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Exact and Approximate Pattern Counting in Degenerate Graphs: New Algorithms, Hardness Results, and Complexity Dichotomies [article]

Marco Bressan, Marc Roth
2021 arXiv   pre-print
Those lower bounds for exact counting are complemented with new algorithms for approximate counting of subgraphs and induced subgraphs in degenerate graphs.  ...  In the language of parameterized complexity, our results yield dichotomies in fixed-parameter tractable and #𝖶[1]-hard cases if we parameterize by the size of the pattern and the degeneracy of the host  ...  Roth is grateful to Lior Gishboliner for introducing him to pattern counting in degenerate graphs.  ... 
arXiv:2103.05588v2 fatcat:pqq53dd72rdjzpc4unymf3igki

FPT Algorithms for Finding Near-Cliques in c-Closed Graphs [article]

Balaram Behera, Edin Husić, Shweta Jain, Tim Roughgarden, C. Seshadhri
2021 arXiv   pre-print
Finding large cliques or cliques missing a few edges is a fundamental algorithmic task in the study of real-world graphs, with applications in community detection, pattern recognition, and clustering.  ...  Given the NP-hardness of variants of clique counting, these results raise a challenge for beyond worst-case analysis of these problems.  ...  Even getting O(n 1−δ )-approximations is NP-hard [42, 87] , and it is hard to non-trivially approximate even with algorithm parameterized by solution size [16] .  ... 
arXiv:2007.09768v4 fatcat:z6eu4ca7orez5cdiexwavuzgg4

Computing and Maintaining Provenance of Query Result Probabilities in Uncertain Knowledge Graphs [article]

Garima Gaur, Abhishek Dang, Arnab Bhattacharya, Srikanta Bedathur
2021 arXiv   pre-print
Modeling the uncertainty as probabilistic confidence scores results in a probabilistic knowledge graph.  ...  Focusing on a popular class of conjunctive basic graph pattern queries on the KG, we compare the performance of HAPPI against a possible-world model of computation and a knowledge compilation tool over  ...  For hard queries, they rely on approaches based on approximation algorithms [27, 28] .  ... 
arXiv:2108.07758v1 fatcat:nc5qggze5zaqxmmwcqpehoh5uy

On the External Validity of Average-Case Analyses of Graph Algorithms [article]

Thomas Bläsius, Philipp Fischbeck
2022 arXiv   pre-print
Moreover, heterogeneity and locality appear to be the core properties impacting the performance of many graph algorithms.  ...  To this end, we evaluate the performance of six graph algorithms on a collection of 2751 sparse real-world networks depending on two properties; the heterogeneity (variance in the degree distribution)  ...  Since then, the list of NP-hard problems is growing every year; see the book by Garey and Johnson [29] for an extensive list of problems that were shown to be hard in the early years of complexity theory  ... 
arXiv:2205.15066v1 fatcat:kernvuvkbra6nix7bkkc2wbxtm

A Complete Dichotomy Rises from the Capture of Vanishing Signatures [article]

Jin-Yi Cai, Heng Guo, Tyson Williams
2018 arXiv   pre-print
A Holant problem defined by a set of constraint functions F is solvable in polynomial time if it satisfies this tractability criterion, and is #P-hard otherwise.  ...  We prove a complexity dichotomy theorem for Holant problems over an arbitrary set of complex-valued symmetric constraint functions F on Boolean variables.  ...  seminar on computational counting.  ... 
arXiv:1204.6445v3 fatcat:skkydzgqd5fzjgxeebpbwlpikm

A Complete Dichotomy Rises from the Capture of Vanishing Signatures

Jin-Yi Cai, Heng Guo, Tyson Williams
2016 SIAM journal on computing (Print)  
This extends and unifies all previous dichotomies for Holant problems on symmetric constraint functions taking values in a field of characteristic zero.  ...  We prove a complexity dichotomy theorem for Holant problems over an arbitrary set of complex-valued symmetric constraint functions F on Boolean variables.  ...  If the new k < k ′ we can continue as in the subtractive Euclid algorithm.  ... 
doi:10.1137/15m1049798 fatcat:qgnqlpuxgrbmjjaqjmkdpphqna

A complete dichotomy rises from the capture of vanishing signatures

Jin-Yi Cai, Heng Guo, Tyson Williams
2013 Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13  
This extends and unifies all previous dichotomies for Holant problems on symmetric constraint functions taking values in a field of characteristic zero.  ...  We prove a complexity dichotomy theorem for Holant problems over an arbitrary set of complex-valued symmetric constraint functions F on Boolean variables.  ...  If the new k < k ′ we can continue as in the subtractive Euclid algorithm.  ... 
doi:10.1145/2488608.2488687 dblp:conf/stoc/CaiGW13 fatcat:gquskzirg5d77d352p3ldooxke

Exact Counting and Sampling of Optima for the Knapsack Problem [article]

Jakob Bossek, Aneta Neumann, Frank Neumann
2021 arXiv   pre-print
We present an algorithm to count exactly the number of optima to a zero-one knapsack problem instance.  ...  We find that the number of global optima can increase exponentially for practically relevant classes of instances with correlated weights and profits which poses a justification for the considered exact  ...  Further examples include counting the number of shortest paths between two nodes in graphs [13] or exact counting of minimum-spanning-trees [1].  ... 
arXiv:2106.07412v1 fatcat:3a2afvlu3jb5xi6gqyo7kzeiru

Statistical Physics of Hard Optimization Problems [article]

Lenka Zdeborová
2008 arXiv   pre-print
We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring.  ...  We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem.  ...  The survey propagation equations (1.41-1.42) and the expression for the complexity function (1.43) are exact on tree graphs.  ... 
arXiv:0806.4112v1 fatcat:74fwqrf3vfg5vlvaggjve5sz4e

Statistical physics of hard optimization problems

Lenka Zdeborová
2009 Acta Physica Slovaca  
We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring.  ...  We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem.  ...  The survey propagation equations (1.41-1.42) and the expression for the complexity function (1.43) are exact on tree graphs.  ... 
doi:10.2478/v10155-010-0096-6 fatcat:7mc6yhbptnc65cf4sg6rzg4vi4

The quantum adiabatic algorithm applied to random optimization problems: The quantum spin glass perspective

V. Bapst, L. Foini, F. Krzakala, G. Semerjian, F. Zamponi
2013 Physics reports  
This paper reviews recent analytical works that extended these studies to incorporate the effect of quantum fluctuations, and presents also some original results in this direction.  ...  These problems correspond to mean field spin glasses that have been extensively studied in the classical case.  ...  Biroli Computations were performed in part at the MesoPSL computing center, with support from Région Ile de France and ANR, in part using HPC resources  ... 
doi:10.1016/j.physrep.2012.10.002 fatcat:s6gnhlt3yzf6xpe3rq6uamqsyy

Algebraic approach to promise constraint satisfaction [article]

Libor Barto, Jakub Bulín, Andrei Krokhin, Jakub Opršal
2019 arXiv   pre-print
We demonstrate how our theory can be applied by improving the state-of-the-art in approximate graph colouring: we show that, for any k≥ 3, it is NP-hard to find a (2k-1)-colouring of a given k-colourable  ...  A new version of the CSP, the promise CSP (PCSP) has recently been proposed, motivated by open questions about the approximability of variants of satisfiability and graph colouring.  ...  Acknowledgements We would like to thank Libor Barto, Mirek Olšák, Alex Kazda, Josh Brakensiek, Venkat Guruswami, Erkko Lehtonen, and Marcello Mamino for valuable discussions.  ... 
arXiv:1811.00970v3 fatcat:r2pgvc74ffcxzec6fqdkwvznm4

Minimum color‐degree perfect b ‐matchings

Mariia Anapolska, Christina Büsing, Martin Comis, Tabea Krabs
2020 Networks  
Schrader, and Graphs III (Wed 20, Room PP, 9:30-10:30) chaired by R. Cordone. Session chairs must remind speakers to load up slides on laptops, and keep the sessions on time.  ...  Opening, plenary and closing sessions will take place in the PP amphitheatre. The cocktail event on Tuesday evening will take place in the salle des textiles room, located in Access 3, 1st floor.  ...  Remarks We presented a new view of Gomory pure and mixed-integer cuts, aimed at incorporating in the familiar column-generation paradigm, employing the primal simplex algorithm.  ... 
doi:10.1002/net.21974 fatcat:4qgtutmxrrcy7anvxks4fivcii

Biological Sequence Indexing Using Persistent Java

Elzbieta Pustulka-Hunt
2001 Zenodo  
an approximate matching algorithm with a large suffix index.  ...  Those results are presented against the background of the changing technological landscape affecting life sciences and bioinformatics research and the resulting need for new computing solutions.  ...  I would like to thank my supervisors, Malcolm Atkinson and Rob Irving, and all my colleagues, both in Computing Science Department and in the area of life sciences for helping me to engage in this exciting  ... 
doi:10.5281/zenodo.1341577 fatcat:jeeostwznzdrtakbhhw4bepsy4

Fast and Lean Immutable Multi-Maps on the JVM based on Heterogeneous Hash-Array Mapped Tries [article]

Michael J. Steindorfer, Jurgen J. Vinju
2016 arXiv   pre-print
We isolate key differences using microbenchmarks and validate the resulting conclusions on a real world case in static analysis.  ...  This data structure is used for applications processing graphs or many-to-many relations as applied in static analysis of object-oriented systems.  ...  The nodes in the graphs are complex recursive ASTs with arbitrarily complex (but linear) complexity for hashCode and equals.  ... 
arXiv:1608.01036v1 fatcat:xkpdkeuxgvdvjpaqn5ln6rs22e
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