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Distributed Approximation Algorithms for Finding 2-Edge-Connected Subgraphs [chapter]

Sven O. Krumke, Peter Merz, Tim Nonner, Katharina Rupp
Lecture Notes in Computer Science  
A 2-ECSS of a graph is a subgraph that, for each pair of vertices, contains at least two edge-disjoint paths connecting these vertices.  ...  We present a distributed 3 2 -approximation algorithm for the unweighted 2-ECSS construction problem that requires O(n) communication rounds and O(m) messages.  ...  Theorem 2. [15] Algorithm A card is a distributed 3 2 -approximation algorithm for unweighted 2-ECSS construction problem.  ... 
doi:10.1007/978-3-540-77096-1_12 dblp:conf/opodis/KrumkeMNR07 fatcat:3jm3t3v2gzgqdlosgj7mzuvdv4

A simple randomized scheme for constructing low-weight k-connected spanning subgraphs with applications to distributed algorithms

Maleq Khan, Gopal Pandurangan, V.S. Anil Kumar
2007 Theoretical Computer Science  
the expected message complexity of our algorithm is significantly better than the best distributed algorithm that finds an optimal k-connected subgraph.  ...  We then show that our scheme can be applied to design an efficient distributed algorithm for constructing such an approximate k-connected spanning subgraph (for any k ≥ 1) in a point-to-point distributed  ...  Acknowledgments We are very grateful to the referees for their careful reading of the paper and detailed comments, which helped greatly in improving the presentation of the paper.  ... 
doi:10.1016/j.tcs.2007.05.028 fatcat:xm2rncvi7rdvrmhmrpe5lew7gq

Power optimization in fault-tolerant topology control algorithms for wireless multi-hop networks

MohammadTaghi Hajiaghayi, Nicole Immorlica, Vahab S. Mirrokni
2003 Proceedings of the 9th annual international conference on Mobile computing and networking - MobiCom '03  
In this case, we present simple and practical distributed algorithms for the cases of 2-and 3-connectivity with constant approximation factors.  ...  We generalize this algorithm to obtain an O(k 2c+2 )-approximation for general k-connectivity (2 ≤ c ≤ 4 is the power attenuation exponent).  ...  For graphs whose edge lengths form a metric, we present simple and practical distributed algorithms with constant approximation factors for the cases of 2-and 3-connectivity.  ... 
doi:10.1145/938985.939016 dblp:conf/mobicom/HajiaghayiIM03 fatcat:cp4yokolmnbn3ixwnlcxjdjvmy

Power Optimization in Fault-Tolerant Topology Control Algorithms for Wireless Multi-hop Networks

M.T. Hajiaghayi, N. Immorlica, V.S. Mirrokni
2007 IEEE/ACM Transactions on Networking  
In this case, we present simple and practical distributed algorithms for the cases of 2-and 3-connectivity with constant approximation factors.  ...  We generalize this algorithm to obtain an O(k 2c+2 )-approximation for general k-connectivity (2 ≤ c ≤ 4 is the power attenuation exponent).  ...  For graphs whose edge lengths form a metric, we present simple and practical distributed algorithms with constant approximation factors for the cases of 2-and 3-connectivity.  ... 
doi:10.1109/tnet.2007.902680 fatcat:g5y2t432pjgcndlkjkvdv7rbfy

Power optimization in fault-tolerant topology control algorithms for wireless multi-hop networks

MohammadTaghi Hajiaghayi, Nicole Immorlica, Vahab S. Mirrokni
2003 Proceedings of the 9th annual international conference on Mobile computing and networking - MobiCom '03  
In this case, we present simple and practical distributed algorithms for the cases of 2-and 3-connectivity with constant approximation factors.  ...  We generalize this algorithm to obtain an O(k 2c+2 )-approximation for general k-connectivity (2 ≤ c ≤ 4 is the power attenuation exponent).  ...  For graphs whose edge lengths form a metric, we present simple and practical distributed algorithms with constant approximation factors for the cases of 2-and 3-connectivity.  ... 
doi:10.1145/939014.939016 fatcat:tx4iw6vnz5gahcwjczcrhfxflu

Deploying Sensor Networks With Guaranteed Fault Tolerance

J.L. Bredin, E.D. Demaine, M.T. Hajiaghayi, D. Rus
2010 IEEE/ACM Transactions on Networking  
We have implemented greedy and distributed versions of this algorithm, and demonstrate in simulation that they produce high-quality placements for the additional sensors.  ...  We design and analyze the first algorithms that place an almost-minimum number of additional sensors to augment an existing network into a k-connected network, for any desired parameter k.  ...  Our algorithm finds an -approximation to the minimum-weight -connected subgraph, and then for every edge of weight , adds sensors.  ... 
doi:10.1109/tnet.2009.2024941 fatcat:imsothprlbfkrgcnvxwry3emnq

Deploying sensor networks with guaranteed capacity and fault tolerance

Jonathan L. Bredin, Erik D. Demaine, MohammadTaghi Hajiaghayi, Daniela Rus
2005 Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing - MobiHoc '05  
We have implemented greedy and distributed versions of this algorithm, and demonstrate in simulation that they produce high-quality placements for the additional sensors.  ...  We design and analyze the first algorithms that place an almostminimum number of additional sensors to augment an existing network into a k-connected network, for any desired parameter k.  ...  Our algorithm finds an α-approximation to the minimum-weight k-connected subgraph, and then for every edge of weight w ≥ 1, adds kw + 2k − 2 < 3kw sensors.  ... 
doi:10.1145/1062689.1062729 dblp:conf/mobihoc/BredinDHR05 fatcat:bk4im6a3ofbjhd2opbpdokgiie

Motif discovery algorithms in static and temporal networks: A survey

Ali Jazayeri, Christopher C Yang, Peter Holme
2020 Journal of Complex Networks  
The complexities associated with graph and subgraph isomorphism problems, as the core of frequent subgraph mining, directly impact the performance of motif discovery algorithms.  ...  In this article, we provide a survey of motif discovery algorithms proposed in the literature for mining static and temporal networks and review the corresponding algorithms based on their adopted strategies  ...  GRAFT [133] is another approximate frequency algorithm for creating graphlet frequency distribution for subgraph up to five vertices.  ... 
doi:10.1093/comnet/cnaa031 fatcat:7hasephaffajdl5bn7gl33qn2a

Distributed Verification and Hardness of Distributed Approximation

Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, Roger Wattenhofer
2012 SIAM journal on computing (Print)  
as connectivity, spanning connected subgraph, and s − t cut verification.  ...  Our result implies that there can be no distributed approximation algorithm for MST that is significantly faster than the current exact algorithm, for any approximation factor.  ...  in H and 2 on other edges and find the MST using an algorithm in [15] .  ... 
doi:10.1137/11085178x fatcat:xkvkvn6hlnh6vi4f56szewjv4m

Distributed verification and hardness of distributed approximation

Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, Roger Wattenhofer
2011 Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11  
as connectivity, spanning connected subgraph, and s − t cut verification.  ...  Our result implies that there can be no distributed approximation algorithm for MST that is significantly faster than the current exact algorithm, for any approximation factor.  ...  in H and 2 on other edges and find the MST using an algorithm in [15] .  ... 
doi:10.1145/1993636.1993686 dblp:conf/stoc/SarmaHKKNPPW11 fatcat:igixoskxrbhntjdntoox7snmnq

Large Very Dense Subgraphs in a Stream of Edges [article]

Claire Mathieu, Michel de Rougemont
2020 arXiv   pre-print
A subgraph S is very dense if it has Ω(|S|^2) edges. We uniformly sample the edges with a Reservoir of size k=O(√(n).log n).  ...  We study the detection and the reconstruction of a large very dense subgraph in a social graph with n nodes and m edges given as a stream of edges, when the graph follows a power law degree distribution  ...  An Ω( ) lower bound is presented in [5] for the -approximation of the maximum density ratio * , i.e. to find a subgraph with a vertex such that ( ) ≥ * / .  ... 
arXiv:2010.07794v1 fatcat:qd3odlcpg5gn3eq6udyc63gmve

Distributed Verification and Hardness of Distributed Approximation [article]

Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, Roger Wattenhofer
2011 arXiv   pre-print
Our result implies that there can be no distributed approximation algorithm for MST that is significantly faster than the current exact algorithm, for any approximation factor.  ...  as connectivity, spanning connected subgraph, and s-t cut verification.  ...  For any Γ, d ≥ 2, p and ǫ ≥ 0, if there exists an ǫ-error distributed algorithm for the spanning connected subgraph verification problem on graph G(Γ, d, p) then there exists an ǫ-error algorithm for verifying  ... 
arXiv:1011.3049v3 fatcat:wctqtam435hxldsbeh2apbt3fy

Distributed Almost Exact Approximations for Minor-Closed Families [chapter]

Andrzej Czygrinow, Michał Hańćkowiak
2006 Lecture Notes in Computer Science  
We give efficient deterministic distributed algorithms which given a graph G from a proper minor-closed family C find an approximation of a minimum dominating set in G and a minimum connected dominating  ...  The algorithms are deterministic and run in a polylogarithmic number of rounds. The approximation accomplished differs from an optimal by a multiplicative factor of (1 + o(1)).  ...  Distributed approximation algorithms for planar graphs were studied in [CH04] and [CHS06] .  ... 
doi:10.1007/11841036_24 fatcat:vgji7jmjjjhu5kwdykiy75f6ki

Motif Discovery Algorithms in Static and Temporal Networks: A Survey [article]

Ali Jazayeri, Christopher C. Yang
2020 arXiv   pre-print
The complexities associated with graph and subgraph isomorphism problems, as the core of frequent subgraph mining, have direct impacts on the performance of motif discovery algorithms.  ...  In this paper, we provide a survey of motif discovery algorithms proposed in the literature for mining static and temporal networks and review the corresponding algorithms based on their adopted strategies  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  ... 
arXiv:2005.09721v1 fatcat:m7ytgi2kajcsdoj2cgz2nba6uy

Distance Approximation in Bounded-Degree and General Sparse Graphs [chapter]

Sharon Marko, Dana Ron
2006 Lecture Notes in Computer Science  
Specifically, these properties are k-edge connectivity, subgraph-freeness (for constant size subgraphs), being a Eulerian graph, and cycle-freeness.  ...  In this model the fraction of edge modifications is taken with respect to n 2 , and the algorithm may ask for the existence of an edge between any pair of vertices of its choice.  ...  A simple modification of our (non-sublinear time) algorithm for approximating the distance to subgraph freeness, yields A local distributed algorithm for approximating the size of a minimum vertex cover  ... 
doi:10.1007/11830924_43 fatcat:vvkdkhnkt5berjzrjnizsgskly
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