However, whether there exists an algorithm whose time complexity is better than O ( n 2 log n ) for solving the Hamiltonian cycle problem on circular-arc graphs has been opened for two decades. In this paper, we
Hamiltonian graphconnected graphline sweepingrestricted backtrackingWhile determining whether a graph is Hamiltonian, it is enough to show existence of a Hamiltonian cycle in it. An algorithm based on restricted backtracking is presented in the paper that uses tie breaking rules to reduce the possible ...
A Space-Efficient Parameterized Algorithm for the Hamiltonian Cycle Problem by Dynamic AlgebraizationAn NP-hard graph problem may be intractable for general graphs but it could be efficiently solvable using dynamic programming for graphs with bounded treewidth. Employing dynamic programming on a......
LetGbe a directed graph withnvertices such that whenever there is no arc from any vertexuto another vertexv, then the sum of the outdegree ofuand the indegree ofvis at leastn. It is known that such a graphGalways contains a Hamiltonian cycle. We show that such a cycle can be computed...
Each Hamiltonian cycle found by this lemma contains all the boundary edges on the three sides of the rectangular graph. This shows that for an even-sized rectangular graph R, we can always find a Hamiltonian cycle such that it contains all the boundary edges except exactly one side of R ...
11.14. The half-Hamiltonian cycle problem is, given a graph G with n vertices, determine whether G has a simple cycle of length exactly [n/2], where the floor function rounds its input down to the nearest integer. Prove that this problem is NP-hard....
Held–Karp is the best known exact algorithm for TSP, and requires O(n22n) time and O(n2n) space. Execution time and memory usage are therefore significant considerations as n grows. The JavaScript implementation computes optimal Hamiltonian cycles for up to 28 cities (paths for up to 27 cit...
Hamiltonian Cycle SCOTCH (9) Graph Partition JOSTLE (9) Graph Partition Mike Trick's Graph Coloring Resources (9) Vertex Coloring,Edge Coloring FLUTE (9) Steiner Tree Triangle (9) Triangulation TRE (9) Approximate String Matching libxsmm (8) ...
An Interior Point Heuristic for the Hamiltonian Cycle Problem via Markov Decision Processes We consider the Hamiltonian cycle problem embedded in a singularly perturbed Markov decision process (MDP). More specifically, we consider the HCP as an op... V Ejov,J Filar,J Gondzio - 《Journal of ...
Held–Karp is the best known exact algorithm for TSP, and requires O(n22n) time and O(n2n) space. Execution time and memory usage are therefore significant considerations as n grows. The JavaScript implementation computes optimal Hamiltonian cycles for up to 28 cities (paths for up to 27 cit...