Questions tagged [hamiltonian-path]
Questions on Hamiltonian paths, that is, paths that visit each vertex exactly once in a graph.
92
questions
0
votes
0
answers
9
views
Are there any good papers that provide good definitions for the Minimum Weight Hamiltonian Path Problem?
I am looking for a paper to cite in a paper of my own regarding the Minimum Weight Hamiltonian Path Problem. This is distinct from the TSP because it is a path, not a cycle, meaning that a return to ...
1
vote
0
answers
34
views
Why does greedy approach of constructing De Bruijin Sequence work?
I have recently discovered a greedy algorithm to construct De Bruijin Sequence.
The greedy approach (prefer-largest specifically) works like the following:
Start with a sequence of all 0's of length ...
- 11
0
votes
0
answers
19
views
To Prove NP-Completeness [duplicate]
Given a Directed Graph G, and some subsets of vertices T1,T2,..Tn(These subset can intersect) , is there a path in this graph such that it is acyclic and contains exactly 3 vertices from each Ti. I'm ...
- 1
0
votes
1
answer
154
views
Finding a Hamiltonian Cycle in a directed graph - graph problem
$N$ towns are given, which we can get to by passing through the northern and southern gates. If you enter a town through a gate, you have to use another gate to leave the town. The merchant would like ...
- 71
2
votes
1
answer
75
views
Why the choice of the adjacent vertex with the least degree is a good heuristic for the hamiltonian path problem?
Even if the hamiltonian path problem is NP-hard there exist heuristics which return a correct path for many instances in linear time. In particular one of the main rules is always choosing the ...
- 167
3
votes
2
answers
145
views
Hamiltonian cycle in $C_n^k$ in polynomial time for constant $k$?
Let $C_n$ denote the cycle graph over $n$ vertices. Let $C_n^k$ denote the $k$-th power of the cycle graph, or namely that for two vertices $i,j$, $(i,j)\in Edges(C_n^k) \iff |i-j|\leq k$ for a ...
- 594
3
votes
0
answers
118
views
Seemingly simple path finding problem, but graph with travelling salesman or shortest path does not work
I am looking for an algorithm to a problem that I encountered when working with 3D modeling:
On a 3D triangle surface mesh, I have multiple lines, some of them are open, some are closed. The are on ...
- 31
3
votes
2
answers
224
views
Is this graph Hamiltonian?
My case is a directed graph with $n$ nodes with $(n-1)^2+1$ edges. I have done the following till now.
We know that the maximum number of edges for a directed graph $K_n$ on $n$ nodes is $n(n-1)$ ...
- 135
0
votes
2
answers
259
views
How to reduce the hamiltonian path problem to 1/2 hamiltonian path problem
Task:
A Hamiltonian path of a graph is a path that visits all nodes of the graph exactly once. The hamiltion path problem (HPP) consists in deciding whether a given graph has such a path. Similarly, ...
1
vote
1
answer
64
views
Non-brute force algorithm for a Eulerian like path
I have a graph with an arbitrary amount of edges and vertexes. Each vertex having an arbitrary amount of edges connecting to it but in practice the number is usually around 3 or 4 no less than one ...
- 11
1
vote
1
answer
140
views
Prove the following claim on Hamilton Path?
I am trying to prove the following claim:
Given DAG graph, there is Hamilton path iff the following algorithm
returns true:
Do topologic sorting.
Move on the graph's vertices one by one (from low to ...
- 11
3
votes
3
answers
811
views
find a path to visit every node in graph not necessarily once
I meet a problem but when I google, there are all Hamiltonian Path Problem: How to find a path to visit every node in directed graph(not necessarily once)?
This problem is different from Hamiltonian ...
- 135
0
votes
1
answer
356
views
If P = NP, do these NP-complete problems reduce to these specific easier versions?
I am trying to understand reductions and NP-completeness from Algorithms by Dasgupta et al.
Chapter 8 has the table below and I am wondering:
if $P = NP$ does each of the problems on the left reduce ...
- 659
1
vote
1
answer
59
views
Given graph G and vertices v and w can you non-deterministically walk the "least Hamiltonian path" from v to w, if it exists?
My understanding of non-deterministic algorithms is that they're "as lucky as you want".
...you can think of the algorithm as being able to make a guess at any point it wants, and a space ...
- 411
2
votes
2
answers
437
views
Proving NP-hardness of Hamiltonian Cycle problem variant
I need to prove that determining whether a graph has a relaxed-Hamiltonian cycle (definition given ahead) is NP-hard.
A relaxed-Hamiltonian cycle in $G$ is a closed walk $C$ that visits every vertex ...
0
votes
0
answers
262
views
Is reduction from Rudrata/Hamiltonian path to Rudrata/Hamiltonian cycle O(1)?
I am reading about P and NP and looking at the reduction of a Rudrata/Hamiltonian path to a Rudrata cycle. I think adding an extra node and 2 edges connecting the start, ...
- 659
0
votes
1
answer
260
views
Is O(1) considered polynomial time?
I am reading about P and NP and looking at the reduction of a Rudrata/Hamiltonian path to a Rudrata cycle. I think adding an extra node and 2 edges connecting the start, ...
- 659
0
votes
0
answers
53
views
Number of Hamilton paths in graphs
I am trying to find a fast algorithm that can compute the number of hamiltonian paths in an undirected graph. I saw this on the web, but it sounds like this finds all hamiltonian paths starting from ...
- 101
1
vote
1
answer
440
views
If there is no Hamiltonian path in a DAG then there are at least two different Topological sorts
I understand the concept that if there is no Hamiltonian path so there will be 2 smaller paths and with them I can build more then one topological sort but I am not sure how make it formal.
Can you ...
2
votes
1
answer
106
views
Examples of difficult Hamiltonian Cycle Problems
I am working on implementing algorithms to solve Hamiltonian Cycle Problem. I need difficult problem graphs to test my implementations but my google-fu is weak and am unable to find any.
Please advise ...
- 25
1
vote
1
answer
274
views
What is the polynomial time reduction between these two Hamiltonian cycle problems?
Problem 1: Given an undirected graph, return the edges of a Hamiltonian cycle, or correctly decide that the graph has no such cycle.
Problem 2: Given an undirected graph, decide whether or not the ...
- 153
0
votes
2
answers
598
views
Confusion in Reduction of Hamiltonian-Path to Hamiltonian-Cycle
The following is an excerpt from a material on NP-Theory:
"Let G be an undirected graph and let s and t be vertices in G. A Hamiltonian path in G is a
path from s to t using edges of G, on which ...
- 42
3
votes
1
answer
871
views
Diameter of a disconnected graph
Given G(V,E) a graph that has 2 connected components, what is the diamter of this graph?
2
votes
1
answer
253
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 ...
- 143
0
votes
0
answers
28
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 ...
- 411
0
votes
0
answers
72
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 - ...
- 411
3
votes
2
answers
77
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 ...
- 201
1
vote
1
answer
766
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 ...
- 345
3
votes
3
answers
339
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
...
- 31
1
vote
1
answer
76
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 ...
- 1,381
2
votes
1
answer
755
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 ...
- 1,381
3
votes
2
answers
82
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 >...
- 131
4
votes
1
answer
1k
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-...
- 385
0
votes
0
answers
50
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 ...
- 13
1
vote
1
answer
136
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 ...
- 13
0
votes
1
answer
93
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 ...
- 1
2
votes
1
answer
49
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 ...
- 77
2
votes
0
answers
104
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 ...
- 19
1
vote
3
answers
1k
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 ...
- 283
5
votes
1
answer
217
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 ...
- 151
2
votes
2
answers
1k
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 ...
- 21
2
votes
1
answer
324
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. ...
- 121
1
vote
2
answers
381
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 ...
- 113
2
votes
1
answer
85
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 ...
- 1,901
1
vote
0
answers
533
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 ...
3
votes
1
answer
5k
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^...
- 451
0
votes
1
answer
777
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 ...
- 141
1
vote
1
answer
2k
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 ...
- 253
4
votes
3
answers
1k
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 ...
- 153
2
votes
1
answer
277
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 ...
- 1,408