Two Streamlined Depth-First Search Algorithms

1986 ◽  
Vol 9 (1) ◽  
pp. 85-94
Author(s):  
Robert Endre Tarjan
Keyword(s):  
Directed Graph ◽  
Graph Algorithms ◽  
Undirected Graph ◽  
Linear Time ◽  
Search Algorithms ◽  
Depth First Search ◽  
Time Graph

Many linear-time graph algorithms using depth-first search have been invented. We propose simplified versions of two such algorithms, for computing a bipolar orientation or st-numbering of an undirected graph and for finding all feedback vertices of a directed graph.

scholarly journals Circumspect descent prevails in solving random constraint satisfaction problems

2008 ◽  
Vol 105 (40) ◽  
pp. 15253-15257 ◽  
Author(s):  
Mikko Alava ◽  
John Ardelius ◽  
Erik Aurell ◽  
Petteri Kaski ◽  
Supriya Krishnamurthy ◽  
...  
Keyword(s):  
Local Search ◽  
Linear Time ◽  
Search Algorithm ◽  
Solution Space ◽  
Search Algorithms ◽  
Constraint Satisfaction Problems ◽  
Problem Instance ◽  
Stochastic Local Search ◽  
Local Search Algorithms ◽  
Local Energy Minimum

We study the performance of stochastic local search algorithms for random instances of the K-satisfiability (K-SAT) problem. We present a stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a problem instance by never going upwards in energy. ChainSAT is a focused algorithm in the sense that it focuses on variables occurring in unsatisfied clauses. We show by extensive numerical investigations that ChainSAT and other focused algorithms solve large K-SAT instances almost surely in linear time, up to high clause-to-variable ratios α; for example, for K = 4 we observe linear-time performance well beyond the recently postulated clustering and condensation transitions in the solution space. The performance of ChainSAT is a surprise given that by design the algorithm gets trapped into the first local energy minimum it encounters, yet no such minima are encountered. We also study the geometry of the solution space as accessed by stochastic local search algorithms.

Undirected Graphs Realizable as Graphs of Modular Lattices

1965 ◽  
Vol 17 ◽  
pp. 923-932 ◽  
Author(s):  
Laurence R. Alvarez
Keyword(s):  
Distributive Lattice ◽  
Partial Order ◽  
Directed Graph ◽  
Undirected Graph ◽  
Single Edge ◽  
Undirected Graphs ◽  
Modular Lattices

If (L, ≥) is a lattice or partial order we may think of its Hesse diagram as a directed graph, G, containing the single edge E(c, d) if and only if c covers d in (L, ≥). This graph we shall call the graph of (L, ≥). Strictly speaking it is the basis graph of (L, ≥) with the loops at each vertex removed; see (3, p. 170).We shall say that an undirected graph Gu can be realized as the graph of a (modular) (distributive) lattice if and only if there is some (modular) (distributive) lattice whose graph has Gu as its associated undirected graph.

Discovering Network Motifs in Protein Interaction Networks

2009 ◽  
pp. 117-143 ◽  
Author(s):  
Raymond Wan ◽  
Hiroshi Mamitsuka
Keyword(s):  
Protein Interaction ◽  
Graph Algorithms ◽  
Protein Interaction Network ◽  
Undirected Graph ◽  
Interaction Network ◽  
Building Blocks ◽  
Software Tools ◽  
Protein Interaction Networks ◽  
Interaction Networks ◽  
Network Motifs

This chapter examines some of the available techniques for analyzing a protein interaction network (PIN) when depicted as an undirected graph. Within this graph, algorithms have been developed which identify “notable” smaller building blocks called network motifs. The authors examine these algorithms by dividing them into two broad categories based on two de?nitions of “notable”: (a) statistically-based methods and (b) frequency-based methods. They describe how these two classes of algorithms differ not only in terms of ef?ciency, but also in terms of the type of results that they report. Some publicly-available programs are demonstrated as part of their comparison. While most of the techniques are generic and were originally proposed for other types of networks, the focus of this chapter is on the application of these methods and software tools to PINs.

Constant Time Graph Algorithms on the Reconfigurable Multiple Bus Machine

1997 ◽  
Vol 46 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Jerry L. Trahan ◽  
Ramachandran Vaidyanathan ◽  
Chittur P. Subbaraman
Keyword(s):  
Graph Algorithms ◽  
Constant Time ◽  
Time Graph

TRANSITIVE CLOSURE IN PARALLEL ON A LINEAR NETWORK OF PROCESSORS

1992 ◽  
Vol 02 (02n03) ◽  
pp. 195-203
Author(s):  
MICHEL GASTALDO ◽  
MICHEL MORVAN ◽  
J. MIKE ROBSON
Keyword(s):  
Parallel Algorithm ◽  
Directed Graph ◽  
Transitive Closure ◽  
Linear Time ◽  
Linear Network

In this paper, we propose a linear time parallel algorithm (in the number of edges of the transitive closure) that computes the transitive closure of a directed graph on a linear network of n processors. The underlying architecture is a linear network of processors with neighbouring communications, where the number of processors is equal to the number of vertices of the graph.

scholarly journals Skew Spectra of Oriented Graphs

10.37236/270 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Bryan Shader ◽  
Wasin So
Keyword(s):  
Directed Graph ◽  
Adjacency Matrix ◽  
Undirected Graph ◽  
Oriented Graph ◽  
Oriented Graphs ◽  
Underlying Graph ◽  
Adjacency Spectrum ◽  
The Relationship ◽  
Skew Adjacency Matrix

An oriented graph $G^{\sigma}$ is a simple undirected graph $G$ with an orientation $\sigma$, which assigns to each edge a direction so that $G^{\sigma}$ becomes a directed graph. $G$ is called the underlying graph of $G^{\sigma}$, and we denote by $Sp(G)$ the adjacency spectrum of $G$. Skew-adjacency matrix $S( G^{\sigma} )$ of $G^{\sigma}$ is introduced, and its spectrum $Sp_S( G^{\sigma} )$ is called the skew-spectrum of $G^{\sigma}$. The relationship between $Sp_S( G^{\sigma} )$ and $Sp(G)$ is studied. In particular, we prove that (i) $Sp_S( G^{\sigma} ) = {\bf i} Sp(G)$ for some orientation $\sigma$ if and only if $G$ is bipartite, (ii) $Sp_S(G^{\sigma}) = {\bf i} Sp(G)$ for any orientation $\sigma$ if and only if $G$ is a forest, where ${\bf i}=\sqrt{-1}$.

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