Questions tagged [graph-algorithms]

Algorithms on graphs, excluding heuristics.

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2
votes
1answer
917 views

How to approximate minimum clique edge cover

I'd like to take an undirected graph and express it (meaning all of its edges) using only cliques (ideally minimizing their sum cardinality). It's clear that actually finding the minimum solution is ...
7
votes
1answer
936 views

K-Clustering of a Graph maximizing intra-cluster weights?

I would like to know if the following problem has already been studied, and if so how is it called. In particular I'm interested in approximability results. Input: A complete graph G with non-...
3
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0answers
476 views

Broadcasting in node-weighted graphs

Given an undirected graph $G=(V,E)$ with non-negative node-weights $\text{w}(v)$, $v \in V$, I want to find a spanning tree $T$ of $G$ with minimum "cost" $\text{w}(T) = \sum_{v\in V} \deg_T(v)\cdot ...
32
votes
3answers
2k views

Are any of the state of the art Maximum Flow algorithms practical?

For the maximum flow problem, there seem to be a number of very sophisticated algorithms, with at least one developed as recently as last year. Orlin's Max flows in O(mn) time or better gives an ...
1
vote
0answers
2k views

Widest path between s and t with additional constraints

Given a directed graph G and vertices s and t, the maximum capacity path between s and t is the path for which the minimum edge on the path is maximum, among all such s-t paths. Now I can use a ...
7
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2answers
2k views

enumerating all connected induced subgraphs

What is the complexity of enumerating all connected induced subgraphs from an undirected graph. Also, Is the complexity of enumerating all maximal connected induced subgraphs the same?
4
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1answer
1k views

Enumerating all s-t paths with cost exactly k

Is there a known algorithm for the following problem? Given a simple weighted directed graph, a pair of vertices $s$ and $t$, and a real value $k$, enumerate all simple paths from $s$ to $t$ with ...
3
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0answers
574 views

Is there a tight lower bound on the complexity of SSSP on a graph?

I'm an undergrad and I'm not sure if this is the right way to ask this question. I want to know the lower bound on single-source shortest path computation in a general graph. The graph is allowed to ...
8
votes
2answers
6k views

Finding a minimum "node" weight path

Suppose a graph with node weights only (no edge weights). For a given source-sink pair, how can I find a path with the minimal sum of node weights? Does this problem have a name? Is it possible to ...
0
votes
1answer
539 views

Find the maximum flux path between two nodes [closed]

Given a graph $G$ and two vertices $s$ and $t$, I want the maximum flux path from $s$ to $t$.That is, imagine $G$ to be a flow network with capacities on the edges. I want to find a single path that ...
6
votes
2answers
903 views

Finding largest subgraph that contains a given edge and admits a cycle cover

I am wondering whether there exists a fast algorithm for the following problem. Given a digraph $G$ possibly with loops (that is edges that begin and end at the same vertex) and the choice of an ...
3
votes
1answer
125 views

complexity of games with just doors and keys

(This essentially copies my unaswnered question from math.stackexchange.com/questions/275685) I was reading http://arxiv.org/abs/1201.4995, and I thought back to a game I used to play, which is ...
1
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0answers
192 views

Map points from one plane into another

Given a point on a plane A, I want to be able to map to a corresponding point on plane B. I have a set of N corresponding pairs of reference points between the two planes, however, the overall mapping ...
2
votes
1answer
186 views

NP-complete problems related to Minimizing Variance

I am interested in references to NP-complete problems that involve some non-linear terms (e.g. quadratic terms). So far I am aware of the "Quadratic Assignment problem" and "Quadratic Programming". ...
-1
votes
1answer
466 views

The existing bound on Edmonds-Karp doesn't seem to be tight

I'm reading CLRS's (Cormen et.a al) Introduction to Algorithm, and arrived at the maximum flow section. It shows that Edmonds-Karp algorithm runs in $O(E^2V)$ time by showing that: 1) If we let $\...
5
votes
1answer
237 views

Revision Tracking Graph

Define the Revision Tracking Graph (RTG), which is an oriented graph (without circles) where each node x has a set C(x) associated with it. C(x) contains all edges on all paths from a node 0 ( C(0) = {...
2
votes
1answer
388 views

All Pairs Shortest Path - Directed graph with integer weights

I don't understand how Distance Product works (or Min Plus Product). If we replace each argument in $A$ from $a_{i,j}$ to $x^{a_{i,j}}$ and each argument in $B$ from $b_{i,j}$ to $x^{b_{i,j}}$ and ...
21
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2answers
3k views

Recognizing line graphs of hypergraphs

The line graph of a hypergraph $H$ is the (simple) graph $G$ having edges of $H$ as vertices with two edges of $H$ are adjacent in $G$ if they have nonempty intersection. A hypergraph is an $r$-...
5
votes
1answer
192 views

Generalizing linear interpolation to posets

Assume that I have an array $A$ of $n$ numerical values where some are known and some are unknown (with $A[0]$ and $A[n-1]$ assumed to be known). If I want to estimate an unknown value $A[i]$, a ...
4
votes
2answers
518 views

Optimal upper bound on the number of non-isomorphic graphs with certain parameter

What are the optimal (or best known) bounds (preferably exact or else asymptotic but not expectation on random graphs) on the number of non-isomorphic (unlabelled) simple (no self-loop), undirected ...
8
votes
1answer
475 views

Are there applications of modular graph decomposition in TCS/complexity theory?

What are there some applications of modular graph decomposition in TCS/complexity theory? I am especially interested in its use in proofs or upper/lower bounds if it occurs. [1] Modular graph ...
8
votes
0answers
477 views

Reducing the maximum degree in a graph

Given a weighted undirected graph $G = (V, E)$ with maximum degree $\mu$ and with positive edge weights, is it possible to construct another graph $H = (V \cup V', E')$ with maximum degree $\mu' = o(\...
2
votes
1answer
5k views

Reducing a minimum cost edge-cover problem to minimum cost weighted bipartie perfect matching

I have a set of edges [m,n] of a bipartie graph U, V with a cost assigned to each edge and I need to find the minimum cost edge-cover covering all nodes in U, V. There is one additional constraint is ...
12
votes
1answer
668 views

automorphism in Cai-Furer-Immerman gadgets

In the famous counter example for graph isomorphism via Weisfeiler-Lehman (WL) method the following gadget was constructed in this paper by Cai, Furer and Immerman. They construct a graph $X_k = (V_k, ...
2
votes
0answers
233 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 ...
12
votes
1answer
332 views

Negative results on identical particles approach to Graph Isomorphism (GI) problem

There has been some efforts to attack graph isomorphism problem using quantum random walk of hard-core bosons (symmetric but no double occupancy). Symmetric power of adjacency matrix, which seemed ...
2
votes
1answer
262 views

Average-degree Bounded Graphs are no harder than Maximum-degree Bounded Graphs (for distance oracles with purely multiplicative stretch)

I'm trying to understand a specific part from an article of Agarwal and co. It is about Distance Oracles but there is a specific explanation of How to convert from average-degree graph to maximum-...
27
votes
1answer
648 views

Is there a problem that is easy for cubic graphs but hard for graphs with maximum degree 3?

Cubic graphs are graphs where every vertex has degree 3. They have been extensively studied and I'm aware that several NP-hard problems remain NP-hard even restricted to subclasses of cubic graphs, ...
2
votes
1answer
160 views

Any graph $G$ can be seen as the sum of complete $k_i$-partite graphs?

Given an undirected graph $G$ with $n$ vertice and $m$ edges, can we construct $p$ complete $k_i$-partite graphs, where $p$ is finite (of course) and each vertex appears at most a constant number of ...
1
vote
0answers
159 views

Connection strength in a weighted social digraph, based on weights of individual links

Given a network where edges represent entities and directed vertices represent relationships between entities, and each vertex has a strength between 0 (no relationship) and 1 (strongest). I'm ...
3
votes
2answers
523 views

Algorithms for graph generation given parameters

I guess there may be a large number of algorithms proposed for generating graphs satisfying some common properties (e.g. clustering coefficient, average path length, degree distribution, etc). I am ...
17
votes
1answer
720 views

What is the fastest deterministic algorithm for dynamic digraph reachability with no edge deletion?

What is the best deterministic result for maintaining the dynamic transitive closure in a directed graph with only edge insertion? I read some papers on the dynamic transitive closure problem with ...
2
votes
0answers
70 views

Vertices that are K away [closed]

Given a graph G(V,E) and a vertex v, how do i find all the vertices that are reachable via simple paths ( no vertex on the path repeats) of length exactly k. Powers of adjacency matrix gives the ...
10
votes
1answer
228 views

Computing the union closure

Given a family $\mathcal F$ of at most $n$ subsets of $\{ 1, 2, \dots, n \}$. The union closure $\mathcal F$ is another set family $\mathcal C$ containing every set that can be constructed by taking ...
24
votes
5answers
3k views

Approximation algorithms for Maximum Independent Set on special classes of graphs

We know that Maximum Independent Set (MIS) is hard to approximate within a factor of $n^{1-\epsilon}$ for any $\epsilon > 0$ unless P = NP. What are some special classes of graphs for which better ...
8
votes
1answer
310 views

Fast deletion / contraction in combinatorial embedding

I wonder if there is a sublinear algorithm to make deletion or contraction of an edge in a combinatorial embedding of, lets say, planar graph? Since in combinatorial embedding we have to maintain ...
0
votes
1answer
158 views

Cubic (3-regular) graph spanning tree

Considering loop free cubic graphs (graphs where every node has 3 neighboring nodes): Is is possible to construct a spanning tree that only has nodes with 3 neighbors in the spanning tree or 1 ...
0
votes
1answer
2k views

Graph building with weighted nodes

I have a set of nodes which can be connected together through arcs. Every node has an associated value, reflecting the "fitness" that this particular node has in the graph. I have to find the best ...
5
votes
1answer
653 views

Shortest cycle with a specific number of vertices

Given an undirected graph with n nodes, I need to find the shortest cycle of involving exactly n/2 vertices (i.e. keeping the distance traveled by the cycle to a minimum). Some nodes cannot directly ...
4
votes
0answers
644 views

What about apply maxplus algebra for all-pairs shortest paths?

I didn't find deep informations on Wikipedia about all-pairs shortest path, in particular I do not know what is the best algorithm to solve this problem beyond Floyd-Warshall's one, then I do not know ...
3
votes
2answers
437 views

Factoring Cartesian bitwise join of bit vectors

(This question has been substantially revised in an attempt to word it clearly.) I am wondering if anyone has seen this problem. Let $[n] = \{1,\ldots,n\}$ for an integer $n$. Consider two finite ...
16
votes
3answers
455 views

Smallest set that intersects some given sets

Let $S_1,S_2,\ldots,S_n$ be sets that may have elements in common. I'm looking for a smallest set $X$ such that $\forall i,\,X\cap S_i \ne \emptyset$. Does this problem have a name? Or does it ...
4
votes
1answer
131 views

Lower bound for orienting an asynchronous ring?

We require a lower message complexity bound of an asynchronous distributed algorithm that do the following: Given a undirected ring, with $n$ vertices, we want to let each node direct its edges to ...
4
votes
1answer
1k views

Matching on bipartite graph - multiple edges

I have a weighted bipartite graph consisting of two sets $S$ and $P$. ($|S| > |P|$). I need to find a matching so that every node $s$ in $S$ matches a node of $P$. But a node $p$ in $P$ can match ...
16
votes
1answer
410 views

Strongly Regular Graph and GI-Completeness

It is not known if graph isomorphism (GI) for strongly regular graphs (SRGs) is in P. Are there any hints that it might or might not be GI-Complete? Are there any strong consequences in such cases? (...
21
votes
2answers
1k views

Is feedback vertex set problem solvable in polynomial time for 3-degree bounded graphs?

Feedback Vertex Set (FVS) is NP-complete for general graphs. It is known to be NP-complete for degree-$8$ bounded graphs due to a reduction from vertex cover. The Wikipedia article says that it is ...
2
votes
1answer
382 views

Graph traversal with vertex and edge deadlines/windows

Hello the question was also posted on stackoverflow, but since this is theoretical oriented, thought I'd give it a try. I have an undirected graph similar to the one below, I need to implement a graph ...
3
votes
0answers
196 views

Randomized rounding on a graph

Assume we are given an arbitrary undirected graph $G = (V, E)$ where $|V| = n$. We are also given real numbers $x_e \in [0, 1]$ for each $e \in E$. These numbers satisfy the following constraint: \...
14
votes
0answers
356 views

Finding all-pairs anti-distance

Thanks for a great forum. This is my first post here. I am working on a signal processing application and the core of one the main algorithms reduces to a graph theoretical problem. Let $G=(V,E)$ ...
10
votes
1answer
2k views

Count $k$-hop neighborhood for every vertex

For a node $v$ of a directed unweighted graph $G$, I define the $k$-hop neighborhood of $v$ as the set of vertices that are reachable from $v$ in $k$ hops or fewer (that is following a path with $k$ ...

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