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Questions tagged [hamiltonian-cycle]

A Hamiltonian cycle is a cycle in a directed or undirected graph that visits each node/vertex exactly once.

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Algorithm for finding a Hamilton Path in a DAG

I am referring to Skienna's Book on Algorithms. The problem of testing whether a graph G contains a Hamiltonian path is NP-hard, where a Hamiltonian path P is a path that visits each vertex exactly once. There does not have to be an edge in G from…
user2302617
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What is the dynamic programming algorithm for finding a Hamiltonian cycle in a graph?

What is dynamic programming algorithm for finding a Hamiltonian cycle in an undirected graph? I have seen somewhere that there exists an algorithm with O(n.2^n) time complexity.
avd
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Difference between Hamiltonian path and ST

I was reading up algorithms for finding the minimum spanning tree(in case of weighted graphs) and for finding if a graph has a hamiltonian path(which depends on the presence of a hamiltonian cycle). I got everything messed up. So whats the…
letsc
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How to detect if the given graph has a cycle containing all of its nodes? Does the suggested algorithm have any flaws?

I have a connected, non-directed, graph with N nodes and 2N-3 edges. You can consider the graph as it is built onto an existing initial graph, which has 3 nodes and 3 edges. Every node added onto the graph and has 2 connections with the existing…
Varaquilex
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Algorithm to find a random Hamiltonian path in a grid?

I'm looking for an efficient algorithm that is able to find an as random as possible Hamiltonian path in a bidirectional N*M grid. Does anyone know where I can find, or how to go about constructing such an algorithm? I've already found an efficient…
Fejuto
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Enumerate *all* hamiltonian paths

I know this has been asked before, but I did not find its answer in any of the posts. Can someone please suggest me an algorithm which enumerates ALL Hamiltonian paths in a graph? A little background: I am working on a problem in which I have to…
Darth.Vader
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Canonical algorithm for "visit each door once" problems

There are a number of puzzles that are variant of the classic "7 Bridges of Konigsberg" puzzle where you must find a route through a set of rooms without ever using a door twice. Here is an example of one without a solution. ... and is a slightly…
ŹV -
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Complete Weighted Graph and Hamiltonian Tour

I ran into a question on a midterm exam. Can anyone clarify the answer? Problem A: Given a Complete Weighted Graph G, find a Hamiltonian Tour with minimum weight. Problem B: Given a Complete Weighted Graph G and Real Number R, does G have a…
user4559497
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Finding Longest Path Grid

I am working with a uniform cost grid that only allows movements in the orthogonal directions. This is used as a base for the game snake where the snake must constantly move and try to eat apples on the board. The location of the food and collision…
Cobey Hollier
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Finding Hamiltonian cycles in cubic planar graphs

I have relatively small (40-80 nodes) cubic (3-regular) planar graphs, and I have to decide their Hamiltonicity. I am aware of the fact that this task is NP-complete, but I hope for asymptotically exponential time algorithms that are nevertheless…
Dániel Varga
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Complete Weighted Graph G, Finding Weights and one Machine

I read a lot about Complete Weighted Graph and Hamiltonian Tour topics in this site that asked by one of users, ask a lots of staff in my university, but couldn't get to a good answer, I change an important part of this question as follows:…
user4249446
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Detect cycles in undirected graph using boost graph library

I've been stuck since yesterday with this problem. Unfortunately/fortunately this problem makes only about 0.5% of the my super huge (for me, a c++ newbie) algorithm thus the need for a library of existing code that one can just adapt and get things…
Daniel
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Can someone introduce me to the Hamiltonian Cycle?

I have this project where I have to come up with Java source code implementing the Hamiltonian cycle. I searched on google and at least now I know what a Hamiltonian cycle is, path that passes through all vertices just once except the starting…
user662181
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How to implement an adjacency matrix in java producing hamilton cycles

I am trying to implement an adjacency matrix in java that will produce an output for a Hamiltonian cycle, which can then be solved with different algorithms such as kruskurals, djikstras and the 2opt approach. i know that i need a 2d array but i…
alchemey89
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How do I find the number of Hamiltonian cycles that do not use "forbidden" edges?

This question actually rephrases that one. The code jam problem is the following: You are given a complete undirected graph with N nodes and K "forbidden" edges. N <= 300, K <= 15. Find the number of Hamiltonian cycles in the graph that do not use…
Michael
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