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

2021
*
arXiv
*
pre-print

In fact, all known algorithms need at least Ω(m) communication

arXiv:2105.08917v1
fatcat:trr2hj5pcrgnpgulwxh3ppzaum
*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*...##
###
Construction of Near-Optimal Vertex Clique Covering for Real-World Networks

2015
*
Computing and informatics
*

We propose a method

dblp:journals/cai/Chalupa15
fatcat:5ibwflpsdrh2lazgwlmzt6xgxa
*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. ...##
###
On the Complexity of Sampling Vertices Uniformly from a Graph

2018
*
International Colloquium on Automata, Languages and Programming
*

Finally, we give lower

doi:10.4230/lipics.icalp.2018.149
dblp:conf/icalp/ChierichettiH18
fatcat:opktyqoucvdbxbfptpbrrzsjsi
*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. ...##
###
Node and Edge Averaged Complexities of Local Graph Problems

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

Finally, we consider

doi:10.1145/3519270.3538419
fatcat:xz4l2ozpgrfxzbxmspaadszd6e
*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. ...##
###
Preconditioner Approximations for Probabilistic Graphical Models

2005
*
Neural Information Processing Systems
*

Our framework yields rigorous upper and lower

dblp:conf/nips/RavikumarL05
fatcat:6faei2kk6rakjd7ynikgko7cdm
*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. ...##
###
Quantum Algorithms for the Triangle Problem
[article]

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] . ...

##
###
Resource Discovery in Networks under Bandwidth Limitations

2006
*
2006 Fifth International Symposium on Parallel and Distributed Computing
*

This is done by proving a lower

doi:10.1109/ispdc.2006.40
dblp:conf/ispdc/KonwarS06
fatcat:jswfkb5qvrgllj6njhy6zwu2zm
*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. ...##
###
Quantum Algorithms for the Triangle Problem

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] . ...

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

1998
*
IEEE Transactions on Information Theory
*

Additionally and independently, we use wellknown information-theoretic measures to derive novel

doi:10.1109/18.661506
fatcat:uo65zcpytzdupkfubrkyrsqs6q
*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. ...##
###
Learning Bayesian Networks in the Presence of Structural Side Information

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

doi:10.1609/aaai.v36i7.20750
fatcat:n5e3mzvzm5eqbo2bpy47rynl7i
*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. ...##
###
A distributed deterministic approximation algorithm for data association

2011
*
2011 International Conference on Distributed Computing in Sensor Systems and Workshops (DCOSS)
*

We then show that

doi:10.1109/dcoss.2011.5982153
dblp:conf/dcoss/Oh11
fatcat:5xxp25hf5vfr5e4mti6kdpdg4q
*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. ...##
###
Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs
[article]

2018
*
arXiv
*
pre-print

We study

arXiv:1806.11282v1
fatcat:cyuqsil4bbe2ffzcscupsis26a
*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. ...##
###
Sample Complexity Bounds for Recurrent Neural Networks with Application to Combinatorial Graph Problems
[article]

2019
*
arXiv
*
pre-print

As our primary contribution, this is

arXiv:1901.10289v2
fatcat:4dcgzxbgffcddmca6oaxwdvpxm
*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. ...##
###
Node and Edge Averaged Complexities of Local Graph Problems
[article]

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] . ...

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

2009
*
Advances in Bioinformatics
*

We propose a network flow-

doi:10.1155/2009/787128
pmid:20182643
pmcid:PMC2826754
fatcat:2ietnaorh5emjfr6khfewts37i
*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*. ...
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