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Can We Break Symmetry with o(m) Communication? [article]

Shreyas Pai and Gopal Pandurangan and Sriram V. Pemmaraju and Peter Robinson
2021 arXiv   pre-print
In fact, all known algorithms need at least Ω(m) communication for these problems, where m is the number of edges in the graph.  ...  While significant progress has been made in understanding and improving the running time of such problems, much less is known about the message complexity of these problems.  ...  To the best of our knowledge, we are not aware of other results on the message complexity (in particular, lower bounds and sublinear upper bounds) on fundamental symmetry breaking problems, vis-a-vis the  ... 
arXiv:2105.08917v1 fatcat:trr2hj5pcrgnpgulwxh3ppzaum

Construction of Near-Optimal Vertex Clique Covering for Real-World Networks

David Chalupa
2015 Computing and informatics  
We propose a method based on combining a constructive and a bounding heuristic to solve the vertex clique covering problem (CCP), where the aim is to partition the vertices of a graph into the smallest  ...  Searching for the solution to CCP is highly motivated by analysis of social and other real-world networks, applications in graph mining, as well as by the fact that CCP is one of the classical NP-hard  ...  Acknowledgement The author would like to thank Jiří Pospíchal and the anonymous referees for their very helpful comments on this work.  ... 
dblp:journals/cai/Chalupa15 fatcat:5ibwflpsdrh2lazgwlmzt6xgxa

On the Complexity of Sampling Vertices Uniformly from a Graph

Flavio Chierichetti, Shahrzad Haddadan, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
Finally, we give lower bounds for the problems of estimating the average degree of the graph, and the number of vertices of the graph.  ...  We also give tight bounds for the problem of returning a close-to-uniform-at-random vertex from the graph.  ...  Acknowledgements The authors would like to thank Anirban Dasgupta, Ravi Kumar, Silvio Lattanzi and Tamás Sarlós for several useful discussions.  ... 
doi:10.4230/lipics.icalp.2018.149 dblp:conf/icalp/ChierichettiH18 fatcat:opktyqoucvdbxbfptpbrrzsjsi

Node and Edge Averaged Complexities of Local Graph Problems

Alkida Balliu, Mohsen Ghaffari, Fabian Kuhn, Dennis Olivetti
2022 Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing  
Finally, we consider the problem of computing a sinkless orientation of a graph. The deterministic worst-case complexity of the problem is known to be Θ(log 𝑛), even on bounded-degree graphs.  ...  We continue the recently started line of work on the distributed node-averaged complexity of distributed graph algorithms.  ...  This for example leads, for the (Δ + 1)-coloring problem, to the following node-averaged complexities. The randomized algorithms of [30, 38] are based on the following idea.  ... 
doi:10.1145/3519270.3538419 fatcat:xz4l2ozpgrfxzbxmspaadszd6e

Preconditioner Approximations for Probabilistic Graphical Models

Pradeep Ravikumar, John D. Lafferty
2005 Neural Information Processing Systems  
Our framework yields rigorous upper and lower bounds on event probabilities and the log partition function of undirected graphical models, using non-iterative procedures that have low time complexity.  ...  We present a family of approximation techniques for probabilistic graphical models, based on the use of graphical preconditioners developed in the scientific computing literature.  ...  Acknowledgments We thank Gary Miller for helpful discussions. Research supported in part by NSF grants IIS-0312814 and IIS-0427206.  ... 
dblp:conf/nips/RavikumarL05 fatcat:6faei2kk6rakjd7ynikgko7cdm

Quantum Algorithms for the Triangle Problem [article]

Frederic Magniez, Miklos Santha, Mario Szegedy
2005 arXiv   pre-print
The Triangle Problem was first treated in bdhhmsw01, where an algorithm with O(n+√(nm)) query complexity was presented, where m is the number of edges of G.  ...  The second algorithm uses Õ(n^13/10) queries, and it is based on a design concept of Ambainis amb04 that incorporates the benefits of quantum walks into Grover search gro96.  ...  Acknowledgments We would like to thank Andris Ambainis for useful discussions and for sending us a preliminary version of [Amb04] .  ... 
arXiv:quant-ph/0310134v3 fatcat:brszkmf4enfw7lrhn26zu3hpca

Resource Discovery in Networks under Bandwidth Limitations

Kishori Konwar, Alex Shvartsman
2006 2006 Fifth International Symposium on Parallel and Distributed Computing  
This is done by proving a lower bound on time of Ω(n), where n is the number of participating nodes.  ...  For this model a randomized algorithm is presented that solves the resource discovery problem in O(n log 2 n) time, i.e., within a poly-logarithmic factor of the corresponding lower bound.  ...  Based on this latter observation it is likely that the time complexity to solve the resource discovery on linear directed graphs G 0 or graphs of bounded degree is poly-logarithmic in n.  ... 
doi:10.1109/ispdc.2006.40 dblp:conf/ispdc/KonwarS06 fatcat:jswfkb5qvrgllj6njhy6zwu2zm

Quantum Algorithms for the Triangle Problem

Frédéric Magniez, Miklos Santha, Mario Szegedy
2007 SIAM journal on computing (Print)  
The Triangle Problem was first treated in [12] , where an algorithm with O(n + √ nm) query complexity was presented, where m is the number of edges of G.  ...  The second algorithm usesÕ(n 13/10 ) queries, and it is based on a design concept of Ambainis [6] that incorporates the benefits of quantum walks into Grover search [18] .  ...  We would like to thank Andris Ambainis for useful discussions and for sending us a preliminary version of [6] .  ... 
doi:10.1137/050643684 fatcat:qzg6r6534zg2destfdzjhv4hqi

Entropy/length profiles, bounds on the minimal covering of bipartite graphs, and trellis complexity of nonlinear codes

I. Reuven, Y. Be'ery
1998 IEEE Transactions on Information Theory  
Additionally and independently, we use wellknown information-theoretic measures to derive novel bounds on the minimal covering of a bipartite graph by complete subgraphs.  ...  all possible probability distributions of the codewords.  ...  ACKNOWLEDGMENT The authors wish to thank V. Sidorenko for his review in which he pointed out the application of the results of this paper to graph theory as presented in Section IV.  ... 
doi:10.1109/18.661506 fatcat:uo65zcpytzdupkfubrkyrsqs6q

Learning Bayesian Networks in the Presence of Structural Side Information

Ehsan Mokhtarian, Sina Akbari, Fateme Jamshidi, Jalal Etesami, Negar Kiyavash
2022 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
In particular, we study two types of structural side information about the underlying BN: (I) an upper bound on its clique number is known, or (II) it is diamond-free.  ...  As a consequence of our work, we show that bounded treewidth BNs can be learned with polynomial complexity.  ...  Acknowledgments The work presented in this paper was in part supported by Swiss National Science Foundation (SNSF) under grant number 200021_20435.  ... 
doi:10.1609/aaai.v36i7.20750 fatcat:n5e3mzvzm5eqbo2bpy47rynl7i

A distributed deterministic approximation algorithm for data association

Songhwai Oh
2011 2011 International Conference on Distributed Computing in Sensor Systems and Workshops (DCOSS)  
We then show that the proposed algorithm naturally partitions a complex problem into a set of local problems and develop a distributed version of the algorithm.  ...  In this paper, we consider the Bayesian formulation of data association problems and present a deterministic polynomial-time approximation algorithm with guaranteed error bounds using correlation decay  ...  This new formulation leads to natural partitioning of a complex problem into a set of local problems and a distributed algorithm is developed based on this property.  ... 
doi:10.1109/dcoss.2011.5982153 dblp:conf/dcoss/Oh11 fatcat:5xxp25hf5vfr5e4mti6kdpdg4q

Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs [article]

Ryan L. Mann, Michael J. Bremner
2018 arXiv   pre-print
We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs.  ...  Our algorithm is based on an approach due to Barvinok for approximating evaluations of a polynomial based on the location of the complex zeros and a technique due to Patel and Regts for efficiently computing  ...  MJB acknowledges support from the Australian Research Council as a member of the ARC Centre of Excellence for Quantum Computation and Communication Technology (CQC2T), project number CE170100012.  ... 
arXiv:1806.11282v1 fatcat:cyuqsil4bbe2ffzcscupsis26a

Sample Complexity Bounds for Recurrent Neural Networks with Application to Combinatorial Graph Problems [article]

Nil-Jana Akpinar, Bernhard Kratzwald, Stefan Feuerriegel
2019 arXiv   pre-print
As our primary contribution, this is the first work that upper bounds the sample complexity for learning real-valued RNNs.  ...  As demonstrated based on the NP-hard edge clique cover number, recurrent neural networks (RNNs) are particularly suited for this task and can even outperform state-of-the-art heuristics.  ...  network complexity based on the number of trainable parameters.  ... 
arXiv:1901.10289v2 fatcat:4dcgzxbgffcddmca6oaxwdvpxm

Node and Edge Averaged Complexities of Local Graph Problems [article]

Alkida Balliu, Mohsen Ghaffari, Fabian Kuhn, Dennis Olivetti
2022 arXiv   pre-print
The deterministic worst-case complexity of the problem is known to be Θ(log n), even on bounded-degree graphs.  ...  As a side result, we obtain the same lower bound for the worst-case randomized round complexity for computing an MIS in trees – this essentially answers open problem 11.15 in the book of Barenboim and  ...  There are different ways to construct lifts with desirable properties for a given base graph. As discussed, our lower bound proof is based on the minimum vertex cover lower bound of [KMW16] .  ... 
arXiv:2208.08213v1 fatcat:w4ooljg7dzfpvnerfnsrlpdyne

Accurate and Scalable Techniques for the Complex/Pathway Membership Problem in Protein Networks

Orhan Çamoğlu, Tolga Can, Ambuj K. Singh
2009 Advances in Bioinformatics  
We propose a network flow-based technique to compute the association probability of a pair of proteins.  ...  A number of methods exist for such analyses, and they can be divided into two main categories based on their treatment of highly connected proteins.  ...  This technique computes bounds on the reliability of the connections between two nodes. These bounds are theoretically proven unlike previously proposed ones.  ... 
doi:10.1155/2009/787128 pmid:20182643 pmcid:PMC2826754 fatcat:2ietnaorh5emjfr6khfewts37i
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