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Deterministic approximation of the cover time

Uriel Feige, Yuri Rabinovich
2003 Random structures & algorithms (Print)  
We present a 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).  ... 
doi:10.1002/rsa.10083 fatcat:ll2afjvrdfdezcaabergawquy4

Deterministic approximation for the cover time of trees [article]

Uriel Feige, Ofer Zeitouni
2009 arXiv   pre-print
We present a 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).  ... 
arXiv:0909.2005v1 fatcat:zwknzgmhprdgvaxt3ca6srcxzi

Deterministically Maintaining a (2 + ∊)-Approximate Minimum Vertex Cover in O(1/∊2) Amortized Update Time [chapter]

Sayan Bhattacharya, Janardhan Kulkarni
2019 Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms  
We show how to maintain a (2 + )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.  ... 
doi:10.1137/1.9781611975482.113 dblp:conf/soda/BhattacharyaK19 fatcat:i6f6ka7op5dgdoimhul5hhuie4

Scheduling Subset Tests: One-Time, Continuous, and How They Relate [chapter]

Edith Cohen, Haim Kaplan, Yishay Mansour
2013 Lecture Notes in Computer Science  
Since one-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.  ... 
doi:10.1007/978-3-642-40328-6_7 fatcat:hpwkzufjizgqriqr7dyyzomsja

Distributed algorithms for edge dominating sets

Jukka Suomela
2010 Proceeding of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '10  
minimum edge dominating sets • using 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  ... 
doi:10.1145/1835698.1835783 dblp:conf/podc/Suomela10 fatcat:ngv36ttsfnakfnnx5o5vlamg34

Randomized greedy algorithms for covering problems

Wanru Gao, Tobias Friedrich, Frank Neumann, Christian Hercher
2018 Proceedings of the Genetic and Evolutionary Computation Conference on - GECCO '18  
In this paper, we explore 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  ... 
doi:10.1145/3205455.3205542 dblp:conf/gecco/Gao0NH18 fatcat:rfugcepupfhc5kup32r4a5vx2q

Deterministic Dominating Set Construction in Networks with Bounded Degree [chapter]

Roy Friedman, Alex Kogan
2011 Lecture Notes in Computer Science  
We show that any 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  ... 
doi:10.1007/978-3-642-17679-1_6 fatcat:sojym5lsirgujmmynq4ia7wgnq

A Deterministic Distributed 2-Approximation for Weighted Vertex Cover in O( nΔ / ^2Δ) Rounds [article]

Ran Ben-Basat, Guy Even, Ken-ichi Kawarabayashi, Gregory Schwartzman
2018 arXiv   pre-print
We present a 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] .  ... 
arXiv:1804.01308v3 fatcat:do3txbqk3vberamwxif7gw6hga

Local Algorithms: Self-stabilization on Speed [chapter]

Christoph Lenzen, Jukka Suomela, Roger Wattenhofer
2009 Lecture Notes in Computer Science  
This work was supported in part by 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.  ... 
doi:10.1007/978-3-642-05118-0_2 fatcat:tp3fdm4hzvcjdjgbqxbeuaqwmy

The Remote Set Problem on Lattices [chapter]

Ishay Haviv
2012 Lecture Notes in Computer Science  
We show a polynomialtime 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.  ... 
doi:10.1007/978-3-642-32512-0_16 fatcat:2rcqybce45cbbo7c2tkkepp3xa

The remote set problem on lattices

Ishay Haviv
2014 Computational Complexity  
We show a polynomialtime 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.  ... 
doi:10.1007/s00037-014-0094-z fatcat:bzd5szmvtzgcjgn7h7fycxxxvy

A simple local 3-approximation algorithm for vertex cover

Valentin Polishchuk, Jukka Suomela
2009 Information Processing Letters  
We present a local algorithm (constant-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  ... 
doi:10.1016/j.ipl.2009.02.017 fatcat:seovxzdeqrez3ox4oh7u5go2xq

Approximation and Inapproximation for the Influence Maximization Problem in Social Networks under Deterministic Linear Threshold Model

Zaixin Lu, Wei Zhang, Weili Wu, Bin Fu, Dingzhu Du
2011 2011 31st International Conference on Distributed Computing Systems Workshops  
We also show that 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.  ... 
doi:10.1109/icdcsw.2011.33 dblp:conf/icdcsw/LuZWFD11 fatcat:3sb5yvtj6rbshiqt4qcxvlbtta

Fast and Deterministic Approximations for k-Cut

Kent Quanrud, Michael Wagner
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.  ... 
doi:10.4230/lipics.approx-random.2019.23 dblp:conf/approx/Quanrud19 fatcat:ffcftkfmlrhypb3bxm7oggfthy

Deterministic Algorithms for Multi-criteria TSP [chapter]

Bodo Manthey
2011 Lecture Notes in Computer Science  
We present 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 ) .  ... 
doi:10.1007/978-3-642-20877-5_27 fatcat:t4ankaqitngmbb6q3keu27tdvm
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