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

learn more… | top users | synonyms

0
votes
0answers
60 views

Understanding The Mapping Of Edges to Nodes In A Graph Theory Problem

I am really confused with this problem. Here's the problem: You have $N$ points numbered $1$ through $N$,inclusive, and $N$ arrows again numbered $1$ through $N$,inclusive. No two arrows start at ...
-3
votes
0answers
20 views

Find orientation graph of undirected graph that mimimizes absolute difference of in-degree and out degree

Here's a question from our uni's ICPC programming competition selections. I'm stating it in simpler terms here. Given an undirected graph, orient the edges of the graph in such a manner that the ...
0
votes
0answers
12 views

Complex Network Betweenness Centrality algorithm [on hold]

I am writing a function in VB.net to calculate the betweenness centrality given in this paper Betweenness Centrality in a directed network. I have written the following code to do so. Please aware ...
-1
votes
0answers
25 views

Number of ways to join n distinct trees

I have been trying to solve a problem in which i need to join N distinct trees with disjoint set of nodes. After searching a lot I came across this formula but i am not able to understand it. Please ...
-3
votes
0answers
18 views

how to make our own graphics [on hold]

happy i want to learn advaced tags of html so please teach me how to use it First developed by Tim Berners-Lee in 1990, HTML is short for HyperText Markup Language. HTML is used to create ...
0
votes
0answers
44 views

given 1/2 separator of a graph, How can we create 1/3 separator of a graph? [on hold]

I have read a note. I have a figure like this. Figure a is the original tree and v1 vertex is 1/2 separator.here n=26 each subtree (after separating v1) contains < n/2. In the proof of lemma 4 ...
3
votes
0answers
39 views

Qualifications for a problem to be solved as a single source shortest path problem

What are the pre-conditions for any problem X to be qualified for being solved in a single source shortest path problem (SSSP) setting? Lets, say we have a problem X. What should be the pre-...
1
vote
2answers
40 views

Describe an algorithm for painting cards in the following game

It's my first question out here, so please don't judge me too strictly. I heard of the following game: there's set of cards with different set of objects (but the same number of them on every card) ...
1
vote
2answers
49 views

Can a graph have multiple identical elements?

Can a graph have multiple nodes that have the same value ? For instance, could a graph holding numbers have the same number present multiple times across the itself ? My current approach is to not ...
0
votes
1answer
39 views

Rules to follow to create edges in graph

I am currently writing a graph object in Swift, I see that there are different types of graphs, some that are undirected and some that are directed. Here are my questions : Can a graph be both ...
2
votes
1answer
180 views

Converting a non-planar graph to planar

Suppose that we have a non-planar graph $G$ which is undirected and connected. Our aim is to remove a set of edges and/or a set of vertices and convert make $G$ planar while keeping the connectedness. ...
1
vote
1answer
45 views

Degree Reduction in Max Cut and Vertex Cover

I have been reading Alimonti and Kann's paper "Some APX-Completeness results for cubic graphs" and I don't understand why the degree-reduction gadgets for Max Cut and Min Vertex Cover have to be ...
0
votes
0answers
37 views

Compression of a complete Directed Acylcic Graph

Consider a DAG $g$ as a label $l$ with a list of sub-nodes $\bar{g}$: $g ::= l \enspace \bar{g}$ This is an "unfolded" representation of the DAG, i.e. it contains double entries, when two paths ...
0
votes
0answers
30 views

Is is possible compute the max flow with max cost through an instance of maxflow-mincost?

I have a flow network with gains. In practical terms, a gain is the opposite of a cost. So, I interested in finding the maximal gain of a network flow, what could be interpreted as finding a maximum ...
2
votes
0answers
20 views

Powerlaw graphs : Number of hubs and fraction of edges incident on them

As per the definition of power law, the fraction P(k) of nodes with k degree for large values of k , given by P(k) ~k ^-r . In this definition, the term large value is not clearly defined. Does ...
3
votes
0answers
41 views

Orient edges in a mixed graph to minimize the critical path

A mixed graph is a graph that has directed and undirected edges. Is there an efficient algorithm that allows the orientation of undirected edges in a mixed graph in such a way that no cycle is ...
7
votes
1answer
189 views

Binary rooted tree isomorphism

My trees are rooted and have at most two children at every vertex. I need references that help me solve any or all of the questions below: How many isomorphism classes of trees with n vertices are ...
3
votes
1answer
59 views

Automorphism of a Graph with a given Set of Permutations

Given a graph $H$. A set of permutations $\alpha$ which contains permutations of vertices of $H$. The permutation set $\alpha$ has automorphisms of subgraph $H_1, H_2,..... H_x$ where $x$ is the ...
0
votes
1answer
8 views

What is the difference in 'logical array blocked' and array list B, and what do they represent?

In Johnson's 1975 Paper 'Finding All the Elementary Circuits of a Directed Graph', his psuedocode refers to two separate data structures, logical array blocked and list array B. What is the difference ...
0
votes
1answer
36 views

Maximize cost in graph with variable costs

Consider the following problem. A prisoner eats once a day, he can either have a low, or a high calorie dish. In order to be allowed to eat the high calorie dish, he must not have eaten the previous ...
0
votes
0answers
6 views

In a maximal planar graph, are two consecutive neighbors of a vertex necessarily adjacent? [migrated]

If we pick a vertex $v$ and two consecutive neighbors of it, $u_1$ and $u_2$, are we sure that $(u_i, u_{i+1}) \in E$? My intuition is that if $(u_1, u_2) \notin E$, you can add an edge by going from ...
2
votes
1answer
37 views

Permutation on matrix to fill main diagonal with non-zero values

I am currently working on some sparse non-singular matrices. One of the algorithms I use requires divisions by the elements on the main diagonal so I have to ensure that my main diagonal is filled ...
2
votes
1answer
35 views

Is there a way to reflect small edge-weight changes after computing Floyd-Warshall on a large graph?

I am working on a hex-based game in which I'm trying to pre-calculate pathfinding for a given map using the Floyd-Warshall algorithm. The map size is on the order of thousands of hexes (so maximum ...
2
votes
1answer
31 views

Flaw in linear programming solution for multi-commodity flow problem?

The multi-commodity flow problem problem statement - wiki According to constraints of multi-commodity flow problem a given material must start at source s with demand d and end up at its target t. ...
-3
votes
0answers
34 views

Number of ways to construct a Regular graph [closed]

For a regular graph (each vertex has same degree k), a part of graph upto level l is given, how to compute the total number of ways in which the graph can be completed given that m edges and n ...
0
votes
0answers
12 views

Does marginalizing on a Bayesian network preserve its original independence assumptions?

I know that marginalizing over a Bayesian network causes changes to the graph (e.g. marginalizing node c in the V-structure given by $a \rightarrow c \leftarrow b$ results in $a$ and $b$ being ...
1
vote
0answers
18 views

Reconstructing a graph from set of sequences of edges

I have posted the same problem to Math Overflow, not sure where it fits better. I have the following problem to solve: Given a set of sequences of edges of an undirected, planar, connected graph, ...
1
vote
0answers
25 views

probability that the vertex set {1,…,k} is component of random graph

Consider a graph with vertices 1,...,n and suppose that each of the $\binom{n}{2}$pairs of vertices is, independently, an edge of this graph with probability p.Let $P_n$ denote the probability that ...
0
votes
1answer
62 views

Voronoi Diagram: Exactly 2n-5 vertices

I want to find some characteristics for a set of points $S$ which contains $n$ points and has some Voronoi Diagram $V(S)$. This diagram should have exactly $2n-5$ vertices. I tried to use the Euler ...
1
vote
0answers
22 views

Variable elimination in Bayesian network

I'm trying to check if my understanding of variable elimination is correct. Assume the above Bayesian network is factorized as: $p(a,b,d,e,l,s,t,x) = p(a)p(t|a)p(e|t,l)p(x|e)p(l|s)p(b|s)p(d|b,e)p(s)$...
3
votes
0answers
64 views

How to determine Isomorphism of Non-Symmetric Matrix when Permutation-Set is given?

Consider, two $m \times n$ matrices $A, B$ such that there is a permutation $\kappa$ that such that such that $A^{\kappa}=B$ (Wielandt's notation), i.e. $A, B$ are isomorphic but not equal. Since,...
1
vote
1answer
32 views

Minimum Weight Directed Subgraph ensuring all pairs reachability?

After some work on Minimum Spanning Trees and Steiner trees in combinatorial problems I came across this problem that I would like to look further in my research, but I want to know if there is an ...
2
votes
2answers
158 views

Basic questions about network flow calculations

Flow networks are often constructed when one is interested in measuring how resilient a graph is. The idea goes as follows: two vertices are designated as source $(s)$ and sink $(t)$ respectively, to ...
1
vote
2answers
94 views

Linear-time algorithm to find an odd-length cycle in a directed graph

Problem: Give a linear-time algorithm to find an odd-length (directed) cycle in a directed graph. (Exercise 3.21 of Algorithms by S. Dasgupta, C. Papadimitriou, and U. Vazirani.) The related post@...
1
vote
1answer
32 views

Relation between MAX CUT and MIN CUT

I'd like to ask a question about MAX CUT and MIN CUT on graphs with unit edge-weight. I know that MAX CUT is NP-Hard, but MIN CUT is in P (i think)? Barahona, in 1982, showed (Lemma 1) finding a cut ...
1
vote
0answers
22 views

What is the psuedo-code for Tremaux's Algorithm as a Depth First Search to solve a maze?

I was interested in the Tremaux Algorithm as a Depth First Search to solve a Maze. Unfortunately I was not able to understand what Data Structures are and how they could be used. For example, I saw a ...
3
votes
0answers
22 views

How to compute amortized complexity of n runs of Dijkstra's algorithm?

I'm trying to figure out how to compute an amortized complexity/ or complexity of this algorithm. We have a Graph which is oriented. And we are going to run Dijkstra's algorithm for finding a shortest ...
1
vote
2answers
51 views

Equivalent definition of minimal spanning tree

Prove that $T$ is MST $\Leftrightarrow$ for any edge $uv \notin T$, $uv$ has the maximal weight on the cycle created by adding $uv$ to $T$. It's my attempt to prove $\Rightarrow$: Consider the ...
-1
votes
1answer
44 views

What do we mean when we say an edge (u,v) connects some component to other component in forest G = (V,A)

Let H = (V,E) be a connected, undirected graph. Let A be a subset of E. Let C = (W , F) be a connected component (tree) in the forest G = (V,A). Let (u,v) be an edge connecting C to some other ...
1
vote
1answer
24 views

How do I find the intersection of subgraphs in a directed acyclic graph efficiently?

I have a directory structure in which each directory can have multiple parents (IOW, a cd .. is ambiguous). AFAICS this means this is equivalent to a directed ...
1
vote
0answers
27 views

Generate a graph to exact size using Kronecker product graph model

In network science, we can take sample a complex system and derive from this sampling a representative network (or graph) that describes the system to some extent. A model of a network, is a powerful ...
3
votes
1answer
34 views

Ford-Fulkerson algorithm with asymmetric adjacency matrix

Suppose that I have a bipartite graph $G=(A \cup B, E)$ and $A = \{1, 2, \dots, n\}$, $B = \{1, 2, \dots, m\}$. After a virtual sink $s = 0$ and a source $t = n+1$ is included into the graph, I want ...
7
votes
0answers
75 views

Optimal meeting point in directed graph

Let $G(V, E)$ be a edge-weighted directed connected graph and $v_1, \dots, v_n \in V$ be some vertices. Let $d(a, b)$ denote the length of the shortest path from $a$ to $b$, for $a,b \in V$. I need ...
0
votes
1answer
85 views

Complexity of the Dijkstra algorithm

I'm little confused by computing a time complexity for Dijkstra algorithm. It is said that the complexity is in $O(|V|^2)$ - Wikipedia - Dijkstra, which I ...
5
votes
2answers
87 views

Efficient algorithms for identifying the diamond fork&join vertices and the diamond pairs in directed acyclic graph?

Given a DAG (directed acyclic graph) $G=(V,E)$ without multiple edges, i.e., edges with the same source and target vertices, we define: A vertex $v_j \in V$ is a diamond-join ($\Diamond_J$) vertex if ...
-1
votes
1answer
24 views

Let G be k-reguler bipartite graph of degree at least 2. show that K(G) not equal 1? [closed]

Let G be k-reguler bipartite graph of degree at least 2, for all v belong to V(G) prove that k(G-v) is connected?
0
votes
0answers
45 views

How to find maxflow with minimum number of edges?

I am struggling with the flowing problem: You are given a source s and a sink t and a biparted graph G. All vertices {v} from the left half are connected to the source s with given capacity C[v]. ...
4
votes
0answers
40 views

find a minimum-cost pair of arc-disjoint paths, both within a given restricted distance

Is there a polynomial algorithm that can find a pair of arc-disjoint paths in a directed graph that has a minimum total cost, subject to the condition that both paths are within the same distance. ...
1
vote
1answer
34 views

TSP Edge Removal

Are there any papers/algorithms for finding edges in a graph that can be removed with affecting the graph's optimal TSP tour length? For instance, in a Euclidean TSP instance, many edges could be ...
4
votes
0answers
21 views

Minimal Steiner Tree in unweighted directed graph

I have an unweighted directed graph $(V, E)$ and a subset $T \subseteq V$ of these vertices. I want to find the minimum tree $(V',E')$ that contains all these $T$ vertices (minimize in number of nodes ...