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Limits and Applications of Group Algebras for Parameterized Problems [chapter]

Ioannis Koutis, Ryan Williams
2009 Lecture Notes in Computer Science  
On the positive side, we give new applications of the method: finding a copy of a given tree on k nodes, a spanning tree with at least k leaves, a minimum set of nodes that dominate at least t nodes, and  ...  Among other results, we show that a combination of dynamic programming and a variation of the algebraic method can break the trivial upper bounds for exact parameterized counting in fairly general settings  ...  It suffices to show how to detect if G has a connected subgraph with at least k degree one nodes. Let the vertices of G be {1, . . . , n}.  ... 
doi:10.1007/978-3-642-02927-1_54 fatcat:v2yxdzzilrautoovjprqdivd2e

LIMITS and Applications of Group Algebras for Parameterized Problems

Ioannis Koutis, Ryan Williams
2016 ACM Transactions on Algorithms  
On the positive side, we give new applications of the method: finding a copy of a given tree on k nodes, a spanning tree with at least k leaves, a minimum set of nodes that dominate at least t nodes, and  ...  Among other results, we show that a combination of dynamic programming and a variation of the algebraic method can break the trivial upper bounds for exact parameterized counting in fairly general settings  ...  It suffices to show how to detect if G has a connected subgraph with at least k degree one nodes. Let the vertices of G be {1, . . . , n}.  ... 
doi:10.1145/2885499 fatcat:jo5zfmif7badrkvtu5kb75qe5a

Graph Homomorphism Polynomials: Algorithms and Complexity [article]

Balagopal Komarath, Anurag Pandey, C. S. Rahul
2020 arXiv   pre-print
These polynomials have received a lot of attention recently for their crucial role in several new algorithms for counting and detecting graph patterns, and also for obtaining natural polynomial families  ...  which are complete for algebraic complexity classes 𝖵𝖡𝖯, 𝖵𝖯, and 𝖵𝖭𝖯.  ...  In detection and counting algorithms for subgraph isomorphism (resp. induced subgraph isomorphism), we want to detect and count subgraphs (resp. induced subraphs) of an n-vertex host graph which is isomorphic  ... 
arXiv:2011.04778v2 fatcat:23bzgro5snf6bazzsykubzzfou

Pattern Morphing for Efficient Graph Mining [article]

Kasra Jamshidi, Keval Vora
2020 arXiv   pre-print
We propose Pattern Morphing, a technique that enables structure-aware algebra over patterns to accurately infer the results for a given set of patterns using the results of a completely different set of  ...  It is a general technique that supports various operations over matches of a pattern beyond just counting (e.g., support calculation, enumeration, etc.), making it widely applicable to various graph mining  ...  A myriad of research has been conducted on efficient algorithms for mining motifs. [17] developed a technique to break symmetries of patterns by enforcing a partial-ordering on pattern vertices.  ... 
arXiv:2012.04553v1 fatcat:dahevnmsdnfvnktw5n7awe4y5a

A Spectral Framework for Anomalous Subgraph Detection

Benjamin A. Miller, Michelle S. Beard, Patrick J. Wolfe, Nadya T. Bliss
2015 IEEE Transactions on Signal Processing  
While the detection of such anomalous subgraphs has received a substantial amount of attention, no application-agnostic framework exists for analysis of signal detectability in graph-based data.  ...  We propose several algorithms based on spectral properties of the residuals matrix, with more computationally expensive techniques providing greater detection power.  ...  Wolf for many helpful comments on this paper.  ... 
doi:10.1109/tsp.2015.2437841 fatcat:z4abweadz5gtth4pqzgqutjpfq

Deterministic subgraph detection in broadcast CONGEST [article]

Janne H. Korhonen, Joel Rybicki
2017 arXiv   pre-print
We present simple deterministic algorithms for subgraph finding and enumeration in the broadcast CONGEST model of distributed computation: -- For any constant k, detecting k-paths and trees on k nodes  ...  can be done in O(1) rounds. -- For any constant k, detecting k-cycles and pseudotrees on k nodes can be done in O(n) rounds. -- On d-degenerate graphs, cliques and 4-cycles can be enumerated in O(d + n  ...  We thank Juho Hirvonen, Dennis Olivetti, Rotem Oshman, Chris Purcell, Stefan Schmid and Jukka Suomela for valuable comments and discussions.  ... 
arXiv:1705.10195v2 fatcat:z56g3wgfpneuldmp4r62ovzw2m

Extensor-Coding [article]

Cornelius Brand, Holger Dell, Thore Husfeldt
2018 arXiv   pre-print
Our results and techniques generalize to the subgraph isomorphism problem when the subgraphs we are looking for have bounded pathwidth.  ...  Finally, we also obtain a randomized algorithm to detect k-multilinear terms in a multivariate polynomial given as a general algebraic circuit.  ...  Without the promise on the number of subgraphs, Fomin et al. [28] detect subgraphs in randomized timeÕ(2 k n tw(H)+1 ) and Fomin et al. [27] do so in deterministic time 2.619 k n O(tw(H)) .  ... 
arXiv:1804.09448v1 fatcat:vr5sbwdwpbbsrgxjgppwlz3him

On Spectral Partitioning of Co-authorship Networks [chapter]

Václav Snášel, Pavel Krömer, Jan Platoš, Miloš Kudělka, Zdeněk Horák
2012 Lecture Notes in Computer Science  
In this paper, we explore two community detection approaches based on the spectral partitioning to analyze a coauthorship network.  ...  The partitioning exploits the concepts of algebraic connectivity and characteristic valuation to form components useful for the analysis of relations and communities in real world social networks.  ...  spectral partitioning of subgraphs for Philip S.  ... 
doi:10.1007/978-3-642-33260-9_26 fatcat:3yppgd43zrccdnxpln6f6zjmai

Efficiently Pinpointing SPARQL Query Containments [chapter]

Claus Stadler, Muhammad Saleem, Axel-Cyrille Ngonga Ngomo, Jens Lehmann
2018 Lecture Notes in Computer Science  
For example, recent SPARQL engines built on Big Data frameworks that precompute solutions to frequently requested query patterns, are conceptually an application of query containment.  ...  Solving the query containment problem can be reduced to the problem of deciding whether a sub graph isomorphism exists between the normalized algebra expressions of two queries.  ...  Acknowledgements This work was partly supported by the grant from the European Unions Horizon 2020 research Europe flag and innovation programme for the projects HOBBIT (GA no. 688227), QROWD (GA no. 732194  ... 
doi:10.1007/978-3-319-91662-0_16 fatcat:gclvxtqkmzbgdfmaga2uuvf4lm

Plan-Based Semantic Enrichment of Event Streams [chapter]

Kia Teymourian, Adrian Paschke
2014 Lecture Notes in Computer Science  
In this paper, we present an efficient technique for event stream enrichment by planning multi-step event enrichment and processing.  ...  We propose an approach for optimization of knowledge-based event detection by using a technique for multi-step and greedy knowledge acquisition and event detection.  ...  In this case this subgraph might have a better filtering functionality for the event detection than the other subgraphs.  ... 
doi:10.1007/978-3-319-07443-6_3 fatcat:yi2nyjg3gjg6veudgoh2ctrwni

Pattern detection in large temporal graphs using algebraic fingerprints [chapter]

Suhas Thejaswi, Aristides Gionis
2020 Proceedings of the 2020 SIAM International Conference on Data Mining  
For the family of pattern-detection problems we define, we establish complexity results and design an algebraicalgorithmic framework based on constrained multilinear sieving.  ...  For example, in a real-world graph dataset with more than six million edges and a multi-set query with ten colors, we can extract an optimal solution in less than eight minutes on a haswell desktop with  ...  Our algorithm relies on a polynomial encoding of temporal walks and the algebraic fingerprinting technique [6, 23, 26, 37] .  ... 
doi:10.1137/1.9781611976236.5 dblp:conf/sdm/ThejaswiG20 fatcat:tbljv2j56jb3riym674xncjxlu

Graphflow

Chathura Kankanamge, Siddhartha Sahu, Amine Mhedbhi, Jeremy Chen, Semih Salihoglu
2017 Proceedings of the 2017 ACM International Conference on Management of Data - SIGMOD '17  
We demonstrate Graphflow, a prototype active graph database that evaluates general one-time and continuous subgraph queries.  ...  Many applications detect the emergence or deletion of certain subgraphs in their input graphs continuously.  ...  We note that, although the idea of delta queries is old and based on techniques from references [2, 3] , our evaluation of dQi using GJ has performance implications that do not exist for existing IVM  ... 
doi:10.1145/3035918.3056445 dblp:conf/sigmod/KankanamgeSMCS17 fatcat:4p2vaahkyrhivce5sczdzc5oaq

Constrained multilinear detection for faster functional motif discovery

Ioannis Koutis
2012 Information Processing Letters  
The GRAPH MOTIF problem asks whether a given multiset of colors appears on a connected subgraph of a vertex-colored graph.  ...  The fastest known parameterized algorithm for this problem is based on a reduction to the k-Multilinear Detection (k-MlD) problem: the detection of multilinear terms of total degree k in polynomials presented  ...  We obtain a faster parameterized algorithm for each of these problems. The algorithm and its proof Proof. We start by reviewing at a high level the purely algebraic algorithm for k-MLD in [5, 9] .  ... 
doi:10.1016/j.ipl.2012.08.008 fatcat:nmusresv6bempmqnza6dvjp7na

Optimality of Graph Scanning Statistic for Online Community Detection [article]

Liyan Xie, Yao Xie
2021 arXiv   pre-print
In particular, we focus on the local change that only affects a subgraph. We adopt the classical Erdos-Renyi model and revisit the generalized likelihood ratio (GLR) detection procedure.  ...  Sequential change-point detection for graphs is a fundamental problem for streaming network data types and has wide applications in social networks and power systems.  ...  In this paper, we focus on the parametric approach for constructing scan statistics to detect a local change in a sequence of graphs.  ... 
arXiv:2102.05821v1 fatcat:6vymftq4xjgxvefuwbawzikqqa

Local Reasoning for Global Graph Properties [chapter]

Siddharth Krishna, Alexander J. Summers, Thomas Wies
2020 Lecture Notes in Computer Science  
Building on this theory, we develop a general proof technique for modular reasoning about global graph properties expressed over program heaps, in a way which can be directly integrated with existing separation  ...  We present mathematical foundations for reasoning about this class of properties, imposing minimal requirements on the underlying theory that allow us to define a suitable separation algebra.  ...  locally in the subgraph) and (b) that it satisfies the same interface (in other words, the effect of the modification on the flow is contained within the subgraph); the meta-level results for our technique  ... 
doi:10.1007/978-3-030-44914-8_12 fatcat:hkr5rv3qpbd2zgflj6jadf2eqe
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