Questions about properties of and problems on graphs, discrete data structures that have the form of nodes connected by edges, that is networks.

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3
votes
0answers
23 views

Computing the “at least k friends in common” graph

Suppose we have the graph of a social network with symmetric connections (e.g. Facebook or LinkedIn). Suppose we would like to find all pairs of people who have at least k friends in common, in order ...
1
vote
1answer
21 views

SimRank on a weighted directed graph (how to calculate node similarity)

I have a weighted directed graph (it's sparse, 35,000 nodes and 19 million edges) and would like to calculate similarity scores for pairs of nodes. SimRank would be ideal for this purpose, except that ...
2
votes
1answer
97 views

Graph Families that are easy to color

What are the non-trivial graph families that have a known chromatic number, or an easy way (polynomial-time algorithm) to compute the latter. Examples would be: Kneser graphs Chordal graphs Do ...
3
votes
0answers
32 views

Directed acyclic graphs and Latin Squares

Every Latin square corresponds to a directed acyclic graph with a lattice arrangement, and whose edges indicate label order (<). For example: I'm interested ...
0
votes
2answers
103 views
+50

scale-free networks and adjacency matrix

Given a distribution over graphs with $n$ nodes having the "scale-free" property, I would like to compute for a pair of vertices $(a,b)$ the probability that they are connected (or more precisely the ...
3
votes
1answer
49 views

Travelling Salesman which can repeat cities

In the TSP problem, we usually assume a complete graph. If we can only visit each city once, we need a complete graph to ensure that there will be a path from every city to every other city. This is ...
0
votes
1answer
13 views

Necessities for two undirected graphs being isomorphic

As far as I know, for two undirected graphs $G = (V, E) $ and $H = (V', E')$, the following criteria is necessary for them to be isomorphic: $|V| = |V'|$ $|E| = |E'|$ $G$ has $j$ nodes of degree $k$ ...
3
votes
1answer
80 views

Locally finite graph without an optimal path

If I have a locally finite graph (every node has finite number of neighbors) with positive edge weights, is it possible for there to be a path between some start node and goal node but no shortest ...
3
votes
0answers
33 views

Finding partial traveling salesman path of specified length

For a given set of nodes, I can find optimal paths that visit all nodes using various traveling salesman algorithms. As a subset of this problem, I would like to be able to find shortest partial ...
-2
votes
2answers
69 views

Undirected graph G that has 12 vertices, 66 edges and 3 connected components?

Why would it be impossible to draw an undirected graph G that has 12 vertices, with 3 connected components if G had 66 edges?
-2
votes
0answers
15 views

Upper Bound Difference between Min Cut and Max cut?

Quick question: Are there any known upper bounds for the difference between the value of a maximum cut(:=M) and a minimum cut(:=m) in a flow network? (|M - m| <= f for some function f)
-1
votes
2answers
52 views

Why is T not a minimum spanning tree of G?

The Problem: Let T be a tree constructed by Dijkstra's algorithm in the process of solving the single source shortest-paths problem for a weighted connected graph G.    a. True of ...
0
votes
1answer
56 views

How to draw a graph to disprove this statement?

The Problem: Indicate whether the following statements are true or false: a. If e is a minimum-weight edge in a connected weighted graph, it must be among edges of at least one minimum ...
0
votes
1answer
28 views

Algorithm deciding if a radius of a graph is two

Given an unweighted, undirected graph, what is the time complexity to decide if its radius is at most 2? Are there any faster algorithms than doing BFS on each node?
2
votes
1answer
83 views

Updating an MST $T$ when the weight of an edge not in $T$ is decreased

Given an undirected, connected, weighted graph $G = (V,E,w)$ where $w$ is the weight function $w: E \to \mathbb{R}$ and a minimum spanning tree (MST) $T$ of $G$. Now we decrease the weight by $k$ ...
2
votes
1answer
19 views

What is the appropriate algorithm for bipartite matching with constraints?

I have a problem that is a bit complex, and I don't know what method/model I should use to express it (much less solve it). Let's say we have a lot of employees and a few jobs to be done. Each ...
2
votes
1answer
43 views

Strongly connected components on a DAG

What is supposed to be the right result of an SCC algorithm running on a DAG. should it return "no components" or "there are V components of size 1"? I suspect it will return the latter (since it ...
2
votes
1answer
30 views

Dominator Tree for DAG

Is there a fast algorithm to compute dominator tree for acyclic graphs? The Lengauer-Tarjan Algorithm is a fast algorithm for general flowgraphs. But if a graph is acyclic, do we have a faster ...
-1
votes
1answer
17 views

Checking a property of all of the cycles in a graph

Suppose $G= (V,E)$ is a directed graph with weights on the edges. I would like to check if $G$ has the following property: if $C \subset E$ is the set of edges in a cycle of length at least $3$, then ...
3
votes
1answer
173 views

Does Ford-Fulkerson always produce the left-most min-cut

When using Ford-Fulkerson to find max-flow between s and t, the exact choice of flow-graph depends on which paths are found. However, if you then use the left-over residual graph to produce a min-cut ...
1
vote
1answer
43 views

How can an maximum flow algorithm for directed graphs, i.e. Edmond-Karp, be adapted to compute a minimum $s$-$t$ cut in a undirected graph?

How can an maximum flow algorithm for directed graphs, i.e. Edmond-Karp, be adapted to compute a minimum $s$-$t$ cut in an undirected graph ? I've seen it stated that one can apply a maximum flow ...
2
votes
1answer
23 views

Ford-Fulkerson Running Time

This question might be really basic but every source seems to skip over a couple of steps neither of which seem trivial to me. It would be great if someone could explain them! In the analysis of ...
1
vote
1answer
80 views

How important is it to find a deterministic polynomial time algorithm to construct Ramanujan graphs? [closed]

As in I don't know what is the difference between say the conferences SODA, STOC or FOCS. Measured in terms of such conferences, where would such a result be publishable? This is not a "technical" ...
3
votes
1answer
52 views

Is the minimal number of colors needed to color a graph some fixed number?

Consider to following decision problem: Input: Undirected graph $G=(V,E)$ Question: Is the minimum numbers of colors needed to color the vertices (such that every two adjacent vertices ...
1
vote
1answer
30 views

Decreasing a digraph's edge-weights while keeping net weights of edges at each vertex constant

Given a directed weighted graph, is there an algorithm that does the following: Removes as many edges possible. Reduces as many weights as possible. Given the constraint that the net weight of all ...
1
vote
0answers
32 views

TSP heuristics for limited distance information [closed]

this is my first question on ComputerScience beta. :) I've posted a similiar question on Mathoverflow and a friendly user advised me to post my question on this site. Problem: I'm looking for ...
3
votes
0answers
17 views

Efficient algorithms for mutual, inverse, or round-trip Personalized PageRank

I'd like to implement a similarity between two nodes (X and Y) of a graph based on a simple extension of the Personalized PageRank algorithm, either: (Mutual PageRank): the product of the PPR of Y ...
0
votes
0answers
18 views

A way to order a shortest path tree

Given the shortest path tree of a directed graph G=(V,E) and w: E-> R , source vertex s and an assumption that there are no negative cycles in the graph. In the homework assignment we need to find ...
3
votes
1answer
34 views

Minimum Length Hamiltonian Path Pair in O(n^2) or better

A friend and I have been discussing turning a $O(n^2)$ graph problem's algorithm into $O(n\log n)$, or at least less than $O(n^2)$. And no - this is not a homework question. We've narrowed it down to ...
6
votes
2answers
104 views

Real world applications for Steiner Tree Problem?

Are there real-world applications of the Steiner Tree Problem (STP)? I understand that VSLI chip design is a good application of the STP. Are there any other examples of real world problems that ...
0
votes
0answers
25 views

Finding the second lightest path in a graph

Assume I have a weighted, directional graph with no cycles. What is the most efficient way to find the second lightest path from the source vertex to a given vertex?
1
vote
0answers
18 views

Coloring a 3-Colorable graph with O(logn) colors

Assume we have a polynomial algorithm that can get approximation ratio of $\frac{1}{2}$ to the Independent-Set problem. I need to prove that there exists a polynomial algorithm that for a 3-Colorable ...
1
vote
1answer
22 views

Proving a language to be Recursively Enumerable?

I know to prove a language to be Recursively Enumerable, it is ideal to represent a Turing machine for it. Let L be set of strings which have alphabet {u,d,l,r}, where u is up 1, d is down 1, etc. L ...
-1
votes
1answer
25 views

Is the empty set a dominating set? [closed]

Is the empty set a dominating set? I don't think it is, because in an empty set there are no vertices to dominate. Is my reasoning correct?
0
votes
1answer
39 views

Can I find a clique with more than 2 nodes in a bipartite graph?

As in the title, is it possible to find a clique with more than 2 nodes in a bipartite graph?
1
vote
1answer
17 views

Is there any relation between Global minimum cut problem and Maximal independent set?

I have simple undirected graph. I want to determine a size of minimum vertex cover, a size of maximal independent set and a size ...
4
votes
0answers
42 views

Generate a random graph with geometrical degree distribution

I'm working on graph generation, trying to implement the RT-nested-Smallworld network model described in this paper. We are talking about generating an undirected graph in a slightly different way ...
1
vote
1answer
27 views

Path in digraph passing through given set of vertices

Suppose we have digraph G, set of its vertices W and two (possibly equal) vertices s and f. I'm looking for an algorithm which will solve the following problem: whether there is path from s to f ...
0
votes
0answers
44 views

What are the application of $\beta$-frugal coloring of Graph and Hypergraph?

A proper coloring of a graph $G$ is called $\beta$-frugal if no color appears more than $\beta$ times in the neighborhood of any vertex of $G$. I am well aware about the application of graph color ...
3
votes
1answer
45 views

Finding all paths between a set of vertices in a DAG

Given a graph G= (V, E) that is: directed, acyclic, non-weighted, may have more than one edge between two vertices (thus, source and destination are not enough ...
0
votes
1answer
39 views

What does every root is at the same level mean

My textbook says a "complete binary tree" is a "full binary tree" where every root is at the same level. My conceptual understanding: All this time, I was led by my textbook to believe a root is ...
2
votes
2answers
83 views

Covering a graph with non-overlapping cliques

I have a problem where I need to split a graph into subgraphs. The conditions for the splitting is as follows: Every subgraph must be a complete graph/clique No vertex can be part of two or more ...
0
votes
1answer
40 views

Application of shortest vertex-disjoint path with time window

I am working on finding shortest disjoint path problem, When there are distinct origin destination pairs and there is a predefined time window (or length) associated with each object (which we want to ...
0
votes
1answer
40 views

Algorithm to recognize Strongly Regular Graph (SRG)

I am looking for an algorithm to determine whether a graph is Strongly Regular Graph (SRG) or not.
1
vote
0answers
72 views

Weighted, Acyclic Graph and Change Weights Problem?

I ran into a question as follows: We have a Code on Weighted, Acyclic Graph G(V, E) with positive and negative edges. we change the weight of this graph with ...
-1
votes
1answer
32 views

Max-Flow Min-Cut Theorem Intuition

What is the intuition behind the Max-Flow Min-Cut Theorem? I know that the Min-Cut is the dual of Max-Flow when formulated as a linear program, but the result seems artificial to me.
1
vote
1answer
40 views

Is a subgraph either a spanning subgraph or a full subgraph?

A graph $G' = (N' ,A')$ is a spanning subgraph of a graph $G = (N, A)$ iff $N ' = N$ and $A' \subseteq A$. A graph $G' = (N',A')$ is a full subgraph of a graph $G = (N, A)$ iff $N' ...
7
votes
2answers
159 views

Maximize distance between k nodes in a graph

I have an undirected unweighted graph $G$ and I want to select $k$ nodes from $G$ such that they are pairwise as far as possible from each other, in terms of geodesic distance. In other words they ...
3
votes
0answers
74 views

Genetic algorithm crossover technique for solving graph colouring problem

I am trying to develop a genetic algorithm to solve a graph colouring problem. The problem is the standard graph colouring problem, given a graph $G = (V,E)$ where $V$ is the set of vertices $V=\{0 ...
-2
votes
1answer
51 views

How many ways are there to add a node to a digraph?

In a digraph with $n$ vertices, how many different ways a new vertex can be added to get the digraphs with $n$+1 vertices? Input digraph with $n$ vertices have following degree criteria : There ...