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.

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

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.

A Parallel Reduction of Hamiltonian Cycle to Hamiltonian Path in Tournaments

1995 ◽  
Vol 19 (3) ◽  
pp. 432-440 ◽  
Author(s):  
E. Bampis ◽  
M. Elhaddad ◽  
Y. Manoussakis ◽  
M. Santha
Keyword(s):  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Parallel Reduction

scholarly journals A Representation of Membrane Computing with a Clustering Algorithm on the Graphical Processing Unit

Processes ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1199
Author(s):  
Ravie Chandren Muniyandi ◽  
Ali Maroosi
Keyword(s):  
Graphics Processing Units ◽  
Clustering Algorithm ◽  
Hamiltonian Path ◽  
Fold Increase ◽  
General Purpose ◽  
Processing Unit ◽  
Thread Block ◽  
Hard Problems ◽  
Graphical Processing ◽  
Graphics Processing

Long-timescale simulations of biological processes such as photosynthesis or attempts to solve NP-hard problems such as traveling salesman, knapsack, Hamiltonian path, and satisfiability using membrane systems without appropriate parallelization can take hours or days. Graphics processing units (GPU) deliver an immensely parallel mechanism to compute general-purpose computations. Previous studies mapped one membrane to one thread block on GPU. This is disadvantageous given that when the quantity of objects for each membrane is small, the quantity of active thread will also be small, thereby decreasing performance. While each membrane is designated to one thread block, the communication between thread blocks is needed for executing the communication between membranes. Communication between thread blocks is a time-consuming process. Previous approaches have also not addressed the issue of GPU occupancy. This study presents a classification algorithm to manage dependent objects and membranes based on the communication rate associated with the defined weighted network and assign them to sub-matrices. Thus, dependent objects and membranes are allocated to the same threads and thread blocks, thereby decreasing communication between threads and thread blocks and allowing GPUs to maintain the highest occupancy possible. The experimental results indicate that for 48 objects per membrane, the algorithm facilitates a 93-fold increase in processing speed compared to a 1.6-fold increase with previous algorithms.

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.

scholarly journals Time-Free Solution to Hamilton Path Problems Using P Systems withd-Division

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Tao Song ◽  
Xun Wang ◽  
Hongjiang Zheng
Keyword(s):  
Execution Time ◽  
Linear Time ◽  
Hamiltonian Path ◽  
P Systems ◽  
Free Solution ◽  
Hamilton Path ◽  
Working Space ◽  
A Cell ◽  
Hard Problems ◽  
Computing Models

P systems withd-division are a particular class of distributed and parallel computing models investigated in membrane computing, which are inspired from the budding behavior of Baker’s yeast (a cell can generate several cells in one reproducing cycle). In previous works, such systems can theoretically generate exponential working space in linear time and thus provide a way to solve computational hard problems in polynomial time by a space-time tradeoff, where the precise execution time of each evolution rule, one time unit, plays a crucial role. However, the restriction that each rule has a precise same execution time does not coincide with the biological fact, since the execution time of biochemical reactions can vary because of external uncontrollable conditions. In this work, we consider timed P systems withd-division by adding a time mapping to the rules to specify the execution time for each rule, as well as the efficiency of the systems. As a result, a time-free solution to Hamiltonian path problem (HPP) is obtained by a family of such systems (constructed in a uniform way), that is, the execution time of the rules (specified by different time mappings) has no influence on the correctness of the solution.

scholarly journals Maximum graphs non-Hamiltonian-connected from a vertex

1984 ◽  
Vol 25 (1) ◽  
pp. 97-98
Author(s):  
G. R. T. Hendry
Keyword(s):  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Hamiltonian Graphs ◽  
Connected Graphs ◽  
Hamiltonian Connected

A path (cycle) in a graph G is called a hamiltonian path (cycle) of G if it contains every vertex of G. A graph is hamiltonian if it contains a hamiltonian cycle. A graph G is hamiltonian-connectedif it contains a u-vhamiltonian path for each pair u, v of distinct vertices of G. A graph G is hamiltonian-connected from a vertex v of G if G contains a v-whamiltonian path for each vertex w≠v. Considering only graphs of order at least 3, the class of graphs hamiltonian-connected from a vertex properly contains the class of hamiltonian-connected graphs and is properly contained in the class of hamiltonian graphs.

scholarly journals Hamiltonian Cycle in K1,r-Free Split Graphs — A Dichotomy

2021 ◽  
pp. 1-32
Author(s):  
P. Renjith ◽  
N. Sadagopan
Keyword(s):  
Polynomial Time ◽  
Maximum Degree ◽  
Optimization Problem ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Np Hard ◽  
Polynomial Time Algorithms ◽  
Split Graphs ◽  
Np Complete ◽  
Cycle Path

For an optimization problem known to be NP-Hard, the dichotomy study investigates the reduction instances to determine the line separating polynomial-time solvable vs NP-Hard instances (easy vs hard instances). In this paper, we investigate the well-studied Hamiltonian cycle problem (HCYCLE), and present an interesting dichotomy result on split graphs. T. Akiyama et al. (1980) have shown that HCYCLE is NP-complete on planar bipartite graphs with maximum degree [Formula: see text]. We use this result to show that HCYCLE is NP-complete for [Formula: see text]-free split graphs. Further, we present polynomial-time algorithms for Hamiltonian cycle in [Formula: see text]-free and [Formula: see text]-free split graphs. We believe that the structural results presented in this paper can be used to show similar dichotomy result for Hamiltonian path problem and other variants of Hamiltonian cycle (path) problems.

scholarly journals Hamiltonian paths in odd graphs

2009 ◽  
Vol 3 (2) ◽  
pp. 386-394 ◽  
Author(s):  
Letícia Bueno ◽  
Luerbio Faria ◽  
Figueiredo De ◽  
Fonseca Da
Keyword(s):  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Transitive Graph ◽  
Direct Computation ◽  
Hamiltonian Paths ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Vertex Transitive Graph ◽  
Transitive Graphs ◽  
Connected Vertex

Lov?sz conjectured that every connected vertex-transitive graph has a Hamiltonian path. The odd graphs Ok form a well-studied family of connected, k-regular, vertex-transitive graphs. It was previously known that Ok has Hamiltonian paths for k ? 14. A direct computation of Hamiltonian paths in Ok is not feasible for large values of k, because Ok has (2k - 1, k - 1) vertices and k/2 (2k - 1, k - 1) edges. We show that Ok has Hamiltonian paths for 15 ? k ? 18. Instead of directly running any heuristics, we use existing results on the middle levels problem, therefore further relating these two fundamental problems, namely finding a Hamiltonian path in the odd graph and finding a Hamiltonian cycle in the corresponding middle levels graph. We show that further improved results for the middle levels problem can be used to find Hamiltonian paths in Ok for larger values of k.

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