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Deterministic approximation of the cover time

2003
*
Random structures & algorithms (Print)
*

We present a

doi:10.1002/rsa.10083
fatcat:ll2afjvrdfdezcaabergawquy4
*deterministic*algorithm that given a tree T with n vertices, a starting vertex v and a slackness parameter ǫ > 0, estimates within an additive error*of*ǫ*the**cover*and return*time*, namely, ... We also show how*the*algorithm can be extended to estimate*the*expected*cover*(without return)*time*on trees. ... Acknowledgements*The*work*of**the*authors is supported in part by*The*Israel Science Foundation (grants No. 873/08 and 938/07, respectively). ...##
###
Deterministic approximation for the cover time of trees
[article]

2009
*
arXiv
*
pre-print

We present a

arXiv:0909.2005v1
fatcat:zwknzgmhprdgvaxt3ca6srcxzi
*deterministic*algorithm that given a tree T with n vertices, a starting vertex v and a slackness parameter epsilon > 0, estimates within an additive error*of*epsilon*the**cover*and return*time*... We also show how*the*algorithm can be extended to estimate*the*expected*cover*(without return)*time*on trees. ... Acknowledgements*The*work*of**the*authors is supported in part by*The*Israel Science Foundation (grants No. 873/08 and 938/07, respectively). ...##
###
Deterministically Maintaining a (2 + ∊)-Approximate Minimum Vertex Cover in O(1/∊2) Amortized Update Time
[chapter]

2019
*
Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms
*

We show how to maintain a (2 + )

doi:10.1137/1.9781611975482.113
dblp:conf/soda/BhattacharyaK19
fatcat:i6f6ka7op5dgdoimhul5hhuie4
*approximate*minimum vertex*cover*,*deterministically*, in this setting in O(1/ 2 ) amortized update*time*. ... Prior to our work,*the*best known*deterministic*algorithm for maintaining a (2 + )-*approximate*minimum vertex*cover*was due to Bhattacharya, Henzinger and Italiano [SODA 2015]. ... We want to design a dynamic algorithm for minimum vertex*cover*that is*deterministic*and has (near) optimal*approximation*ratio and amortized update*time*. ...##
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Scheduling Subset Tests: One-Time, Continuous, and How They Relate
[chapter]

2013
*
Lecture Notes in Computer Science
*

Since one-

doi:10.1007/978-3-642-40328-6_7
fatcat:hpwkzufjizgqriqr7dyyzomsja
*time*and continuous testing can be viable alternatives, we study*the*overhead*of*continuous testing, captured by*the*ratio*of*optimal one-*time*to continuous*cover**times*. ...*The*schedule is a sequence*of*test invokations with*the*goal*of**covering*all elements. ... For an element e, M t [e|σ] is*the*maximum over*time*t*of**the**cover**time**of*e at*time*t, and E t [e|σ] is*the*(limit*of*)*the*average over*time*t*of**the**cover**time**of*e at*time*t. ...##
###
Distributed algorithms for edge dominating sets

2010
*
Proceeding of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '10
*

minimum edge dominating sets
• using

doi:10.1145/1835698.1835783
dblp:conf/podc/Suomela10
fatcat:ngv36ttsfnakfnnx5o5vlamg34
*deterministic*distributed algorithms, in*the*port-numbering model • But why would we care? ... • Contribution: full characterisation*of**approximability**of*edge dominating sets in regular graphs and bounded-degree graphs Edge dominating sets:*deterministic*algorithms in port-numbering model ...##
###
Randomized greedy algorithms for covering problems

2018
*
Proceedings of the Genetic and Evolutionary Computation Conference on - GECCO '18
*

In this paper, we explore

doi:10.1145/3205455.3205542
dblp:conf/gecco/Gao0NH18
fatcat:rfugcepupfhc5kup32r4a5vx2q
*the*use*of*randomness in greedy algorithms for*the*minimum vertex*cover*and dominating set problem and compare*the*resulting performance against their*deterministic*counterpart ... Our algorithms are based on a parameter γ which allows to explore*the*spectrum between uniform and*deterministic*greedy selection in*the*steps*of**the*algorithm and our theoretical and experimental investigations ...*of*an n-by-n grid by dominos is a problem, where*the*best known*deterministic*algorithms are exponential*time*, but there are efficient randomized*approximation*algorithms [11] ), and (3)*the*dining philosophers ...##
###
Deterministic Dominating Set Construction in Networks with Bounded Degree
[chapter]

2011
*
Lecture Notes in Computer Science
*

We show that any

doi:10.1007/978-3-642-17679-1_6
fatcat:sojym5lsirgujmmynq4ia7wgnq
*deterministic*algorithm with non-trivial*approximation*ratio requires Ω(log * n) rounds, meaning effectively that no o(Δ)-*approximation**deterministic*algorithm with a running*time*independent ... On*the*positive side, we show two*deterministic*algorithms that achieve log Δ and 2 log Δ-*approximation*in O(Δ 3 + log * n) and O(Δ 2 log Δ + log * n)*time*, respectively. ... Acknowledgments We would like to thank Fabian Kuhn and Jukka Suomela for fruitful discussions on*the*subject, and to anonymous reviewers whose valuable comments helped to improve*the*presentation*of*this ...##
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A Deterministic Distributed 2-Approximation for Weighted Vertex Cover in O( nΔ / ^2Δ) Rounds
[article]

2018
*
arXiv
*
pre-print

We present a

arXiv:1804.01308v3
fatcat:do3txbqk3vberamwxif7gw6hga
*deterministic*distributed 2-*approximation*algorithm for*the*Minimum Weight Vertex*Cover*problem in*the*CONGEST model whose round complexity is O( n Δ / ^2 Δ). ... Our solution generalizes*the*(2+ϵ)-*approximation*algorithm*of*[BCS17], improving*the*dependency on ϵ^-1 from linear to logarithmic. ... For any constant ǫ > 0, if*the*Unique Games conjecture holds, no polynomial-*time*algorithm can compute a (2 − ǫ)*approximation**of**the*minimum vertex*cover*[KR08] . ...##
###
Local Algorithms: Self-stabilization on Speed
[chapter]

2009
*
Lecture Notes in Computer Science
*

This work was supported in part by

doi:10.1007/978-3-642-05118-0_2
fatcat:tp3fdm4hzvcjdjgbqxbeuaqwmy
*the*Academy*of*Finland, Grant 116547, by Helsinki Graduate School in Computer Science and Engineering (Hecse), and by*the*Foundation*of*Nokia Corporation. ... For example, in*the*case*of*a constant ∆,*the*above-mentioned algorithm finds a 2-*approximation**of*a minimum vertex*cover*in constant*time*. ...*The*endpoints*of*a maximal matching form a 2-*approximation**of*vertex*cover*. ...##
###
The Remote Set Problem on Lattices
[chapter]

2012
*
Lecture Notes in Computer Science
*

We show a polynomialtime

doi:10.1007/978-3-642-32512-0_16
fatcat:2rcqybce45cbbo7c2tkkepp3xa
*deterministic*algorithm that on rank n lattice L outputs a set*of*points at least one*of*which is log n/n · ρ(L)-far from L, where ρ(L) stands for*the**covering*radius*of*L (i.e ... As an application, we show that*the**Covering*Radius Problem with*approximation*factor n/ log n lies in*the*complexity class NP, improving a result*of*Guruswami, Micciancio and Regev by a factor*of*log ... one*of*them from*the*lattice*approximates**the**covering*radius to within a factor*of*n/ log n. ...##
###
The remote set problem on lattices

2014
*
Computational Complexity
*

We show a polynomialtime

doi:10.1007/s00037-014-0094-z
fatcat:bzd5szmvtzgcjgn7h7fycxxxvy
*deterministic*algorithm that on rank n lattice L outputs a set*of*points at least one*of*which is log n/n · ρ(L)-far from L, where ρ(L) stands for*the**covering*radius*of*L (i.e ... As an application, we show that*the**Covering*Radius Problem with*approximation*factor n/ log n lies in*the*complexity class NP, improving a result*of*Guruswami, Micciancio and Regev by a factor*of*log ... one*of*them from*the*lattice*approximates**the**covering*radius to within a factor*of*n/ log n. ...##
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A simple local 3-approximation algorithm for vertex cover

2009
*
Information Processing Letters
*

We present a local algorithm (constant-

doi:10.1016/j.ipl.2009.02.017
fatcat:seovxzdeqrez3ox4oh7u5go2xq
*time*distributed algorithm) for finding a 3-*approximate*vertex*cover*in bounded-degree graphs. ...*The*algorithm is*deterministic*, and no auxiliary information besides port numbering is required. ... This research was supported in part by*the*Academy*of*Finland, Grants 116547 and 118653 (ALGODAN), by Helsinki Graduate School in Computer Science and Engineering (Hecse), and by*the*Foundation*of*Nokia ...##
###
Approximation and Inapproximation for the Influence Maximization Problem in Social Networks under Deterministic Linear Threshold Model

2011
*
2011 31st International Conference on Distributed Computing Systems Workshops
*

We also show that

doi:10.1109/icdcsw.2011.33
dblp:conf/icdcsw/LuZWFD11
fatcat:3sb5yvtj6rbshiqt4qcxvlbtta
*the*exact computation*of**the*final influence given a seed set can be solved in linear*time*in*the**deterministic*linear threshold model. ... Using an analysis framework based on Set*Cover*, we show a O(logn)*approximation*in*the*case that a people become active when one*of*its neighbors is activated. ... This research work is supported in part by National Science Foundation*of*USA under grants CNS 1016320 and CCF 0829993. ...##
###
Fast and Deterministic Approximations for k-Cut

2019
*
International Workshop on Approximation Algorithms for Combinatorial Optimization
*

*The*first concerns

*the*role

*of*randomization. Is there a

*deterministic*algorithm for 2-

*approximate*k-cuts matching

*the*randomized running

*time*

*of*Õ(km)? ... We give a

*deterministic*

*approximation*algorithm that computes (2 + )-minimum k-cuts in O m log 3 n/ 2

*time*, via a (1 + )-

*approximation*for an LP relaxation

*of*k-cut. ...

*The*main result We make progress on both

*of*these questions with a

*deterministic*and nearly linear

*time*(2 + )-

*approximation*scheme for minimum k-cuts. ...

##
###
Deterministic Algorithms for Multi-criteria TSP
[chapter]

2011
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/978-3-642-20877-5_27
fatcat:t4ankaqitngmbb6q3keu27tdvm
*deterministic**approximation*algorithms for*the*multi-criteria traveling salesman problem (TSP). Our algorithms are faster and simpler than*the*existing randomized algorithms. ... Our algorithms are self-contained and do not use existing*approximation*schemes as black boxes. Second, we adapt*the*generic cycle*cover*algorithm for Min-TSP. ... For every k ≥ 2 and ε > 0, Algorithm 3 is a*deterministic**approximation*algorithm for k-Max-STSP that achieves an*approximation*ratio*of*1 2k − ε and has a running-*time**of*n O(k 3 /ε 3 ) . ...
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