# Questions tagged [graph-algorithms]

Algorithms on graphs, excluding heuristics.

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### 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 ...
1answer
143 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 ...
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 ...
1answer
416 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? (...
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 ...
1answer
388 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 ...
0answers
197 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: \...
0answers
357 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 $G=(V,E)$ ...
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 $k$ ...
0answers
2k views

### Can the Hungarian method be used with real edge weights?

I had a problem where I need to apply bipartite weighted matching on a graph where the edge weights are real (positive and negative). I have looked at several implementations of the Hungarian method ...
1answer
529 views

### Number of subgraphs with given edge parity

I would like to know whether counting number of induced (full) subgraphs (of an undirected graph) that have even number of edges is P or #P-complete. Additionally, is the problem easier if we assume ...
2answers
536 views

### The ODD EVEN DELTA problem

Let $G = ( V, E )$ be a graph. Let $k \leq |V|$ be an integer. Let $O_k$ be the number of edge induced subgraphs of $G$ having $k$ vertices and an odd number of edges. Let $E_k$ be the number of edge ...
1answer
703 views

### Number of subgraphs with a given number of nodes

Let $G = ( V_G, E_G )$ be a graph. Let $E_H \subseteq E_G$. The subgraph of $G$ edge-induced by $E_H$ is $H = ( V_H, E_H)$, where $V_H = \{ v \in V_G : \exists ( u, w ) \in E_H\ v = u \lor v = w \}$ ...
1answer
263 views

### Finding a path with certain properties in a directed graph

Define a directed graph $G(V,E)$. We divide its vertex set $V$ into $t$ partitions: $p_1, p_2, \ldots, p_t$. Suppose we have a path $v_1 \to v_2 \to v_3 \to \ldots \to v_n$ where the same vertex can ...
0answers
118 views

### Min-cut variation

I'm searching for an algorithm to do the following I have a graph $G = (V, E)$ and a set of terminal pairs $\{(s_i, t_i)\}$. I need to find a cut smaller than a given quantity $k$, such that there is ...
1answer
559 views

### Choosing one number from each set so that the difference between maximum and minimum is minimized

Suppose I have four sets A={0, 4, 9}, B={2, 6, 11}, C={3, 8, 13}, and D={7, 12}. I need to choose exactly one number from each of these sets, so that the difference between the largest and smallest ...
0answers
185 views

1answer
411 views

### In a random perfect matching of a regular bipartite graph, are all edges equally probable?

Consider a d-regular bipartite graph G, for d>=1. Obviously, G contains a perfect matching. Consider a perfect matching M in G chosen uniformly at random from all perfect matchings in G. Is it the ...
0answers
112 views

1answer
320 views

### Do you know a shortest path algorithm for weighted graphs with hard time windows on the edges and waiting allowed?

Title says it all. I have a weighted Graph G={V,E,ETW} where V is the node set, E the edge set and ETW is a set of edge time windows. A edge time window is a 3-Tuple (edge, starttime, endtime) with ...
1answer
550 views

### techniques or examples of analyzing a series of graphs

Let there be a sequence of graphs $G_1, G_2, G_3, ...$ constructed using some particular approach or algorithm. in this particular case $G_n$ is constructed by modifying $G_{n-1}$ in some "...
4answers
742 views

### How to find the cycles which, together, involve the biggest number of non-shared edges in a directed graph?

I am not a computer science theorist, but think this real world problem belongs here. The problem My company have several units accross the country. We offered to employees the possibility to work ...
1answer
187 views

### Graph partitioning, balancing on within subset edge weights

I'm interested in pointers to algorithms (approximation algorithms are fine) that attempt to partition a graph into two subsets such that the sum of the edge weights within each subset is (...
4answers
896 views