Questions tagged [hamiltonian-path]

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

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96 views

What is an example of a Monte-Carlo algorithm for finding a Hamiltonian path?

I've recently been made aware that there exist Monte-Carlo algorithm(s?) for determining whether a Hamiltonian path exists in a graph. I am struggling to figure out how it would work. What is the ...
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18 views

Does this imply Hamiltonian path cannot be decided in nondeterministic logspace?

Suppose I nondeterministically walk around in a graph with n vertices. When looking for a Hamiltonian path, at some point I’ve walked n/2 vertices. There are (n choose n/2) different combinations of ...
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30 views

Does this imply checking a candidate Hamiltonian Path solution can be done in logspace?

Assume vertices are integers base 2. Smallest vertex is 1. There are n vertices. Our input is: the number of vertices (n expressed in log(n) bits - ...
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2answers
40 views

Finding a hamiltonianISH path in a graph

Problem statement Given a graph of all the blue squares in the following image where each blue square is connected to other blue squares in all 4 cardinal directions. Given any starting node. What ...
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1answer
101 views

Hamiltonian cycle, verifying and finding

If we have an algorithm that in polynomial time says if a graph G has an hamiltonian cycle, can we have an algorithm that in polynomial time find an hamiltonian cycle? My attempt is to delete an edge ...
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3answers
162 views

How to find a path that connects all the dots in the matrix?

I have a matrix that consists of 0, 1, 2. 0 - dot. 1 - block. 2 - start dot (initial position in the path). I have to create a path from the start dot, that connects all the dots in the matrix and ...
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21 views

How can I convert this graph into CNF to solve the hamiltonian path with SAT?

So I have this graph, I am following the rules outlined in these slides: https://www.csie.ntu.edu.tw/~lyuu/complexity/2011/20111018.pdf The rules for converting the graph to CNF and the proof are in ...
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1answer
20 views

How complete directed graph with n-vertices is connected to the n-dimensional simplex and its triangulation?

Answer https://stackoverflow.com/a/26151549/1375882 suggests that Sperner's lemma can be used to prove the existence of index for the search Hamiltonian path in complete directed graph. But Sperner's ...
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1answer
110 views

Does topological sort exist for any complete directed acyclic graph?

Let's assume that DAG is complete: there is directed edge among every to nodes. Does topological sort of vertices exist for any such graph? I.e. is it possible to make linear list of nodes in which ...
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59 views

Finding a Hamiltonian path in this graph family

Given a directed graph $G = (V, E)$, you have been told that a Hamiltonian path $p_0p_1\ldots p_V$ exists with the property that for each edge $p_ip_j$ that is not part of the Hamiltonian path, $i >...
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1answer
473 views

Minimum Path cover in a Directed Acyclic Graph

Given a weighted directed acyclic graph $G=(V,D,W)$ and a set of arcs $D'$ of $D$, where the weights of $W$ are on the vertices. The problem is to partition $G$ into a minimum number of vertex-...
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34 views

Non intersecting paths of graphs with obstacle number one

There are $N$ points inside a polygon. If two points are connected by an edge (a line segment) if the edge is completely inside the polygon. We could conclude finding a Hamiltonian path is NPC, but ...
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1answer
42 views

Hamiltonian non intersecting path in plane

$N$ points are located in 2D plane. Some of the pair of the points are connected by line segments. What is the complexity of the problem of existence of Hamiltonian non intersecting path? What if we ...
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1answer
43 views

Decomposition of a directed graph into Hamiltonian paths

I was wondering if anyone knew of an algorithm that when given a directed graph will split it up into separate Hamiltonian paths. I don't really mind about nodes that can't be added to a path but as ...
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1answer
42 views

Shortest hamiltonian path for different dimension points

The shortest Hamiltonian path (solution) for a set of points in $\mathbb{R}^k$ (in Euclidean space) changes subject to $k$. For example if for $k=1$, the shortest Hamiltonian path will be the sorted ...
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88 views

Comparing locally maximal and localy minimal Hamiltonian paths [closed]

Let $K_n$ be a weighted complete graph on $n$ vertices. Two Hamiltonian paths are formed as follows. The first one, $H$, is formed by starting at an arbitrary vertex, and at each stage proceeding from ...
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3answers
551 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 ...
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1answer
117 views

Why is Adleman's molecular algorithm for Hamiltonian Path linear?

In Adleman's 1994 paper (archived), he describes a method of manipulating DNA molecules in a lab that results in a solution to the Hamiltonian Path problem with high probability. He claims that "The ...
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2answers
532 views

Is the longest Hamiltonian cycle NP-complete?

As I understand it to prove something is NP-complete you have to show that it's NP-hard by reducing and a known NP-complete problem to your problem and also prove that it is in NP which you do showing ...
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1answer
99 views

Proving that Hamiltonian Cycle is reducible to a travelling problem?

I chanced upon the following question online: A company has two trucks, and must deliver a number of parcels to a number of addresses. They want both drivers to be home at the end of the day. ...
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2answers
293 views

Solve Hamilton Circuit with Hamilton Path

I want to show the reduction $HC \leq HP$. Let $G=(V,E)$ be my undirected graph. My idea is: For each edge $e=(u,v) \in E$ check whether $(V,E\backslash\{e\})$ has a Hamiltonian Path. If this is true ...
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1answer
45 views

Can this Arrow-Ring puzzle be encoded as an integer programming problem?

I would like to write a solver for these kind of Arrow-Ring puzzles. However, I can't encode all the constraints correctly. I noticed that Sudoku can be solved using integer programming and I am ...
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0answers
410 views

Minimum weight Hamiltonian path on a weighted (0 and 1) tournament graph

Suppose we have a weighted tournament graph. (A directed graph in which every pair of distinct vertices is connected by a single directed edge.) The weights are constrained to be 0 and 1. I know ...
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1answer
3k views

Detecting Hamiltonian path in a graph

There are various methods to detect hamiltonian path in a graph. Brute force approach. i.e. considering all permutations T(n)=O(n*n!) Backtracking T(n)=O(n!) Using Dynamic programming T(n)=O(2^n * n^...
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1answer
488 views

DAG Hamiltonian Path NP-complete

The book computers and Intractability mentions that Hamiltonian Path problem is not NP-complete in DAG. But if Hamiltonian Cycle is NP-complete in digraph then I can split a vertex and create two ...
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1answer
931 views

Hamiltonian path and minimum spanning tree

Suppose i have a graph and i want to find minimum-spanning-tree. As in imperative languages we have to take specific steps from everynode(example ,we use kruskal's algorithm or prim's algorithm) to ...
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2answers
891 views

Rearranging strings so that the Hamming distance between them is 1

This is a question from CodeFights.com: Given an array of equal-length strings, check if it is possible to rearrange the strings in such a way that after the rearrangement the strings at ...
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1answer
163 views

Find the $k$-th lexicographically smallest hamiltonian circuit

Let's say we have given unweighted directed graph with $N$ nodes and $M$ edges, and we want to find the $K$-th hamiltonian circuit, ordered in lexicographical order. For example, if we have complete ...
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How can the shortest traveling salesman tour be found in $O(2^n poly(n))$ time and less than exponential space?

I'm stuck on problem 9.4 from The Nature of Computation which reads: Dynamic Salesman. A naive search algorithm for TSP takes $O(n!)$ time to check all tours. Use dynamic programming to reduce this ...
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1answer
192 views

Reducing one variant of Hamiltonian path to another

Define $A = \{<G,s,t> :G$ is un directed graph that has a Hamilton path from $s$ to $t\}$ $B = \{<G> :G$ is un directed graph that has a Hamilton path$\}$ I would like to show that $...
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1answer
69 views

How a NTM guessing depends on the input?

After looking at the definition of nondeterministic TMs, it seems that, while guessing, the machine could go to at most $|Q|\times | \Gamma |$ configurations, being in a particular one. However, if ...
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1answer
3k views

Hamiltonian path in directed graph

Let G be a directed graph such that every two vertices are connected by a single edge. How do I proof that such G has an hamiltonian path?
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1answer
129 views

Solving Hidoku problem using reduction to Hamilton path

It seems like people have discussed this reduction here: Is Hidoku NP complete? But it looks like the solution that was given only tells you if the Hidoku problem has a solution or not (if an ...
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2k views

Prove that a hamiltonian DAG has a single topological sort

I've been straggling a little proving the argument "a hamiltonian directed acyclic graph has a single topological sort". This is pretty much the idea of what I've come along: lets prove by ...
2
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1answer
182 views

Is the search for a k-Hamiltonian Path NP-hard?

A $k$-Hamiltonian Path is an Hamiltonian Path where each node (but the last $k$ nodes on the path) is connected to his $k$ successors, and the last $k$ nodes are connected to all of their successors. ...
3
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1answer
264 views

Number of “hamiltonian tours” from upper left to lower left corner of a grid graph?

I got the following as an interview question: Count the number of tours from the upper left corner to the lower left corner in a grid world where you can move in any manhattan direction. This is the ...
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2answers
2k views

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 ...
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1answer
260 views

NP-Hardness of Hamiltonian cycle with $|V|$ divisible by 3

Let SHAM3 be the problem of finding a Hamiltonian cycle in a graph $G=(V,E)$ with $|V|$ divisible by 3 and DHAM3 be the problem of determining if a Hamiltonian cycle exists in such graphs. Are ...
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1answer
600 views

NP-completeness of the exact distance problem

I am currently learning about NP-complete problems and I want to make sure my understanding is correct. Here is a problem I am working on currently: The exact distance problem is, given an edge-...
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3answers
972 views

Path in directed, weighted, cyclic graph with total distance closest to D?

Input: Directed, weighted, cyclic graph G. Two distinct vertices in that graph, A and B, where there exists a path from A to B. A distance d. Output: A path between A and B with distance closest to d....
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1answer
645 views

Why is Hamiltonian Path and graph coloring np complete and shortest path p when the former can also be solved using DFS recursively?

NP is a complexity class that represents the set of all decision problems for which the instances where the answer is "yes" have proofs that can be verified in polynomial time. But hamiltonian path ...
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1answer
1k views

How to build the Reduction from Hamiltonian Cycle problem to Subgraph isomorphism? [duplicate]

I'm trying to prove that the Subgraph isomorphism problem is NPC using the Hamiltonian Cycle problem. Unfortunately I feel (or don't understand) that the solution is "empty" and doesn't explain the ...
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Poly-time reduction from directed Hamiltonian Path to undirected HP, both with with known start and end

this is homework, so PLEASE do not give me the solution(!), but help me get there on my own. I've got to proof that directed Hamilton Path with fixed stard and ending and undirected Hamilton Path ...
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2answers
1k views

How to generate graphs with a Hamiltonian path?

I need to create a graph generator for my next project. Generally algorithms are trying to find a Hamiltonian path in a graph. So I can create a graph generator, generate a graph, and then I can ...
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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 ...
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1answer
338 views

Does the Bondy-Chvátal theorem have algorithmic applications beyond Ore's theorem?

I'm toying around with graph properties and I want to make some effort to check whether a given graph is Hamiltonian. I understand that the general problem is NP-complete, but I'm looking for simple ...
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1answer
833 views

Almost Hamiltonian

A graph is almost Hamiltonian if it contains a cycle that visits every node at least once and at most twice. Is the problem of determining whether a graph is almost Hamiltonian NP-complete?
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5k views

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 ...
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336 views

Finding partial traveling salesman path of specified length

For a given set of nodes, I can find optimal paths that visit all nodes using various traveling salesman algorithms. As a subset of this problem, I would like to be able to find shortest partial ...
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180 views

Upper bound on the number of hamiltonian cycles on a $n \times n $ grid graph

What is the best upper bound that is known for the number of hamiltonian cycles on a $n \times n $ grid graph? I did some searching and found that the number of hamiltonian cycles on a planar graph ...