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Correlation decay and partition function zeros: Algorithms and phase transitions
[article]

2022
*
arXiv
*
pre-print

This extension allows us to give the first

arXiv:1906.01228v6
fatcat:6qeo7cwcangt7n2dto6rhxp2c4
*deterministic*FPTAS*for**counting*the number of q-*colorings*of*a*graph of maximum degree*Δ*provided only that q≥*2**Δ*. ... This matches the natural bound*for*randomized*algorithms*obtained by*a*straightforward application of Markov chain Monte Carlo. ... Acknowledgments We thank Guus Regts and anonymous reviewers*for*their various helpful comments. JL was*a*PhD student at UC Berkeley when this work was carried out. ...##
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Local Multicoloring Algorithms: Computing a Nearly-Optimal TDMA Schedule in Constant Time

2009
*
Symposium on Theoretical Aspects of Computer Science
*

We prove that there is

doi:10.4230/lipics.stacs.2009.1852
dblp:conf/stacs/Kuhn09
fatcat:73jcuckk6necnfcskc2usc55wy
*a**deterministic**algorithm*that uses*a*total of |C| = O(∆*2*log(N )/ε*2*)*colors*such that*for*every node v of G (i.e.,*for*every , Ω(∆*2*+ log log N )*colors*are necessary even to ...*For*graphs*with*maximum degree ∆ = Ω(log |V |), Ω(∆ log |V |/ log log |V |)*colors*are needed in expectation, even to compute*a*valid*coloring*. ...*A*node v*with*degree*δ*chooses the*colors*of all instances*for*which*2*i ≥*δ*. ...##
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Balanced families of perfect hash functions and their applications

2010
*
ACM Transactions on Algorithms
*

Using the technique of

doi:10.1145/1798596.1798607
fatcat:yxwtjntrbzgcfo44vxkyrm2xba
*color*-coding we can apply our explicit constructions to devise approximation*algorithms**for*various*counting*problems in graphs. ... Our main result is that*for*any constant*δ*> 1,*a**δ*balanced (n, k)-family of perfect hash functions of size*2*O(k log log k) log n can be constructed in time*2*O(k log log k) n log n. ... We settle in the affirmative the open question they raise concerning the existence of*a**deterministic*approximate*counting**algorithm**for*this problem. ...##
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Local Multicoloring Algorithms: Computing a Nearly-Optimal TDMA Schedule in Constant Time
[article]

2009
*
arXiv
*
pre-print

Many channel access schemes assign

arXiv:0902.1868v1
fatcat:qmik7yjekbdbdkv4mkiw5jyany
*a*fixed set of time slots, frequencies, or (orthogonal) codes to the nodes of*a*network such that nodes that interfere*with*each other receive disjoint sets of time slots ... Finding*a*valid assignment of time slots, frequencies, or codes hence directly corresponds to computing*a*multicoloring of*a*graph G. ...*A*node v*with*degree*δ*chooses the*colors*of all instances*for*which*2*i ≥*δ*. ...##
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Balanced Families of Perfect Hash Functions and Their Applications

2008
*
arXiv
*
pre-print

Using the technique of

arXiv:0805.4300v1
fatcat:tmnirbqvgfba3lms6glnxebvku
*color*-coding we can apply our explicit constructions to devise approximation*algorithms**for*various*counting*problems in graphs. ... Our main result is that*for*any constant*δ*> 1,*a**δ*-balanced (n,k)-family of perfect hash functions of size*2*^O(k k) n can be constructed in time*2*^O(k k) n n. ... We settle in the affirmative the open question they raise concerning the existence of*a**deterministic*approximate*counting**algorithm**for*this problem. ...##
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Generalized Reordering Buffer Management

2014
*
Symposium on Theoretical Aspects of Computer Science
*

We further demonstrate that if our

doi:10.4230/lipics.stacs.2014.87
dblp:conf/stacs/AzarEGK14
fatcat:4atds2ch2jcsfl3h7deyrnqnty
*deterministic**algorithm*can employ k/(1 −*δ*) servers where*δ*∈ (0, 1), then it achieves*a*competitive ratio of O(min{ln b/*δ**2*, b/*δ*}) against an optimal offline adversary ... We complement our randomized approach by presenting*a**deterministic**algorithm*that attains*a*competitive ratio of O(min{k*2*ln b, kb}). ...*A**Deterministic**Algorithm*We develop two*deterministic**algorithms*: the first has*a*competitive ratio of O(ln b/*δ**2*) in*a**δ*-augmentation setting and*a*competitive ratio of O(k*2*ln b) when there is no ...##
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Distributed (Δ+1)-Coloring in Sublogarithmic Rounds
[article]

2018
*
arXiv
*
pre-print

We give

arXiv:1603.01486v4
fatcat:esqg5746onfyjprhdl2lhoso6i
*a*new randomized distributed*algorithm**for*(*Δ*+1)-*coloring*in the LOCAL model, running in O(√(*Δ*))+*2*^O(√( n)) rounds in*a*graph of maximum degree*Δ*. ... Our*algorithm*also extends to list-*coloring*where the palette of each node contains*Δ*+1*colors*. ... Acknowledgments: We would like to thank Seth Pettie*for*his valuable comments. We thank the anonymous reviewers*for*many helpful suggestions and comments. ...##
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Optimization of data allocation in hierarchical memory for blocked shortest paths algorithms

2021
*
Sistemnyj Analiz i Prikladnaâ Informatika
*

In second case, the paper formulates

doi:10.21122/2309-4923-2021-3-40-50
fatcat:pxf7pjf3azcwpobyxc5llcpvna
*a*problem of weighted defective*color*-*count*constrained*coloring*of the conflict graph and solves it by developing*a*random*algorithm*. ...*a*non-conflict matrix allocation is possible at*δ*= 0.5*for*M = 4 and at*δ*= 0.1*for*M = 20. ... The Hajnal-Szemerédi theorem [17] proves that any graph*with*maximum degree*Δ*has an equitable*coloring**with**Δ*+ 1*colors*. ...##
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Distributed Edge Coloring in Time Polylogarithmic in Δ

2022
*
Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing
*

This improves

doi:10.1145/3519270.3538440
fatcat:skc5omvjyre4df3hx6d2a4vcwa
*a*result of Balliu, Kuhn, and Olivetti [PODC '20], who gave an*algorithm**with**a*quasi-polylogarithmic dependency on*Δ*. ... The best previous 𝑂 (*Δ*)-edge*coloring**algorithm*that can be implemented in the CONGEST model is by Barenboim and Elkin [PODC '11] and it computes*a**2*𝑂 (1/𝜀)*Δ*edge*coloring*in time 𝑂 (*Δ*𝜀 + log * ... While*for*MIS and matching, there is*a*linear-in-*Δ*lower bound,*for*(*Δ*+ 1)-vertex*coloring*and (*2**Δ*− 1)-edge*coloring*, there are in fact*algorithms**with**a*sublinear-in-*Δ*complexity. ...##
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Distributed local approximation algorithms for maximum matching in graphs and hypergraphs
[article]

2020
*
arXiv
*
pre-print

This gives an

arXiv:1807.07645v7
fatcat:4yaui54cd5ahhhac7byids5k6u
*algorithm**for*(*2**Δ*- 1)-edge-list*coloring*in Õ(log^*2**Δ*log n) rounds*deterministically*or Õ( (loglog n)^3 ) rounds randomly. ... Our main result is*a**deterministic**algorithm*to generate*a*matching which is an O(r)-approximation to the maximum weight matching, running in Õ(r log*Δ*+ log^*2**Δ*+ log^* n) rounds. ... Let G be*a*graph*with*maximum degree ∆. (1) There is aÕ(log n log*2*∆)-round*deterministic**algorithm**for*(*2*∆ − 1)-list-edge-*coloring*. (*2*) There is aÕ((log log n) 3 )-round randomized*algorithm**for*(*2*∆ ...##
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Correlation decay and deterministic FPTAS for counting list-colorings of a graph
[article]

2007
*
arXiv
*
pre-print

We propose

arXiv:math/0606143v2
fatcat:bc54aenln5bk3d4fhq5ridsmxi
*a**deterministic**algorithm**for*approximately*counting*the number of list*colorings*of*a*graph. ...*For*the case when the size of the each list is*a*large constant, we show the existence of*a**deterministic*FPTAS*for*computing the total number of list*colorings*. ... Acknowledgements The authors are very thankful to Devavrat Shah*for*contributing many important comments*for*this work. ...##
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Correlation decay and deterministic FPTAS for counting colorings of a graph

2012
*
Journal of Discrete Algorithms
*

We construct

doi:10.1016/j.jda.2010.10.002
fatcat:jod2arkcsnfcrd3mp5oo2u4wh4
*a**deterministic**algorithm**for*approximately*counting*the number of*colorings*of*a*graph. ... The same*deterministic**algorithm*has complexity*2*O (log*2*n) , without any assumptions on the number of*colors*, where n is the instance size. ... Acknowledgements The authors are very thankful to Devavrat Shah*for*contributing many important comments*for*this work, and to the anonymous reviewers*for**a*careful reading of the manuscript and providing ...##
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MIS on trees

2011
*
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '11
*

This basic symmetry breaking structure is vital

doi:10.1145/1993806.1993813
dblp:conf/podc/LenzenW11
fatcat:nqaqwrvtlncu5ju62yhg2x3qpq
*for*many distributed*algorithms*, which by now has been fueling the search*for*fast local*algorithms*to find such sets over several decades. ... Our*algorithm*is uniform and nodes need to exchange merely O(log n) many bits*with*high probability. ... This was changed by Barenboim and Elkin [3] , who devised*a**deterministic**algorithm**with*running time o(log n)*for*graphs*with*arboricity*2*o( √ log n). ...##
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Simple deterministic approximation algorithms for counting matchings

2007
*
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing - STOC '07
*

Additionally,

doi:10.1145/1250790.1250809
dblp:conf/stoc/BayatiGKNT07
fatcat:ihuxkfheevgcdjmlyikmdfvtve
*for*an arbitrary graph, we construct*a**deterministic**algorithm**for*computing approximately the number of matchings within running time exp(O( √ n log*2*n)), where n is the number of vertices ... We construct*a**deterministic*fully polynomial time approximation scheme (FPTAS)*for*computing the total number of matchings in*a*bounded degree graph. ... Conclusions We have constructed*a**deterministic**algorithm**for**counting*approximately the number of matchings of*a*given graph. ...##
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Approximating the Number of Network Motifs

2009
*
Internet Mathematics
*

We present several

doi:10.1080/15427951.2009.10390645
fatcat:andmbsem3zanpke5rgriqkhhum
*algorithms**with*time complexity O e 2k k • n • |E| • log 1*δ*/*2*that,*for*the first time, approximate*for*every vertex the number of non-induced occurrences of the motif the vertex ... Some of our*algorithms*use the*color*coding technique. ... Acknowledgment: We thank Dana Ron*for*many hours of fruitful discussions. ...
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