scholarly journals An Effective Algorithm for and Phase Transitions of the Directed Hamiltonian Cycle Problem

2010 ◽  
Vol 39 ◽  
pp. 663-687 ◽  
Author(s):  
G. Jäger ◽  
W. Zhang
Keyword(s):  
Phase Transitions ◽  
Hamiltonian Cycle ◽  
Directed Graphs ◽  
Combinatorial Problem ◽  
Combinatorial Problems ◽  
Effective Algorithm ◽  
Intrinsic Properties ◽  
Award Winning ◽  
Close Relationship ◽  
Hamiltonian Cycle Problem

The Hamiltonian cycle problem (HCP) is an important combinatorial problem with applications in many areas. It is among the first problems used for studying intrinsic properties, including phase transitions, of combinatorial problems. While thorough theoretical and experimental analyses have been made on the HCP in undirected graphs, a limited amount of work has been done for the HCP in directed graphs (DHCP). The main contribution of this work is an effective algorithm for the DHCP. Our algorithm explores and exploits the close relationship between the DHCP and the Assignment Problem (AP) and utilizes a technique based on Boolean satisfiability (SAT). By combining effective algorithms for the AP and SAT, our algorithm significantly outperforms previous exact DHCP algorithms, including an algorithm based on the award-winning Concorde TSP algorithm. The second result of the current study is an experimental analysis of phase transitions of the DHCP, verifying and refining a known phase transition of the DHCP.

The Parity Hamiltonian Cycle Problem in Directed Graphs

2016 ◽  
pp. 50-58
Author(s):  
Hiroshi Nishiyama ◽  
Yukiko Yamauchi ◽  
Shuji Kijima ◽  
Masafumi Yamashita
Keyword(s):  
Hamiltonian Cycle ◽  
Directed Graphs ◽  
Hamiltonian Cycle Problem

scholarly journals Feature Selection and Parameter Optimization of Support Vector Machines Based on Modified Artificial Fish Swarm Algorithms

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Kuan-Cheng Lin ◽  
Sih-Yang Chen ◽  
Jason C. Hung
Keyword(s):  
Feature Selection ◽  
Parameter Optimization ◽  
Combinatorial Problem ◽  
Combinatorial Problems ◽  
Support Vector ◽  
Local Optimum ◽  
Artificial Fish Swarm Algorithm ◽  
Swarm Algorithms ◽  
Artificial Fish Swarm ◽  
Information And Communication

Rapid advances in information and communication technology have made ubiquitous computing and the Internet of Things popular and practicable. These applications create enormous volumes of data, which are available for analysis and classification as an aid to decision-making. Among the classification methods used to deal with big data, feature selection has proven particularly effective. One common approach involves searching through a subset of the features that are the most relevant to the topic or represent the most accurate description of the dataset. Unfortunately, searching through this kind of subset is a combinatorial problem that can be very time consuming. Meaheuristic algorithms are commonly used to facilitate the selection of features. The artificial fish swarm algorithm (AFSA) employs the intelligence underlying fish swarming behavior as a means to overcome optimization of combinatorial problems. AFSA has proven highly successful in a diversity of applications; however, there remain shortcomings, such as the likelihood of falling into a local optimum and a lack of multiplicity. This study proposes a modified AFSA (MAFSA) to improve feature selection and parameter optimization for support vector machine classifiers. Experiment results demonstrate the superiority of MAFSA in classification accuracy using subsets with fewer features for given UCI datasets, compared to the original FASA.

scholarly journals Semi-Degree Threshold for Anti-Directed Hamiltonian Cycles

10.37236/3610 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Louis DeBiasio ◽  
Theodore Molla
Keyword(s):  
Directed Graph ◽  
Hamiltonian Cycle ◽  
Minimum Degree ◽  
Directed Graphs ◽  
Hamiltonian Cycles ◽  
Alternate Direction ◽  
Degree Conditions

In 1960 Ghouila-Houri extended Dirac's theorem to directed graphs by proving that if $D$ is a directed graph on $n$ vertices with minimum out-degree and in-degree at least $n/2$, then $D$ contains a directed Hamiltonian cycle. For directed graphs one may ask for other orientations of a Hamiltonian cycle and in 1980 Grant initiated the problem of determining minimum degree conditions for a directed graph $D$ to contain an anti-directed Hamiltonian cycle (an orientation in which consecutive edges alternate direction). We prove that for sufficiently large even $n$, if $D$ is a directed graph on $n$ vertices with minimum out-degree and in-degree at least $\frac{n}{2}+1$, then $D$ contains an anti-directed Hamiltonian cycle. In fact, we prove the stronger result that $\frac{n}{2}$ is sufficient unless $D$ is one of two counterexamples. This result is sharp.

NONLINEAR COMPUTABILITY BASED ON CHAOS

2000 ◽  
Vol 10 (02) ◽  
pp. 415-429 ◽  
Author(s):  
GABRIELE MANGANARO ◽  
JOSE PINEDA DE GYVEZ
Keyword(s):  
Hamiltonian Path ◽  
Combinatorial Problem ◽  
Combinatorial Problems ◽  
Information Coding ◽  
Computing Power ◽  
Complete Problems ◽  
Np Complete ◽  
Systematic Solution ◽  
Chaotic Simulated Annealing ◽  
Computing Models

Two new computing models based on information coding and chaotic dynamical systems are presented. The novelty of these models lies on the blending of chaos theory and information coding to solve complex combinatorial problems. A unique feature of our computing models is that despite the nonpredictability property of chaos, it is possible to solve any combinatorial problem in a systematic way, and with only one dynamical system. This is in sharp contrast to methods based on heuristics employing an array of chaotic cells. To prove the computing power and versatility of our models, we address the systematic solution of classical NP-complete problems such as the three colorability and the directed Hamiltonian path in addition to a new chaotic simulated annealing scheme.

AN EFFICIENT LOTOS-BASED FRAMEWORK FOR DESCRIBING AND SOLVING (TEMPORAL) CSPs

2009 ◽  
Vol 19 (06) ◽  
pp. 765-789
Author(s):  
SAMIRA SADAOUI ◽  
MALEK MOUHOUB ◽  
BO CHEN
Keyword(s):  
Constraint Satisfaction Problem ◽  
Combinatorial Problem ◽  
Experimental Tests ◽  
Search Space ◽  
Constraint Propagation ◽  
Combinatorial Problems ◽  
Temporal Constraints ◽  
Transition Systems ◽  
Time Performance ◽  
Novel Approach

Simulation of complex Lotos specifications is not always efficient due to the space explosion problem of their corresponding transition systems. To overcome this difficulty in practice, we present in this paper a novel approach which integrates constraint propagation techniques into the Lotos specifications. These solving techniques are used to reduce the size of the search space before and during the search for a solution to a given combinatorial problem under constraints. In order to do that, we first tackle the challenging task of describing combinatorial problems in Lotos using the Constraint Satisfaction Problem (CSP) framework. In this regard, we provide two generic Lotos templates for describing CSPs and temporal CSPs (CSPs involving temporal constraints). To evaluate the time performance of the framework we propose, we have conducted several experimental tests on instances of the N-Queens, the machine scheduling and randomly generated CSPs. The results of these experiments are promising and demonstrate the efficiency of Lotos simulation when CSP techniques are integrated.

KNOTTED HAMILTONIAN CYCLES IN LINEAR EMBEDDING OF K7 INTO ℝ3

2012 ◽  
Vol 21 (14) ◽  
pp. 1250132 ◽  
Author(s):  
YOUNGSIK HUH
Keyword(s):  
Complete Graph ◽  
Hamiltonian Cycle ◽  
Hamiltonian Cycles ◽  
Intrinsic Properties ◽  
Linear Embedding

In 1983 Conway and Gordon proved that any embedding of the complete graph K7 into ℝ3 contains at least one nontrivial knot as its Hamiltonian cycle. After their work knots (also links) are considered as intrinsic properties of abstract graphs, and numerous subsequent works have been continued until recently. In this paper, we are interested in knotted Hamiltonian cycles in linear embedding of K7. Concretely it is shown that any linear embedding of K7 contains at most three figure-8 knots.

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