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Questions tagged [graph-algorithms]

Algorithms on graphs, excluding heuristics.

3
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0answers
98 views

Graph-related applications of the fast Fourier transform (and other algebraic algorithms)

The fast matrix multiplication algorithm is useful for numerous graph problems (e.g. matchings and shortest paths). However, while the fast Fourier transform algorithm implies several other near-...
16
votes
1answer
397 views

What is the complexity of this graph problem?

Given a simple undirected graph $G$, find a subset $A\neq \emptyset$ of vertices, such that for any vertex $x\in A$ at least half of the neighbors of $x$ are also in $A$, and the size of $A$ is ...
2
votes
1answer
113 views

What is the name of this algorithm on direct acyclic graph?

I am trying to linearize the history of a git branch for display purpose. I want commits to be collocated by branch instead of simply displaying commits in the order given by the time of commit. In ...
0
votes
0answers
28 views

Partitions of regular graphs with upper bounds on bipartition width

Are there efficient graph partitioning algorithms with guaranteed upper bounds on the bipartition width in terms of the total number of vertices of the graph, or another non-spectral quantity (...
1
vote
0answers
95 views

Generalized path cover problem in DAG

Let $G=(V,E)$ be a directed acyclic graph. Two vertices is transitive if there is a directed path between them. A Path Cover for a Set of Transitive Pairs (PCSTP) is a set of directed paths such that ...
-1
votes
1answer
35 views

Maximize graph with k cut edge operations

I have undirected graph with N nodes each with some weight. There are M edges and in exactly K operations I want to maximize the XOR sum of connected components of the graph. ((n1 XOR n2 XOR n3) + (c1 ...
5
votes
2answers
221 views

Efficient way to generate random planar cubic bipartite graphs

3-regular bipartite planar graphs appear in a variety of NP- / #P-complete problems. Suppose one wants to test the complexity of these problems via numerical experiments. Is there an efficient way to ...
5
votes
0answers
63 views

Series-parallel extension of a partial order respecting a given total order

Consider a partial order $P$, a series-parallel order $Q$ and a total order $R$, such that $P \subseteq Q \subseteq R$. Given $P$ and $R$, we are asked to find $Q$ of minimum length. An $O(n^3)$ ...
1
vote
0answers
25 views

Complexity of recognizing generalized graph join

A join of two graphs is the union of both graphs with additional edges such that every vertex of the first graph is connected to every vertex of the second graph. There is a generalization of this, ...
2
votes
1answer
359 views

Maximum difference between two shortest paths

My problem is the following maximization problem: Given: A graph $G=(V,E)$, lower bounds $l \in \{0,1,..,K\}^E$ and upper bound $u \in \{0,1,..,K\}^E$ for the edge weights, a source $s$ and two ...
3
votes
2answers
2k views

How to solve the Shortest Hamiltonian Path problem on Sparse Graphs?

Problem: Given a positive-weighted undirected graph, find the shortest path (in terms of total sum of edges) that visits each node exactly once. For a subset $S$ of nodes and a node $i\in S$, let $D[...
1
vote
0answers
75 views

Counting the number of connected components in a dynamic plane graph

I'm working on the following problem: let $G = (V, E)$ be a connected, planar graph. Our goal is to find a $d$-partition of $G$, $P = \{V_1, \ldots, V_d\}$, such that $G[V_i]$ is connected, and $\min_{...
2
votes
0answers
81 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 ...
6
votes
1answer
314 views

Why isn't the Charikar algorithm for finding the densest subgraph optimal?

I read about the algorithm in Greedy Approximation Algorithms for Finding Dense Components in a Graph by Moses Charikar, and I tried to find an instance/graph where the algorithm returns a different ...
0
votes
0answers
70 views

Number of maximally different DAG's in a digraph?

Given a digraph $\overrightarrow{G}$, I'm interested in extracting all DAGs from $\overrightarrow{G}$ such that: Each DAG's vertices are differently sorted, Each DAG is maximal (adding any extra ...
0
votes
1answer
203 views

How to design an algorithm which turns an undirected graph into directed with all nodes of indegree higher than 0? [closed]

Given an undirected graph $G=(V,E)$ devise an algorithm that will check whether its edges can be directed in such a way that the vertices of the resulting directed graph will all have indegree higher ...
7
votes
3answers
356 views

What are graph grammars?

I have found information on graph grammars and graph rewriting, but the papers that I find on it are a bit thick. Can someone give a quick overview of what graph grammars are, as well as an overview ...
1
vote
0answers
40 views

Are query-dependent ranking algortihms for web search doomed to be impractical? [closed]

Algorithms like HITS and SALSA are query dependent, and I've been given the impression that this makes them able to retrieve more accurate results. However, the query-dependent nature of these ...
1
vote
1answer
90 views
8
votes
1answer
164 views

Complexity of finding semi-ordered Eulerian tours in a 4-regular graph

I'm trying to figure out the time-complexity of the problem I describe below, which I call the semi-ordered Eulerian tour problem or the SOET problem. Either finding an efficient algorithm for this ...
1
vote
0answers
123 views

Cluster Assignment in the Stochastic Block Model

Recently, numerous papers have been published about the stochastic block model (SBM). In the literature about SBMs, a plethora of different settings are considered. I am interested in how vertices are ...
2
votes
2answers
209 views

One Generalization of Graph Isomorphism Problem

Say I generalize the language which consists of pairs of isomorphic graphs to take the following form: $GI(f) = \{ (G, H) \mid \exists \psi : V_G \rightarrow V_H, Pr_{a, b \in V_G} ((a, b) \in E_G \...
1
vote
0answers
56 views

\alpha-path on Euclidean graphs

Consider the following problem: Suppose we are given a G=(V, E) Euclidean Graph in the plane and a real $\alpha > 0$. For simplicity assume, there exists only one path whose summation of weights ...
-2
votes
1answer
80 views

Algorithm finding path with maximal ratio of white vertices [closed]

Recently I encountered an interesting graph problem and couldn't find proper solution: given undirected graph G = <V, E>, each vertex is either white or black....
8
votes
1answer
146 views

Decomposition of edges of eulerian graph into maximum number of cycles

I'm interested in the following problem. Given an eulerian graph $G=(V,E)$, we are to find a partition of its edges $C_1, C_2, \ldots, C_k$ ($\cup_i C_i=E$ and $i \neq j \leftrightarrow C_i \cap C_j =...
2
votes
1answer
173 views

Algorithm for computing unordered tree edit distance

I am trying to compute the edit distance between two dendrograms, one produced from hierarchical clustering, and the other manually constructed from some tree structure. In this setting, the rename ...
4
votes
0answers
488 views

Optimizing Maximum Weighted Matching (Edmonds Blossom)

Background: I've ported Edmonds Blossom Algorithm with Maximum Weighted Matching to Java: https://github.com/simlu/EdmondsBlossom/blob/master/src/Blossom.java The original Python implementation ...
2
votes
0answers
53 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 ...
3
votes
1answer
758 views

Minimal Cost of Eulerian Path

Problem: Given a planar (undirected and mostly sparse) graph with an Eulerian Path, we introduce a cost function f: (v, e1, e2) for all two edges e1 and e2 that share a vertex v. The function also ...
5
votes
1answer
273 views

Modifying Edmonds' Blossom Algorithm

Given a connected road network on an Island without one-way streets, where should I para-shoot in and what route should I take to deliver mail to all houses on the island (being picked up again by ...
1
vote
1answer
420 views

Clique cover problem

Consider the following graph problem. We are given a graph $\mathcal{G} = (\mathcal{V},\mathcal{E})$, where $\mathcal{V}$ is the set of vertices and $\mathcal{E}$ is the set of edges. For each vertex $...
1
vote
1answer
179 views

Max weight travel on a graph with deadline

Given a deadline $D>0$ and a complete graph $K_n$ (with loops) in which each edge $e_{ij}$ has a weight $w(e_{ij}) \ge 0$ and a travel time $l(e_{ij}) > 0$. Starting from one of the nodes, we ...
1
vote
1answer
161 views

Max-weight connected & co-connected subgraph problem

The max-weight connected subgraph problem (MWCS) may be described as follows: given a simple graph $G=(V,E)$ and a weight function $w:V\to\mathbb{R}$, one seeks for a subset $L\subseteq V$ for which ...
5
votes
1answer
82 views

What is known about learning a maximal independent set in a (very) sparse graph?

Maximal independent set is known to be hard in many meanings (hard to approximate, $W[1]$-hard, etc.). But if the number of edges is very small, then the problem becomes simpler. Here, I'm interested ...
1
vote
1answer
162 views

Does a weighted graph have a path with weight zero?

Given a weighted digraph $G=(V,E)$, where each edge is associated with a weight (could be positive, negative, or zero). We define the weight of a path to be the sum of the weights along this path. ...
4
votes
0answers
121 views

Efficiently computing the union of all minimal unsatisfiable constraint sets in a first-order unification problem

Suppose we are given a standard first-order unification problem, represented as a set $D$ of term equality constraints, such that the system $D$ as a whole is unsatisfiable. Consider the minimal ...
2
votes
0answers
155 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 ...
-1
votes
1answer
131 views

A conceptual question regarding hardness proofs by reduction [closed]

If we restrict the input domain of a known NP-hard problem P so that this restricted domain is equal to the input domain of another problem S, then show that we can reduce a solution to P given input ...
0
votes
1answer
81 views

Complexity status of restricted k-clique [closed]

Restricted $k$-clique: Input: $(G,v,k)$ where $v$ is vertex in $V$ Output: k-clique containing vertex $v$. What is the space and time complexity status of this Restricted $k$-clique problem? Is ...
4
votes
0answers
81 views

Restricted k-set cover is in NL or L

Restricted $k$-set cover: Input: $(U,S_1,S_2,\cdots, S_n, k)$, $U=[n]$ and $S_i\subseteq U$ for all $1\leq i \leq n$. Output: $\bigcap_{i\in I}S_i$ where $I=\{1,i_1,i_2\cdots,i_k\}, i_1=min(S_1),i_2=...
0
votes
0answers
107 views

k-Vertex Cover problem is in NC_1 or AC_0

$k$-Vertex Cover: Given a graph $G = (V, E)$ where $V$ is a set of vertices and $E$ a set of edges, and an integer $k$, the $k$-Vertex Cover problem determines if there exists a subset of vertices $...
0
votes
0answers
127 views

How to partition a graph while minimizing the count of intra-edges?

Suppose we are given an undirected graph $G(V,E)$. The objective is to partition the graph vertices $V$ into $n$ partitions $P_1, P_2, ..P_n$ such that following criteria is satisfied: $|P_i| = |V|/n$...
3
votes
1answer
250 views

Solving a “tree-equation”?

Given two trees A and B, each of their nodes except some leaves have a "type" (which also determines the number of children, the node has, having that type). The leaves which don't have a type are ...
0
votes
1answer
97 views

Reachability in Dynamic Line Graph

Given a directed line graph $G = v_1 \rightarrow v_2 \rightarrow \cdots \rightarrow v_n$, there are two operators, namely $\mathsf{move}(v_i, v_j)$: this operator moves $v_i$ to the position ...
3
votes
2answers
74 views

Maximal non-reducible vertex cover of a graph

Let $G=(V,E)$ be a graph (i.e. an undirected simple finite graph). We say that a vertex cover $V'$ of $G$ is non-reducible if any $V''$ with $V''\subsetneq V'$ is not a vertex cover of $G$. We say ...
1
vote
0answers
55 views

parametrized logspace algorithm for k-dominating set for planar graphs

$k$-Dominating set: Given a graph $G=(V,E)$ where $V$ is a set of vertices and $E$ a set of edges, and an integer $k$, the $k$-Dominating set problem determines if there exists a subset of vertices $...
0
votes
1answer
53 views

How to check whether graph of n vertex contains n/k disjoint k - complete graph by linear programming? [closed]

Edges are given in form of $X_{ij}$, which denotes whether there is edge in between $i^{th}$ and $j^{th}$ vertex. I am solving integer optimization problem and want to add this constraint to it.
1
vote
0answers
212 views

Can Lexicographic BFS be implemented in logspace?

Input: Given graph $G=(V,E)$ vertex labeling in some order Output: Change the labeling of vertices's such that labeling start $v_1$ as $u_1$, next label the neighbors of $v_1$ as $u_2,u_3,u_4,...$ ...
6
votes
2answers
231 views

Log space algorithms for modular decomposition tree

Can we have log space algorithms for modular decomposition tree (see definition) for any graph? If not, can we have log space algorithms for modular decomposition tree for any particular graph class? ...
3
votes
0answers
101 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-...