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Questions tagged [hamiltonian-path]

Questions on Hamiltonian paths, that is, paths that visit each vertex exactly once in a graph.

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Hamiltonian path in grid graph

Here is my situation. I have a grid-type graph with obstacles. Every move (horizontally, vertically or diagonally with a range of 1) has a cost of exactly 1 (the graph is not weighted) provided that ...
5
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2answers
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Greedy and backtracking solutions to an arrangement problem with constraints

I'm revising for my finals. I have found a pattern in past papers in terms of a recurring question, reworded coming up every year. But I've no idea what the marker actually wants... I've asked class ...
2
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2answers
2k views

CNF Generator for Factoring Problems

I've been reading these: Fast Reduction from RSA to SAT CNF Generator for Factoring Problems (Also have C code implementation) I don't understand how the reduction from FACT to $3\text{-SAT}$ works. ...
3
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2answers
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What TSP variant doesn't return to start point?

For my case I have starting point and several cities. I want the shortest route to visit all cities without returning starting point. I have read several TSP algorithm and all include the return a ...
3
votes
2answers
2k views

Find hamilton cycle in a directed graph reduced to sat problem

I need to find a Hamiltonian cycle in a directed graph using propositional logic, and to solve it by sat solver. So after I couldn't find a working solution, I found a paper that describes how to ...
2
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1answer
158 views

Lower bounding the minimum equivalent graph

The transitive reduction $G^t = (V,E^t)$ of a graph $G=(V,E)$ is the smallest graph with the same reachability as $G$ with the property $E^t \subseteq V \times V$. The minimum equivalent graph $G' = (...
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3answers
207 views

Which of the following problems can be reduced to the Hamiltonian path problem?

I'm taking the Algorithms: Design and Analysis II class, one of the questions asks: Assume that P ≠ NP. Consider undirected graphs with nonnegative edge lengths. Which of the following problems ...
0
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0answers
56 views

A polynomial reduction from HAMPATH to LONG-PATH [duplicate]

$\text{HAMPATH} = \{(G=(V,E),s',t')| \text{ G has a Hamilton path from s' to t' } \}$ $\text{LONG-PATH} = \{(G,s,t,k) | \text{G has a simple path p from s to t, length(p) $\geq$ k} \}$ I'm trying ...