scholarly journals Layered graph traversals and Hamiltonian path problems — An algebraic approach

1998 ◽  
pp. 96-121 ◽  
Author(s):  
Thomas Brunn ◽  
Bernhard Möller ◽  
Martin Russling
Keyword(s):  
Hamiltonian Path ◽  
Algebraic Approach ◽  
Hamiltonian Path Problems ◽  
Layered Graph

Winding indexes of Max. and Min. Hamiltonians in N-Gons

2017 ◽  
Vol 09 (05) ◽  
pp. 1750061
Author(s):  
Blanca Isabel Niel
Keyword(s):  
Hamiltonian Path ◽  
Hamiltonian Cycles ◽  
Arithmetic Algorithm ◽  
Hamiltonian Path Problems

The resolutions of the different Shortest and Longest Euclidean Hamiltonian Path Problems on the vertices of simple regular [Formula: see text]-Gons, by means of a geometric and arithmetic algorithm allow us to define winding indexes for Euclidean Hamiltonian cycles. New statements characterize orientation of non-necessarily regular Hamiltonian cycles on the [Formula: see text]th roots of the unity embedded in the plane and deal with the existence of reflective bistarred Hamiltonian tours on vertices of coupled [Formula: see text]-Gons.

Parallel algorithms for the hamiltonian cycle and hamiltonian path problems in semicomplete bipartite digraphs

Algorithmica ◽  
1997 ◽  
Vol 17 (1) ◽  
pp. 67-87 ◽  
Author(s):  
J. Bang-Jensen ◽  
M. El Haddad ◽  
Y. Manoussakis ◽  
T. M. Przytycka
Keyword(s):  
Parallel Algorithms ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Hamiltonian Path Problems

Approximation algorithms for multiple terminal, Hamiltonian path problems

2010 ◽  
Vol 6 (1) ◽  
pp. 69-85 ◽  
Author(s):  
Jungyun Bae ◽  
Sivakumar Rathinam
Keyword(s):  
Approximation Algorithms ◽  
Hamiltonian Path ◽  
Hamiltonian Path Problems

A successful algorithm for solving directed Hamiltonian path problems

1984 ◽  
Vol 3 (1) ◽  
pp. 35-42 ◽  
Author(s):  
Gerald L. Thompson ◽  
Sharad Singhal
Keyword(s):  
Hamiltonian Path ◽  
Hamiltonian Path Problems

EVERY LONGEST HAMILTONIAN PATH IN EVEN n-GONS

2012 ◽  
Vol 04 (04) ◽  
pp. 1250057 ◽  
Author(s):  
BLANCA I. NIEL
Keyword(s):  
Traveling Salesman Problem ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Traveling Salesman ◽  
Maximum Traveling Salesman Problem ◽  
Longest Path ◽  
Hamiltonian Path Problems ◽  
Planar Rotations

We single out every longest path of n-1 order that solves each of the [Formula: see text] Longest Euclidean Hamiltonian Path Problems on the even nth root of the unity, by means of a geometric and arithmetic procedure. This identification is done regardless of planar rotations and orientation. In addition, the uniqueness of the Euclidean Hamiltonian cycle that resolves the Maximum Traveling Salesman Problem is shown.

scholarly journals Universal Biochip Readout of Directed Hamiltonian Path Problems

2003 ◽  
pp. 168-181 ◽  
Author(s):  
David Harlan Wood ◽  
Catherine L. Taylor Clelland ◽  
Carter Bancroft
Keyword(s):  
Hamiltonian Path ◽  
Hamiltonian Path Problems

scholarly journals Various variants of Hamiltonian problems

2018 ◽  
Author(s):  
Thinh D. Nguyen
Keyword(s):  
Hamiltonian Cycle ◽  
Short Note ◽  
Hamiltonian Path ◽  
Hamiltonian Problems ◽  
Hard Problems ◽  
Hamiltonian Path Problems ◽  
Mathematics Community

Hamiltonian cycle and Hamiltonian path problems are famous hard problems. The Hamiltonian cycle seems to have received more attention from the mathematics community. In this short note, we want to mitigate this bias a little bit. Keeping on track with the Prasolov and Sharygin kinds of doing mathematics, we give several simple constructions to show the hardness of some variants of Hamiltonian path problems.

Roulette Wheel Selection based Heuristic Algorithm for the Orienteering Problem

2014 ◽  
Vol 13 (1) ◽  
pp. 4127-4145
Author(s):  
Madhushi Verma ◽  
Mukul Gupta ◽  
Bijeeta Pal ◽  
Prof. K. K. Shukla
Keyword(s):  
Triangle Inequality ◽  
Time Budget ◽  
Control Point ◽  
Hamiltonian Path ◽  
Real Life ◽  
Tourism Industry ◽  
Orienteering Problem ◽  
Complete Graphs ◽  
Roulette Wheel Selection ◽  
Roulette Wheel

Orienteering problem (OP) is an NP-Hard graph problem. The nodes of the graph are associated with scores or rewards and the edges with time delays. The goal is to obtain a Hamiltonian path connecting the two necessary check points, i.e. the source and the target along with a set of control points such that the total collected score is maximized within a specified time limit. OP finds application in several fields like logistics, transportation networks, tourism industry, etc. Most of the existing algorithms for OP can only be applied on complete graphs that satisfy the triangle inequality. Real-life scenario does not guarantee that there exists a direct link between all control point pairs or the triangle inequality is satisfied. To provide a more practical solution, we propose a stochastic greedy algorithm (RWS_OP) that uses the roulette wheel selectionmethod, does not require that the triangle inequality condition is satisfied and is capable of handling both complete as well as incomplete graphs. Based on several experiments on standard benchmark data we show that RWS_OP is faster, more efficient in terms of time budget utilization and achieves a better performance in terms of the total collected score ascompared to a recently reported algorithm for incomplete graphs.

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