Questions tagged [graph-algorithms]

Algorithms on graphs, excluding heuristics.

229 questions with no upvoted or accepted answers
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354 views

Connected Components over Graph with “colored” edges.

We have an undirected graph $G(V,E)$. Each edge $e \in E$ is associated with a set $C_{e}\neq \emptyset$ of colors, $C_{e} \subseteq C$. The problem is to find all the colored connected components. ...
3
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0answers
118 views

Are local canonical labellings of a graph ever a subsequence of the global canonical labelling?

So a canonical labelling of a graph G is a function CL(G) that maps each vertex to a numerical label. Sorry if my definitions are a bit obvious or clumsy, by the way. For every isomorphic graph G', CL(...
3
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2answers
425 views

Optimization Problem on a Directed Graph

I have the following graph optimization problem. In a directed graph $G$, each node $i$ is endowed with a real value $v_i$ (input) that encodes the minimum "activation threshold" of that node. For ...
2
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0answers
76 views

Variation of edge-disjoint spanning trees

In a directed graph, I want to find 2 edge-disjoint spanning trees (arborescence), with the extra restrictions that edges in the 1st tree are not forward arcs in the 2nd tree. Are there existing ...
2
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0answers
94 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 ...
2
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0answers
47 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 ...
2
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0answers
78 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. ...
2
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0answers
86 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). ...
2
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0answers
142 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 ...
2
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0answers
136 views

Crime prevention using graph theory and machine learning

I am looking for a way to the model the incidence of crime among a network of individuals. Part of it will use machine learning, and part of it will have to resort to some graph theoretic ...
2
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0answers
108 views

Counting the maximum number of paths of length $n$ that differ in at least $k$ edges

What is known about the complexity of solving (or approximately solving) the following problem? INPUT: Graph $G=(V,E)$ and constants $L$ and $K$. OUTPUT: The maximum size of any set $S$ of simple ...
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0answers
150 views

A variant of the Maximum Weight Clique problem

I am trying to solve a problem that I could reduce to the following: Given a graph $G=(V,E)$ with both edge and vertex weights, all weights being non-negative, find a clique $Q\subseteq V$ s.t. $\sum_{...
2
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0answers
46 views

Min cut problem on unbalanced partitions for planar graphs with unit capacity edges

The question is: given a planar graph $G$ with unit capacity edge weights and a fixed positive integer $k$, what is an approximation algorithm for finding the minimum size of a cut $(A,B)$ with $|A|=k$...
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0answers
96 views

Unbalanced connected partition

Let $G = (V, E)$ be a connected graph with (possibly negative) vertex weights $w(v)\in\mathbb{Z}$. We want to partition the vertices into two parts such that the induced graphs $G'$ and $G''$ are ...
2
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0answers
65 views

Complexity consequence of logarithmic boolean width of co-bounded degree graphs?

The paper On graph classes with logarithmic boolean-width claims that the boolean width of co-k-degenerate graphs is at most $k\log{n}$ and a lot of graph vertex partition problems can be solved in ...
2
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0answers
171 views

Approximating the Radius of a (Dense) Graph

For a (dense) graph, computing its radius is as hard as computer "All Pairs Shortest Paths" (APSP) [1]. So we can focus on approximating the radius. A $(1+\epsilon)$-approximating of APSP for a ...
2
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0answers
164 views

Paper regarding the complexity of the longest path problem on weighted directed graphs of bounded treewidth

I would like to cite a paper/report/etc that solves the following problem polynomially in $n$: Given a weighted directed graph $G=(V,E)$, $|V|=n$, of bounded treewidth $k \in \mathbb{N}$ and a source-...
2
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0answers
969 views

Is there a better than brute-force solution to the shortest simple path problem?

Given as input graph which can possibly contain negative weight cycles, we can still ask for the weight of the shortest simple path between two vertices (i.e., a path that does not visit any vertex ...
2
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0answers
153 views

Computational Complexity of cycle double cover

Let $\mathcal{G}$ be the set of all finite simple graphs. Let graph $G\in \mathcal{G}$ and $C_G=\left <C_1,...,C_m \right >$ be a sequence of cycles of $G$ for some $m$. For every edge $e$ of $G$...
2
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0answers
52 views

Examples of “Sandpile” TSP Instances

This question is closely related to this MO question. I would like to know, whether any (planar Euclidean) TSP instances are known, that exhibit avalanche effects similar to those ecountered in ...
2
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0answers
194 views

zero-sum path problem on a digraph

Consider a digraph $G=(V,A)$ with each arc weighted by either $+1$ or $-1$. A path is called a zero-sum path, if and only if all the arcs in its first half have weight $+1$, and all the arcs in the ...
2
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0answers
502 views

Path finding on graph with state dependent edge costs

I'm looking for a version of path planning that is able to find paths in a graph where edge costs depend on the state of the moving entity. In such cases, it is required to also consider trade-offs, i....
2
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0answers
84 views

Max common sub forest on $k$ graphs

Not sure how to phrase this really, but here goes. Suppose you are given $k$ simple graphs, each having exactly $m$ edges. The edges in each graph are labeled from 1 to $m$. The problem is to find ...
2
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0answers
36 views

Nearest Common Ancestor on DFS Tree (with Addition of Leaves in DFS Order) on Pointer Machines

What is the complexity status for the Nearest Common Ancestor Problem on Trees in which the leaves are attached to the tree in DFS order ? i.e. Suppose one is visiting a tree T in DFS, and at any ...
2
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0answers
540 views

Shortest non-crossing geometric paths

I have a plane graph $G$ and a set of $k$ vertex pairs $\{s_1,t_1\}, \dots, \{s_k, t_k\}$. The goal is to find $k$ non-crossing paths connecting the pairs of terminals $s_i$ with $t_i$ in the graph so ...
2
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0answers
96 views

Claw finding using quantum walk: superposition for Szegedy's framework

Within Claw Finding Algorithms Using Quantum Walk there is the subroutine $claw_{detect}$ described. As in above paper: Let $J_f(N, l)$ and $J_G(M, m)$ be Johnson graphs. Let $F$ and $G$ be vertices ...
2
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0answers
39 views

centralized deterministic Spanner construction with low degree and low stretch

Does there exist a centralized deterministic spanner construction with low degree and low stretch both independent of the graph diameter (no log D factor), but can be dependent on the number of nodes. ...
2
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0answers
115 views

Hardness of approximately counting independent sets with a PRAS, rather than FPRAS

It is known that approximately counting the independent sets of a graph is hard, even if randomness can be used, and even if we restrict ourselves to bounded degree graphs with degree bound at least 6....
2
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0answers
145 views

How much faster is solving Clique in properly colored graph?

Given a graph $G$ and a proper vertex coloring $C$ with the minimum numbers of colors, how much faster can a maximum clique be found than when just $G$ is given? Additional information doesn't make ...
2
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0answers
100 views

What mathematical models can analyze and optimize such message passing system?

I look for a mathematical model that can accommodate, analyze and suggest optimizations for a system that can be humanly described as message passing black box programs to which where optimal message ...
2
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0answers
134 views

Realization of a bipolar orientation by a mixed graph

Given an undirected graph $G(V,E)$ and a bipolar orientation $s$ over $G$, consider the problem of identifying $s$ by finding the minimum number of edges such that when orienting them in a particular ...
2
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0answers
145 views

Weighted graph as average of many unweighted graphs

I have a measure $L(G)$ that is only valid for unweighted graphs because is based on discrete distributions and can't be extended to weighted graphs. My idea is that if I consider a weighted graph as ...
2
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0answers
194 views

What is the name for this special case of the Travelling Salesman involving dynamic edge costs?

This is a modeling / taxonomy question. Is there a name for this type of problem? I came up with the following graph problem for a pizza delivery truck, which starts with zero dollars and enough fuel ...
2
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0answers
163 views

Graph partition with objective over intra-partition weights

I have a problem in which I need to find an optimal graph cut that maximizes an objective over weights not on the cut. I have looked at the literature but have not been able to find any similar ...
2
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0answers
183 views

Eulerian Triangulations

Hi i am looking for algorithms to decide whether a planar pointset has a eulerian triangulation i.e. a triangulation that makes every vertex of even degree. I cam across this page http://cs.anu.edu....
2
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0answers
62 views

Hungarian Search and min net-cost-length paths

Consider the Hungarian Search algorithm for max/min weighted bipartite matching. Let G be a bipartite graph weighted by $w:E\rightarrow\mathbb{R}$ and let $M$ be a matching in $G$, let $S$ be a subset ...
2
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0answers
1k views

Maximum number of triangles in a constrained delaunay triangulation

I'm looking for an upper bound for the number of triangles in a constrained planar delaunay triangulation. I know for d=2 delaunay triangulation, there are at most n+1 triangles where n is the number ...
2
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0answers
220 views

Quadratic Binary Optimization formulation of Steiner Tree problem

can someone point out to me a solution or give advice on how to formulate as efficiently as possible in terms of number of bits the minimum Steiner tree problem as a 0-1 quadratic optimization problem?...
2
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0answers
92 views

Has anybody studied the problem of finding maximal weighted rooted spanning DAGs?

Let G=(V,E) be a directed weighted graph (not necessarily a tournament) and s be a special node of G so that all nodes in G are reachable from s. The problem is to find a subgraph G'=(V,E') of G so ...
2
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0answers
229 views

Initial paper of the Moore Neighborhood algorithm

I don't exactly know if this is the place to ask it, but I'm looking for the original paper of the Moore Neighborhood algorithm. I need to make a reference to it (or whoever came up with it). I can't ...
2
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0answers
338 views

Recursive parallel topological sorting in linear time

While doing some research on topological sorting I came across a paper Parallel Topological Sorting Algorithm, TADA, A. and MIGITA, M. and NAKAMURA, R. which claims a recursive divide-and-conquer ...
2
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0answers
268 views

Algorithm for choosing unique items from a collection of sets of items

I have a number of sets, each containing items with a numerical value and a string. I want to choose one item out of each set, so that: 1. the strings of the chosen items form a set (i.e. the strings ...
2
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0answers
495 views

Data set for Degree Constrained MST?

Degree Constrained Minimum Spanning Tree is an NP-hard problem. It differs from Minimum Spanning Tree in that, degree of every vertex should be $\leq$ some degree constrained. This is a well studied ...
2
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1answer
1k views

Finding the nearest node to a given set of nodes in a graph

I am looking for an algorithm that, given a large weighted undirected graph, would find the node that has minimum average distance from a given set of nodes in the graph.
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33 views

Efficient algorithm for finding segregators in a directed acyclic graph

Given a directed acyclic graph $G=(V,E)$, we define a $(\alpha,\beta)$-segregator of $G$ to be a subset $S$ of $V$ of size $\alpha$ such that no vertex in $G\setminus S$ has more than $\beta$ ...
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0answers
22 views

Are the intermediary sets in maximum cardinality search optimal in some way?

The maximum cardinality search (MCS) algorithm works as follows. Given a weighted graph $G = (V, E)$ where $w(u, v)$ denotes the weight of the edge $\{u, v\}$, we select a start node $a \in V$ and do ...
1
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1answer
94 views

Reference request: Depth- (or Breadth-) first search with hints?

Consider the standard s-t reachability problem of finding a path between nodes $s$ and $t$ in a directed graph $G$. A DFS or BFS could solve it. Would it be possible to pre-process the graph and ...
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0answers
29 views

Minimum rank graph cut

Consider the following problem: Input: A graph $G=(V,E)$ and a matroid $M$ on $E$, given by an independence oracle. Task: Find a cut $C\subseteq E$ in the graph, such that the rank of $C$ in the ...
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0answers
88 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 ...
1
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0answers
51 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 ...