Hamiltonian Cycle Parameterized by Treedepth in Single Exponential Time and Polynomial SpaceComputer Science - Data Structures and AlgorithmsFor many algorithmic problems on graphs of treewidth \\(t\\), a standard dynamic programming approach gives an algorithm with time and space complexity \\(2^{...
complexity classNPHamiltonian 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 ...
AlgorithmBacktrackinGraphHamiltonian pathTSPBacktracking is one of the strategies to reduce the complexity of a problem. Backtracking mainly useful when there is a no solution by going forward in that direction so we required backtracking from it to reduce the complexity and save the time. ...
cycle, then the original graph must have a Hamiltonian cycle,and the other way around.Then,reduce directed Hamiltonian cycle to directed Hamiltonian path:suppose we are given a digraph.Construct a new graph as follows:Pick and arbitrary vertex and split it into two vertices:and.Let ...
When the coupling parameter g g is less than the critical value g_c g_c , the ground state is a superposition of all configurations with closed strings of spins in a same single-spin state, which can be obtained by using an adiabatic quantum algorithm with time complexity O(\frac{1}{g...
This allows an inexpensive simulation of the entire group of terms. We further show that the cost can in some cases be reduced by partially allocating Hamiltonian terms to several groups and provide a polynomial time classical algorithm that can greedily allocate the terms to appropriate groupings....
Figure1:(a)Acubic,bipartitegraphwithHamiltoniancycleinbold.(b)A simple2-regularbipartitegraph. Threequbitsofthefirstregister,denotedα,areinvolvedineverystepofthe algorithm.Theothern−1registerscontainqubitswhichinthemainareinthe state|0,exceptforthequbitcorrespondingtothewalkerscurrentposition. Toclarify...
Quantum computing Hamiltonian cycles
These problems are significant because of their relationships to each other: every NP-complete problem can be cast in the form of any other using a polynomial-time algorithm, meaning that an efficient algorithm for one NP-complete problem can be used to solve all others. Expert computer ...
A polynomial time algorithm for constructing a Hamiltonian cycle is also presented.doi:10.3923/itj.2006.851.859Riaz KhadijaMalik Sikander Hayat KhiyalAsian Network for Scientific InformationInformation Technology JournalRiaz, K. & Khiyal, M.S.I. (2006). Finding Hamiltonian cycle in polynomial time. ...