, b) = 1, d(a, c) = 7, d(a, d) = 5, d(a, e) = 8, d(b, c) = 4, d(b, d) = 2, d(b, e) = 10, d(c, d) = 3, d(c, e) = 9, d(d, e) = 6 Consider 3-*servers**on*this graph ...##
###
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*... This article surveys some major results for

*the*

*k*-

*server*. * University of Athens, elias@di.uoa.gr. ... This is supported by all results

*on*

*the*problem in

*the*last two decades and it is exactly what

*the*

*k*-

*server*

*conjecture*states:

*Conjecture*1 (

*The*

*k*-

*server*

*conjecture*). ...

##
###
Page 5195 of Mathematical Reviews Vol. , Issue 98H
[page]

1998
*
Mathematical Reviews
*

However, we provide credence to

*the**conjectures*by establishing that for balanced sys- tems,*the**conjectured*asymptotic loss of*the*HW policy is a lower bound*on**the*asymptotic loss of all policies, while ... Summary: “In this paper we analyze a discrete-time single*server*queue where*the*service time equals*one*slot. ...##
###
A lower bound for the Erlang C formula in the Halfin–Whitt regime

2011
*
Queueing systems
*

Mathematics Subject Classification (2000) 60K25

doi:10.1007/s11134-011-9244-z
fatcat:6d3age4wcnhqbktptgwcl5pauy
*One*of*the*classical models of queueing theory is*the*M/M/s queue or Erlang delay model. This model has s homogeneous*servers*working in parallel. ... This probability is known as*the*Erlang C formula, given by (with ρ = a/s) C(s, a) = a s s!(1−ρ) s−1*k*=0 a*k*/*k*! + a s s! ... Acknowledgements We thank an anonymous referee for subjecting*Conjecture*1 to close scrutiny and for suggesting*Conjecture*2. ...##
###
Introduction to special issue on open problems

2011
*
Queueing systems
*

In addition, if

doi:10.1007/s11134-011-9259-5
fatcat:7g2xhvgw3jdgpi24dcsv77dkbq
*the*open problem is in*the*form of a*conjecture*, there is some motivation why*the*author/authors thinks/think*the**conjecture*is true. ...*The*open problems thus provide*the*readership with a state of*the*art, and will hopefully trigger new efforts, new collaborations, and new approaches. ... First Gupta and Osogami postulate a*conjecture*regarding upper and lower bounds*on**the*mean waiting time for*the*M/G/*K*queue, analogously to*the*classical Markov-Krein theorem. ...##
###
On the competitive ratio of the work function algorithm for the k-server problem

2004
*
Theoretical Computer Science
*

*The*

*k*-

*server*problem is

*one*of

*the*most fundamental online problems.

*The*problem is to schedule

*k*mobile

*servers*to visit a sequence of points in a metric space with minimum total mileage. ...

*The*

*k*-

*server*

*conjecture*of Manasse, McGeogh, and Sleator states that there exists a

*k*-competitive online algorithm.

*The*

*conjecture*has been open for over 15 years. ...

*The*notorious

*k*-

*server*

*conjecture*states that there is an online algorithm that has competitive ratio

*k*

*on*any metric space. ...

##
###
A Survey of Stability Results for Redundancy Systems
[article]

2021
*
arXiv
*
pre-print

Redundancy mechanisms consist in sending several copies of a same job to a subset of

arXiv:2103.10942v1
fatcat:6um5vozfovahheiolww7sxolui
*servers*. It constitutes*one*of*the*most promising ways to exploit diversity in multiservers applications. ... We also point out open questions and*conjectures*. ... Ayesta has received funding from*the*Department of Education of*the*Basque Government through*the*Consolidated Research Group MATHMODE (IT1294-19) . ...##
###
Towards the Capacity of Private Information Retrieval from Coded and Colluding Servers
[article]

2021
*
arXiv
*
pre-print

This positively settles

arXiv:1903.12552v7
fatcat:wpgypxt4krbidjx524oxelcbym
*the*capacity*conjectures*stated by Freij-Hollanti et al. and Tajeddine et al. in*the*presented cases. ...*servers*for*the*recently introduced concept of matched randomness. ... ACKNOWLEDGMENT*The*authors would like to thank Prof. Syed Jafar, Prof. Chao Tian, and Dr. Qiwen Wang for helpful discussions. ...##
###
The Delayed k-Server Problem
[chapter]

2005
*
Lecture Notes in Computer Science
*

We show that

doi:10.1007/11537311_25
fatcat:oj775ukdqfbxflw6nynoelugcu
*the*delayed*k*-*server*problem is equivalent to*the*(*k*− 1)-*server*problem in*the*uniform case, but not in general. ... In this problem, once a*server*moves to serve a request, it must wait for*one*round to move again, but could serve a repeated request to*the*same point. ... Acknowledgement Wolfgang Bein thanks Kazuo Iwama for*the*generous support he received while he visited Kyoto University to work*on*this project during December 2004 and January 2005. ...##
###
A General Decomposition Theorem for the k-Server Problem

2002
*
Information and Computation
*

*The*first general decomposition theorem for

*the*

*k*-

*server*problem is presented. ... Whereas all previous theorems are for

*the*case of a finite metric with

*k*+ 1 points,

*the*theorem given here allows an arbitrary number of points in

*the*underlying metric space. ... Central to

*the*

*k*-

*server*problem is

*the*

*k*-

*server*

*conjecture*, which proposes that there is a deterministic

*k*-

*server*algorithm which is

*k*-competitive for all metrics. ...

##
###
A general private information retrieval scheme for MDS coded databases with colluding servers
[article]

2017
*
arXiv
*
pre-print

We build a general private information retrieval scheme for MDS coded databases with colluding

arXiv:1704.06785v1
fatcat:xmpvzhzch5bzxloemyhf5dkfw4
*servers*. Our scheme achieves*the*rate (1+R+R^2+...+R^M-1), where R=1-N-T*K*/N*K*. ... PIR capacity is*the*maximal number of bits privately retrieved per*one*bit of downloaded bit.*The*capacity has been fully solved for some degenerating cases. ... For*the*non-degenerating cases,*one*can see that our rate is strictly smaller than*the**conjectured*capacity in (2) . ...##
###
Design Heuristic for Parallel Many Server Systems under FCFS-ALIS
[article]

2018
*
arXiv
*
pre-print

We consider

arXiv:1603.01404v2
fatcat:ykkyxwkkwzdlbgjcfn2hgqyzcm
*the*service policy that always assigns*servers*to*the*first, longest waiting compatible customer, and that always assigns customers to*the*longest idle compatible*server*if*on*arrival, multiple ... In particular,*the*calculation of matching rates,*the*fraction of services of customer-*server*type, is intractable. ... Khinchine [20] ), which indicates that our*conjecture**on**server*availability may in fact be true. ...##
###
Stability of multi-server polling system with server limits

2011
*
Queueing systems
*

We postulate a

doi:10.1007/s11134-011-9254-x
fatcat:dh4wk4dt3bct3ielchkyd3adl4
*conjecture*for*the*stability condition in this case that is supported by our simulation results. ... We consider a multi-*server*polling system with*server*limits, that is*the*number of*servers*that can attend a queue simultaneously is limited. ...*The*stability condition of a multi-*server*polling system with a*K*-limited service policy (i.e.,*on*each visit,*the**server*takes*K*customers or empties*the*queue if number waiting is less than*K*) 1 was ...
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