Questions tagged [graph-algorithms]
Algorithms on graphs, excluding heuristics.
861
questions
1
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0answers
13 views
Does distance-2 coloring fit in Telle and Proskurowski 's algorithm for partial-k trees?
(This question is inteneded for people who have heard of "Vertex Partitioning Problems" framework of Telle and Proskurowski. Others may dig in only if they are interested in practical algorithms for ...
-2
votes
1answer
81 views
Minimum vertex cover and odd cycles
Suppose we have a graph G without odd cycles. Consider the minimum vertex cover problem of G formulated as a linear programming problem, that is for each vertex $v_{i}$ we have the variable $x_{i}$, ...
2
votes
1answer
80 views
How to choose good diagonals when partitioning an orthogonal polygon into rectangles?
Following this answer on MathOverflow and section 3 of the linked paper by David Eppstein on how to split an orthogonal polygon into rectangles I came to a point where I just fail to understand how to ...
1
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0answers
74 views
How to approach the “traveling salesman problem” with cost changing every time salesman reaches a new city
Let's say instead of finding the shortest path we have to maximize the profit in a year of the salesman under the following constraints.
Salesman can go to a different city only on weekends, all ...
0
votes
1answer
54 views
Reduction graph to planar bounded treewidth and bounded diameter graph
We got reduction graph to planar bounded treewidth graph,
but this is unlikely to be true.
Let $H$, the planarizing gadget, be planar graph with four
distinguished vertices $u,u',v,v'$ on the outer ...
4
votes
1answer
113 views
Hardness of finding if a vertex lies on a simple directed path between two vertices
Given a directed graph $G = (V, E)$ and three vertices $u, v, w \in V$. Is it NP-Hard to find whether there is a simple path from $u$ to $v$ passing through $w$?
I found a couple of hardness ...
2
votes
1answer
47 views
Maximum subgraph problem with unknown complexity
Let $Q$ be a polynomial time decidable graph property. In a graph let us call a subgraph $S$ a $Q$-subgraph, if $S$ has the property $Q$. Consider the following optimization problem:
Maximum $Q$-...
2
votes
0answers
43 views
Efficient game traversal of a DAG of 3-colorings
Let $X$ be a set of size $n$. Consider a game played on board $X$ by two players black and white. Starting with the empty board, each player chooses an empty spot to place a stone. Black moves ...
1
vote
1answer
46 views
Existence of graphs of every order related to Barnette’s conjecture
Consider the class C3CBP of $3$-connected cubic bipartite planar graphs. They form the class on which the (in)famous Barnette’s conjecture is based. My interest in C3CBP graphs is somewhat orthogonal ...
0
votes
2answers
56 views
Fast algorithm to find pair of triangles with a common edge in a complete graph
Suppose we have a complete graph with 4 nodes. To each triangle in this graph we assign a value $energy$ that is the multiplication of its edge weights. The question is to first find pair of triangles ...
9
votes
2answers
111 views
Complexity of finding an edge set yielding specified vertex degrees
I'm trying to figure out if the following two problems are known in general to be in P or NP-complete:
Q1: Given a graph $G=(V,E)$ and integers $d_i,\,1\leq\,i\leq|V|$, does there exist a subset $E'...
7
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0answers
126 views
Algebraic methods for testing planarity
Mac Lane's planarity criterion states that a graph is planar if and only if it has a cycle basis such that each edge is contained in at most two cycles, we call such a basis a 2-basis. A 2-basis of a ...
6
votes
1answer
188 views
Complexity of finding the largest induced subgraph with all even degrees
What is the complexity of the following problem?
Instance: Simple, undirected graph $G$, and a positive integer $k$.
Question: Does $G$ have an induced subgraph on at least $k$ vertices, such that ...
10
votes
1answer
689 views
Relationship between two graph optimization problems
Let $Q$ be a polynomial time computable graph property of simple, undirected graphs. Consider the following two optimization problems on any input graph:
P1. Find a largest induced subgraph of the ...
9
votes
0answers
128 views
What are some examples of algorithmic applications of noncommutative rational identity testing?
The problem of polynomial identity testing (PIT) is known to be in $\mathsf{RP}$, but not known to be in $\mathsf{P}$.
The related problem of noncommutative rational identity testing (NCIT) is known ...
8
votes
0answers
118 views
Is APSP verification easier than APSP?
In APSP, the input is an $n$-node directed weighted graph $G$, and the output is an $n \times n$ matrix holding pairwise shortest path distances between nodes in $G$. Define "APSP-Verification" as ...
2
votes
1answer
89 views
Diameter vs. Tractability
I would like to find examples of (unweighted) optimization problems $\Pi$ that satisfy 1) or 2):
1) $\Pi$ is NP-hard but polytime solvable in the class of graphs with diameter $\le k$, for all $k\ge ...
1
vote
1answer
99 views
Finding simple fixed length paths in directed graphs
Is there an efficient algorithm to enumerate unique simple fixed-length paths (of size $k$) in directed graphs? What would be its time complexity?
0
votes
1answer
73 views
Dividing a complete graph into two cliques with maximal sum of edge weights
Problem: Considering a complete weighted graph $G$ with $n$ vertices, where $n\in2\mathbb Z$ is an even number, remove edges in such a way that you end up with two cliques of graph $G$, each having $\...
9
votes
2answers
274 views
How long does it take to find a short cycle in a random graph?
Let $G \sim G(n, n^{-1/2})$ be a random graph on $\approx n^{3/2}$ edges. With very high probability, $G$ has many $4$-cycles. Our goal is to output any one of these $4$-cycles as quickly as ...
10
votes
2answers
183 views
“Relatives” of the shortest path problem
Consider a connected undirected graph with non-negative edge weights, and two distinguished vertices $s,t$. Below are some path problems that are all of the following form: find an $s-t$ path, such ...
3
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0answers
129 views
Enumerating Minimal (a,b) vertex separators in a DAG
A vertex subset $S \subseteq V$ is an $(a,b)$ separator for nonadjacent vertices $a$ and $b$ if the removal of $S$ from a graph $G$ separates $a$ and $b$ into distinct connected components.
$S$ is a ...
2
votes
1answer
110 views
Relationship between $O(\log n)$ (bounded) treewidth and H-minor-free
What is the relationship between graphs which have $O(\log n)$ treewidth and $\mathcal{H}$-minor-free graphs? Are graphs which have $O(\log n)$ treewidth $\mathcal{H}$-minor-free? I know that graphs ...
6
votes
1answer
215 views
What is the fastest known algorithm for computing a 1.99-approximation of Vertex Cover?
It is known that computing $(\sqrt 2 -\epsilon)$-approximation for VC is NP-hard and that UGC implies that even a $(2 -\epsilon)$-approximation is hard.
There is also a parameterized algorithm for ...
1
vote
0answers
81 views
Shortest s-t Path with a covering constraint
Instance: an undirected graph $G=(V,E)$ with edge-weights $w:E\to{\mathbb{R}}$;
a source $s\in V$ and a sink $t\in V$;
a ground set $X=\{x_1, ..., x_k\}$, and for every $v\in V$ a corresponding ...
9
votes
1answer
233 views
3-coloring planar graphs in $O\left(3^{n^.5}\right)$?
I was wondering if the task of searching for planar 3-colorings is known to be of complexity $O\left(c^{\sqrt{n}}\right)$ or lower? This feels like it would be an intuitive consequence based from ...
2
votes
0answers
74 views
Algorithm for computing the smallest subset of nodes to remove from a graph to make it a tree
I have encountered an interesting problem that I couldn't find any references to solve:
Determine the smallest subset of nodes that
need to be removed from an undirected graph to make it a tree.
...
0
votes
0answers
45 views
Matching of two weighted graphs allowing one-to-many mapping
I am looking for a heuristic for a graph matching problem as follows.
Given two graphs: $A$ (consisting of nodes $a_i$) and $B$ (consisting of nodes $b_i$). Typically the size of $B$ is larger than ...
1
vote
0answers
50 views
Directed Acyclic Graph partition into minimum subgraphs with a constraint
I have this problem, not sure there is a name for it, wherein a Directed Acyclic Graph has different colored nodes. The idea is to partition it into minimum number of subgraphs with the following 2 ...
2
votes
0answers
77 views
Common techniques for the acyclic orientation problem under some special constraint?
An acyclic orientation of an undirected graph is an assignment of a direction to each edge(an orientation) that does not form any directed cycle and therefore generates a directed acyclic graph(DAG). ...
5
votes
0answers
270 views
Does Depth-First-Search admit a quasilinear time algorithm in mutitape Turing Machine model?
Depth-First-Search (DFS) has a quasilinear (i.e.,$\widetilde{O}(m+n)$) time algorithm in random access model (RAM). I am curious about whether DFS still admits a $\widetilde{O}(m+n)$ time algorithm in ...
10
votes
1answer
216 views
Efficient graph isomorphism for similar graph queries
Given the graph G1, G2 and G3, we want to perform isomorphism test F between G1 and G2 as well as G1 and G3. If G2 and G3 are very similar such that G3 is formed by deleting one node and inserting one ...
0
votes
0answers
21 views
Connectivity with ordered adjacency list
In the adjacency list model, a graph is described through lists that contain the neighbors of any node $i \in [n]$. A query is of the form "What is the $k$-th neighbor of node $i$?". BFS allows to ...
2
votes
1answer
70 views
Computing the existence of a path in a code execution graph
I have a need for an algorithm which I can express as a reachability problem in a graph.
Note that I'd appreciate any advices with respect to better wording this question. Also please tell me if this ...
0
votes
0answers
68 views
Unknown gaps in computation models
I'm looking for computatuon models where it is known that there are problems that we can solve in time T1 and T2.
where T1 is smaller then T2 and it is unknown if there are problems where their ...
0
votes
1answer
94 views
finding maximum weight subgraph
My graph is as follows:
I need to find a maximum weight subgraph.
The problem is as follows:
There are n Vectex clusters, and in every Vextex cluster, there are some vertexes. For two vertexes in ...
3
votes
0answers
53 views
Algorithms for Maximum weight connected subgraph in planar graphs
I wonder what is known about the two following maximisation problems.
Maximum weight connected subgraph :
Input : A graph $G$, with weights $w_v\in \mathbb{R}$ for each vertex $v \in V(G)$
Output :...
-1
votes
1answer
56 views
Min Cut with Vertices
I have an undirected graph G with a set of vertices and edges. Each vertex has a weight w. Let's assume we have all vertices connected with some paths. I'm looking ...
1
vote
0answers
56 views
Graph automorphism with prescribed values
Consider a graph $G$ with vertices labeled $1,...,n$ and edge weights $w_{ij}$. Recall an automorphism of G is a permutation $\sigma$ of the vertex labels such that $w_{\sigma(i),\sigma(j)}=w_{ij}$ ...
2
votes
1answer
166 views
How many samples are needed to reconstruct a path?
Consider an input set of vertices $V$ and vertices $s,t\in V$.
The goal is to learn some unknown shortest path from $s$ to $t$; the set of edges of the graph is hidden at first and there may be ...
0
votes
0answers
19 views
The set of weight functions for which the assignment problem has non-trivial solutions
The standard assignment problem is specified with a square matrix ${\bf W}$ of weights (values, costs):
$$
V_{\cal P} = \sum_i w(i, b(i)) = \sum_{(i, j) \in {\cal P}} w_{ij},
$$
where $\cal P$ is a ...
0
votes
1answer
76 views
Finding a Hamiltonian cycle from perfect matching of a bipartite graph
A disjoint vertex cycle cover of G can be found by a perfect matching on the bipartite graph, H, constructed from the original graph, G, by forming two parts G (L) and its copy G(R) with original ...
4
votes
3answers
299 views
Is counting simple cycles in $P$ for graphs of bounded tree width?
Motivation:
Determining if a graph has a Hamiltonian cycle is $NP$-hard in general. However, determining if there is a Hamiltonian cycle is in polynomial time on graphs of bounded tree width, either ...
0
votes
0answers
30 views
Alternating Delivery Problem
What is known about the complexity of the following problem:
Suppose we have a complete bipartite graph $G(V,E)$ with disjoint sets $C$ and $T$. The candidate vertices, and the target vertices ...
1
vote
0answers
81 views
Minimum cut with nonlinear objective function
Let $G$ be an undirected graph. The classic minimum (cardinality) cut problem asks for a cut $C\subseteq E(G)$, such that $|C|$ is minimum.
Let us generalize it the following way: let $f$ be a ...
0
votes
1answer
83 views
Densest k subgraph problem for outerplanar graphs?
The densest k subgraph problem aims to find a subgraph $H$ of a graph $G$ with exactly $k$ vertices that maximizes the number of edges $|E(H)|$.
Does anyone know if there exists a polynomial-time ...
6
votes
0answers
183 views
Largest “non-disturbing” subset in a graph
The definition:
The subset of vertices in a graph is called "non-disturbing" if any two vertices from this subset could be connected by a path not passing through other vertices of this subset.
...
5
votes
1answer
158 views
Minimum cost cut with discount - what is the complexity?
Consider an undirected graph $G=(V,E)$ with non-negative edge costs. Given an integer $k$ with $0\leq k\leq |E|$, let us call an edge set $C\subseteq E$ a $k$-discounted cut, if the following hold:
$...
2
votes
0answers
128 views
Shortest s-t path when is allowed to ignore k weights
Given an undirected graph $G$ with $n$ vertices and $m$ edges, with non-negative weights on the edges, what's the best algorithm that computes the shortest path from $s$ to $t$, where you are allowed ...
1
vote
1answer
65 views
Complexity status of the Edge Deletion problem to bounded degree graphs
I'm interested in the complexity status of the following problem.
Input: a graph $G=(V,E)$ and two natural numbers $k$ and $d$.
Output: Yes, if there exists a subset $E' \subseteq E$ of cardinality ...
