scholarly journals Relating Vertex and Global Graph Entropy in Randomly Generated Graphs

2018 ◽  
Author(s):  
Philip Tee ◽  
George Parisis ◽  
Luc Berthouze ◽  
Ian Wakeman
Keyword(s):  
Computational Complexity ◽  
Recent Work ◽  
Random Graphs ◽  
Real World ◽  
Close Correlation ◽  
Complete Problem ◽  
Entropy Measures ◽  
Vertex Set ◽  
Np Complete ◽  
The Greedy Algorithm

Combinatoric measures of entropy capture the complexity of a graph, but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an inaccessible calculation. Recent work by Dehmer et al. and Tee et al. identified a number of alternative vertex level measures of entropy that do not suffer from this pathological computational complexity. It can be demonstrated that they are still effective at quantifying graph complexity. It is intriguing to consider whether there is a fundamental link between local and global entropy measures. In this paper, we investigate the existence of correlation between vertex level and global measures of entropy, for a narrow subset of random graphs. We use the greedy algorithm approximation for calculating the chromatic information and therefore Körner entropy. We are able to demonstrate close correlation for this subset of graphs and outline how this may arise theoretically.

scholarly journals Solving Vertex Cover in Polynomial Time on Hyperbolic Random Graphs

2021 ◽  
Author(s):  
Thomas Bläsius ◽  
Philipp Fischbeck ◽  
Tobias Friedrich ◽  
Maximilian Katzmann
Keyword(s):  
Computational Complexity ◽  
Structural Properties ◽  
Random Graphs ◽  
Polynomial Time ◽  
Real World ◽  
Degree Distribution ◽  
High Probability ◽  
Vertex Cover ◽  
Optimal Solution ◽  
Np Complete

AbstractThe computational complexity of the VertexCover problem has been studied extensively. Most notably, it is NP-complete to find an optimal solution and typically NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on many real-world networks the run time to solve VertexCover is way smaller than even the best known FPT-approaches can explain. We link these observations to two properties that are observed in many real-world networks, namely a heterogeneous degree distribution and high clustering. To formalize these properties and explain the observed behavior, we analyze how a branch-and-reduce algorithm performs on hyperbolic random graphs, which have become increasingly popular for modeling real-world networks. In fact, we are able to show that the VertexCover problem on hyperbolic random graphs can be solved in polynomial time, with high probability. The proof relies on interesting structural properties of hyperbolic random graphs. Since these predictions of the model are interesting in their own right, we conducted experiments on real-world networks showing that these properties are also observed in practice.

scholarly journals On the Computational Complexity of Gossip Protocols

2017 ◽  
Author(s):  
Krzysztof R. Apt ◽  
Eryk Kopczyński ◽  
Dominik Wojtczak
Keyword(s):  
Computational Complexity ◽  
Private Information ◽  
Epistemic Logic ◽  
Distributed Programs ◽  
Distributed Protocols ◽  
Partial Correctness ◽  
Complete Problem ◽  
Gossip Protocol ◽  
Np Complete ◽  
Gossip Protocols

Gossip protocols deal with a group of communicating agents, each holding a private information, and aim at arriving at a situation in which all the agents know each other secrets. Distributed epistemic gossip protocols are particularly simple distributed programs that use formulas from an epistemic logic. Recently, the implementability of these distributed protocols was established (which means that the evaluation of these formulas is decidable), and the problems of their partial correctness and termination were shown to be decidable, but their exact computational complexity was left open. We show that for any monotonic type of calls the implementability of a distributed epistemic gossip protocol is a P^{NP}_{||}-complete problem, while the problems of its partial correctness and termination are in coNP^{NP}.

scholarly journals Assessing the computational complexity of multilayer subgraph detection

2019 ◽  
Vol 7 (2) ◽  
pp. 215-241 ◽  
Author(s):  
Robert Bredereck ◽  
Christian Komusiewicz ◽  
Stefan Kratsch ◽  
Hendrik Molter ◽  
Rolf Niedermeier ◽  
...  
Keyword(s):  
Computational Complexity ◽  
Real World ◽  
Maximum Cardinality ◽  
Clique Relaxations ◽  
Vertex Set ◽  
Real World Problems

AbstractMultilayer graphs consist of several graphs, called layers, where the vertex set of all layers is the same but each layer has an individual edge set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the border of computational (in)tractability for the class of subgraph detection problems on multilayer graphs, including fundamental problems such as maximum-cardinality matching, finding certain clique relaxations, or path problems. Mostly encountering hardness results, sometimes even for two or three layers, we can also spot some islands of computational tractability.

scholarly journals P Systems with Evolutional Communication and Division Rules

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 327
Author(s):  
David Orellana-Martín ◽  
Luis Valencia-Cabrera ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
Computational Complexity ◽  
Complexity Theory ◽  
Membrane Computing ◽  
P Systems ◽  
Membrane Systems ◽  
Sat Problem ◽  
Complete Problem ◽  
Intractable Problems ◽  
Np Complete ◽  
The One

A widely studied field in the framework of membrane computing is computational complexity theory. While some types of P systems are only capable of efficiently solving problems from the class P, adding one or more syntactic or semantic ingredients to these membrane systems can give them the ability to efficiently solve presumably intractable problems. These ingredients are called to form a frontier of efficiency, in the sense that passing from the first type of P systems to the second type leads to passing from non-efficiency to the presumed efficiency. In this work, a solution to the SAT problem, a well-known NP-complete problem, is obtained by means of a family of recognizer P systems with evolutional symport/antiport rules of length at most (2,1) and division rules where the environment plays a passive role; that is, P systems from CDEC^(2,1). This result is comparable to the one obtained in the tissue-like counterpart, and gives a glance of a parallelism and the non-evolutionary membrane systems with symport/antiport rules.

scholarly journals An exact tensor network for the 3SAT problem

2012 ◽  
Vol 12 (3&4) ◽  
pp. 283-292
Author(s):  
Artur Garcia-Saez ◽  
Jose I. Latorre
Keyword(s):  
Computational Complexity ◽  
Explicit Solutions ◽  
Experimental Task ◽  
Satisfying Assignment ◽  
Physical Realization ◽  
Number Of Solutions ◽  
Complete Problem ◽  
Tensor Network ◽  
Np Complete ◽  
Local Observables

We construct a tensor network that delivers an unnormalized quantum state whose coefficients are the solutions to a given instance of 3SAT, an NP-complete problem. The tensor network contraction that corresponds to the norm of the state counts the number of solutions to the instance. It follows that exact contractions of this tensor network are in the \#P-complete computational complexity class, thus believed to be a hard task. Furthermore, we show that for a 3SAT instance with $n$ bits, it is enough to perform a polynomial number of contractions of the tensor network structure associated to the computation of local observables to obtain one of the explicit solutions to the problem, if any. Physical realization of a state described by a generic tensor network is equivalent to finding the satisfying assignment of a 3SAT instance and, consequently, this experimental task is expected to be hard.

scholarly journals POLYNOMIAL SOLVABILITY OF NP-COMPLETE PROBLEMS

2014 ◽  
Author(s):  
Anatoly Panyukov
Keyword(s):  
Computational Complexity ◽  
Polynomial Algorithm ◽  
Hamiltonian Circuit ◽  
Graph Vertex ◽  
Polynomial Solvability ◽  
Complete Problems ◽  
Vertex Set ◽  
Np Complete

A polynomial algorithm for solving the ''Hamiltonian circuit'' problem is presented in the paper. Computational complexity of the algorithm is equal to $O\left(n^8\log_2^2{n}\right)$ where $n$ is the cardinality of the observed graph vertex set. Thus the polynomial solvability for ${\mathcal NP}$-complete problems is proved.

scholarly journals Popular Matching in Roommates Setting Is NP-hard

2021 ◽  
Vol 13 (2) ◽  
pp. 1-20
Author(s):  
Sushmita Gupta ◽  
Pranabendu Misra ◽  
Saket Saurabh ◽  
Meirav Zehavi
Keyword(s):  
Computational Complexity ◽  
Np Hard ◽  
Np Complete ◽  
Open Question ◽  
Popular Matching

An input to the P OPULAR M ATCHING problem, in the roommates setting (as opposed to the marriage setting), consists of a graph G (not necessarily bipartite) where each vertex ranks its neighbors in strict order, known as its preference. In the P OPULAR M ATCHING problem the objective is to test whether there exists a matching M * such that there is no matching M where more vertices prefer their matched status in M (in terms of their preferences) over their matched status in M *. In this article, we settle the computational complexity of the P OPULAR M ATCHING problem in the roommates setting by showing that the problem is NP-complete. Thus, we resolve an open question that has been repeatedly and explicitly asked over the last decade.

scholarly journals Reservoir Sediment Management Using Artificial Neural Networks: A Case Study of the Lower Section of the Alpine Saalach River

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 818
Author(s):  
Markus Reisenbüchler ◽  
Minh Duc Bui ◽  
Peter Rutschmann
Keyword(s):  
Real World ◽  
Close Correlation ◽  
Critical Issue ◽  
Management Tool ◽  
Lower Section ◽  
Reservoir Sediment ◽  
Efficiency And Effectiveness ◽  
Artificial Neural ◽  
Artificial Neural Network Ann

Reservoir sedimentation is a critical issue worldwide, resulting in reduced storage volumes and, thus, reservoir efficiency. Moreover, sedimentation can also increase the flood risk at related facilities. In some cases, drawdown flushing of the reservoir is an appropriate management tool. However, there are various options as to how and when to perform such flushing, which should be optimized in order to maximize its efficiency and effectiveness. This paper proposes an innovative concept, based on an artificial neural network (ANN), to predict the volume of sediment flushed from the reservoir given distinct input parameters. The results obtained from a real-world study area indicate that there is a close correlation between the inputs—including peak discharge and duration of flushing—and the output (i.e., the volume of sediment). The developed ANN can readily be applied at the real-world study site, as a decision-support system for hydropower operators.

scholarly journals Transforming Cultural Ideas of Aging and Disability to Improve Policy and Practice

2020 ◽  
Vol 4 (Supplement_1) ◽  
pp. 645-645
Author(s):  
Anne Ordway
Keyword(s):  
Older Adults ◽  
Health Care ◽  
Recent Work ◽  
Interest Group ◽  
Quality Of Health Care ◽  
Real World ◽  
People With Disabilities ◽  
Policy And Practice ◽  
Full Participation

Abstract Aging and disability are normative processes that extend across the lifespan. However, ageism and ableism are incorporated into many of our practices, programs, and policies—devaluing the lives of older adults and people aging with disabilities and ultimately preventing their full participation in society. Ageism and ableism are closely connected. For example, both systems identify impairment as an individual and social liability. As recent studies have demonstrated, this has real world implications for the quantity and quality of health care requested, delivered, and received by both older adults and people with disabilities. In this session, we discuss the connections between these two forms of oppression and present recent work by researchers in both fields and the FrameWorks Institute that shows how to transform our cultural ideas of aging and disability and development more inclusive policies and services. Part of a symposium sponsored by the Lifelong Disabilities Interest Group.

Sign in / Sign up

Export Citation Format

Share Document