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Graph properties in node-query setting: effect of breaking symmetry [article]

Nikhil Balaji, Samir Datta, Raghav Kulkarni, Supartha Podder
2015 arXiv   pre-print
Apart from being combinatorially rich, this setting allows us to initiate a systematic study of breaking symmetry in the context of query complexity of graph properties.  ...  In particular, we focus on hereditary graph properties. The monotone functions in the node-query setting translate precisely to the hereditary graph properties.  ...  Effect of breaking symmetry Another reason why our setting is interesting is that it allows us to study the effect of breaking symmetry on query complexities of graph properties.  ... 
arXiv:1510.08267v1 fatcat:m6iegnep2nhbxh5jm63zxfj2q4

Querying subgraph sets with g-tries

Pedro Ribeiro, Fernando Silva
2012 Proceedings of the 2nd ACM SIGMOD Workshop on Databases and Social Networks - DBSocial '12  
In this paper we present an universal methodology for finding all the occurrences of a given set of subgraphs in one single larger graph.  ...  Using a specialized canonical form and symmetry breaking conditions, a single non-redundant search of the entire set of subgraphs is possible.  ...  In order to counter this and to effectively find each subgraph instance just once, we introduce symmetry breaking conditions of the form a < b.  ... 
doi:10.1145/2304536.2304541 dblp:conf/dbsocial/RibeiroS12 fatcat:hcfuluqavvg3noxtwfmcp2krde

Quantum Walk Sampling by Growing Seed Sets [article]

Simon Apers
2019 arXiv   pre-print
to create a superposition over the isomorphisms of an n-node graph in time O(2^n/3), surpassing the Ω(2^n/2) barrier set by index erasure.  ...  This improves on existing strategies by initially growing a classical seed set in the graph, from which a quantum walk is then run.  ...  Part of this work was supported by the CWI-Inria International Lab.  ... 
arXiv:1904.11446v1 fatcat:kdmhp35esrf6fpn3phznenmo6y

Quantum Walk Sampling by Growing Seed Sets

Simon Apers, Michael Wagner
2019 European Symposium on Algorithms  
to create a superposition over the isomorphisms of an n-node graph in time O(2 n/3 ), surpassing the Ω(2 n/2 ) barrier set by index erasure.  ...  This improves on existing strategies by initially growing a classical seed set in the graph, from which a quantum walk is then run.  ...  , the graph is effectively an edge contraction of the random transposition graph.  ... 
doi:10.4230/lipics.esa.2019.9 dblp:conf/esa/Apers19 fatcat:ov7wu3byozbffmg5gfnbsgqh7m

Extension Complexity of Independent Set Polytopes

Mika Göös, Rahul Jain, Thomas Watson
2018 SIAM journal on computing (Print)  
We exhibit an n-node graph whose independent set polytope requires extended formulations of size exponential in Ω(n/ log n).  ...  In this work, we focus only on the monotone setting.  ...  Moreover, the polytope can be taken to be the independent set polytope P G of an n-node graph G, i.e., the convex hull of (the indicator vectors of) the independent sets of G.  ... 
doi:10.1137/16m109884x fatcat:zzxykn7kojbhjc4f7nxebzs43e

Extension Complexity of Independent Set Polytopes [article]

Mika Göös, Rahul Jain, Thomas Watson
2016 arXiv   pre-print
We exhibit an n-node graph whose independent set polytope requires extended formulations of size exponential in Ω(n/ n).  ...  Previously, no explicit examples of n-dimensional 0/1-polytopes were known with extension complexity larger than exponential in Θ(√(n)).  ...  Moreover, the polytope can be taken to be the independent set polytope P G of an n-node graph G, i.e., the convex hull of (the indicator vectors of) the independent sets of G.  ... 
arXiv:1604.07062v1 fatcat:hekvvm2dq5fhhasmmxacvdpoky

Symmetry Breaking in the Congest Model: Time- and Message-Efficient Algorithms for Ruling Sets [article]

Shreyas Pai, Gopal Pandurangan, Sriram V. Pemmaraju, Talal Riaz, Peter Robinson
2017 arXiv   pre-print
A β-ruling set is an independent set such that every node in the graph is at most β hops from a node in the independent set.  ...  We study local symmetry breaking problems in the CONGEST model, focusing on ruling set problems, which generalize the fundamental Maximal Independent Set (MIS) problem.  ...  By the symmetry breaking step (Step 15), category-1 nodes form an independent set.  ... 
arXiv:1705.07861v1 fatcat:r5nyjp4he5aurflws2rgosfoze

The Sixth Answer Set Programming Competition

Martin Gebser, Marco Maratea, Francesco Ricca
2017 The Journal of Artificial Intelligence Research  
Answer Set Programming (ASP) is a well-known paradigm of declarative programming with roots in logic programming and non-monotonic reasoning.  ...  This edition maintained some of the design decisions introduced in 2014, e.g., the conception of sub-tracks, the scoring scheme, and the adherence to a fixed modeling language in order to push the adoption  ...  Such performance improvements are owed to compactly formulated symmetry breaking in the alternative encoding (cf.  ... 
doi:10.1613/jair.5373 fatcat:pjgjrinsc5a2xk4trq6sp22r2u

Pointer Data Structure Synthesis from Answer Set Programming Specifications [article]

Sarat Chandra Varanasi, Neeraj Mittal, Gopal Gupta
2020 arXiv   pre-print
We develop an inductive proof-technique to generate imperative programs for pointer data structures from behavioural specifications expressed in the Answer Set Programming (ASP) formalism.  ...  This work is in the realm of constructing programs that are correct according to a given specification.  ...  We first describe the specification of linked-list representation in terms of nodes and edges, then describe transitive properties of nodes involved in a list such as reachability.  ... 
arXiv:2006.07440v2 fatcat:zq6fv2dwbzalnhqsr4luksz5ca

NemoMap: Improved Motif-centric Network Motif Discovery Algorithm

Tien Huynh, Somadina Mbadiwe, Wooyoung Kim
2018 Advances in Science, Technology and Engineering Systems  
We also compare the performance of NemoMap and ParaMODA (introduced previously to improve MODA), and the result shows that NemoMap yields better runtime due to the implementation of Grochow-Kellis' symmetry-breaking  ...  Researchers who are interested in larger motifs and have established a set of potential motif patterns could utilize motif-centric tools to check whether such patterns are truly network motifs by mapping  ...  Acknowledgment We thank the Computing and Software Systems, School of STEM, at the University of Washington Bothell for the support of this research.  ... 
doi:10.25046/aj030523 fatcat:wsl2iawvkvdmnk3xlv45ugylxa

On the Axioms of Causal Set Theory [article]

Benjamin F. Dribus
2013 arXiv   pre-print
This paper offers suggested improvements to the causal sets program in discrete gravity, which treats spacetime geometry as an emergent manifestation of causal structure at the fundamental scale.  ...  This approach circumvents undesirable structural features in causal set theory, such as the permeability of maximal antichains, studied by Major, Rideout, and Surya, and the configuration space pathology  ...  Both transitions break the unique nontrivial symmetry of D i .  ... 
arXiv:1311.2148v3 fatcat:nw4itctovnhrfcgiq7zxj4jg7a

The Index-Based Subgraph Matching Algorithm with General Symmetries (ISMAGS): Exploiting Symmetry for Faster Subgraph Enumeration

Maarten Houbraken, Sofie Demeyer, Tom Michoel, Pieter Audenaert, Didier Colle, Mario Pickavet, Peter Csermely
2014 PLoS ONE  
More advanced network motif finding techniques, focusing on graph properties and data structures, are proposed in [6] and [7] .  ...  By incorporating the symmetry of the subgraph in their search, they reduce the search space exploration and speed up queries.  ...  The G4 graph was selected to show the effects of the optimisation of the set operations in ISMAGS (compared to ISMA) as it does not have any symmetric properties.  ... 
doi:10.1371/journal.pone.0097896 pmid:24879305 pmcid:PMC4039476 fatcat:v6hluetejfae7lkfme43peasgy

Abstraction for non-ground answer set programs

Zeynep G. Saribatur, Thomas Eiter, Peter Schüller
2021 Artificial Intelligence  
coloring of the nodes of a given graph.  ...  If a given graph is non-colorable, then we may try to find some subgraph (e.g., a clique) which causes the unsolvability, and we would not care about other nodes in the graph.  ...  Employing symmetry breaking techniques [34, 37] in order to get hints on a good initial abstraction is a promising subject of future research.  ... 
doi:10.1016/j.artint.2021.103563 fatcat:nyhzwgry3vc4tbwaci6g2aoqay

Supporting Efficient Record Linkage for Large Data Sets Using Mapping Techniques

Chen Li, Liang Jin, Sharad Mehrotra
2006 World wide web (Bussum)  
Since the scalability issue of record linkage was addressed in [21] , the repertoire of database techniques dealing with multidimensional data sets has significantly increased.  ...  The recordlinkage problem arises naturally in the context of data cleansing that usually precedes data analysis and mining.  ...  It can effectively reduce the queue size, since pairs of objects in the leaf nodes can be processed early, and they can be dequeued from the queue.  ... 
doi:10.1007/s11280-006-0226-8 fatcat:zkjr3mktkvcvphtyeinp2xxunm

Improving the Reliability of Causal Discovery from Small Data Sets Using Argumentation

Facundo Bromberg, Dimitris Margaritis
2009 Journal of machine learning research  
Statistical tests on finite data sets may result in errors in these tests and inconsistencies in the knowledge base.  ...  data sets.  ...  each node in the network is conditionally independent of all its non-descendants in the graph given its parents.  ... 
dblp:journals/jmlr/BrombergM09 fatcat:xl57j6mt6rhzdcszi6kkp5z4ue
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