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Questions tagged [graph-algorithms]

Algorithms on graphs, excluding heuristics.

3
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1answer
106 views

How is SDP an extension of spectral algorithms?

In one of his lectures, Uri Feige described semidefinite programming (SDP) as ... an algorithmic technique that extends both linear programming and spectral algorithms. I know the basic ...
0
votes
1answer
117 views

Data Strcuture to represent dependencies amongst modules

Consider several software modules $m_1, m_2, ... m_n$. Each module has some inputs and outputs and the inputs to some of the modules are dependent on the outputs of some other modes. For example, in ...
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0answers
14 views

Spidergon Networks-on-Chips

What do you guys think about Spidergon NoC ? Why mod 4 ? And do you guys understand how the shortest path routing algorithm depends on the value of RelAd ? The original paper : Spidergon: a novel on-...
3
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0answers
68 views

Generating a random connected bipartite graph

A (n, m, k)-bipartite graph is a bipartite graphs with: independent sets of size $\{n, m\}$ a total of $k \geq n+m-1$ edges We want an algorithm to generate a (n, m, k)-bipartite selected uniformly ...
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0answers
121 views

Star seperators to explain computational complexity of algorithms on a class of graphs?

A lot of NP-hard optimization problems on graphs which are perfect become solvable in polynomial time. Unfortunately, the class of graphs that arise in my problem are not perfect. The graphs can be ...
1
vote
1answer
80 views

Algorithm for K-best NON perfect bipartite matchings

I was reading this great article: https://core.ac.uk/download/pdf/82129717.pdf It solves a generalization of the maximum sum assignment problem by finding the k best assignments and not only the best....
6
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0answers
110 views

Grid-Minor Theorem of Robertson and Seymour and its Algorithmic Applications

Graph-Minor Theorem of Robertson and Seymour [1] states that if graph G has large treewidth, then it contains a large grid as minor. Most approximation results on general classes of graphs with ...
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0answers
39 views

Optimally fair stable matching

There's a nice post by Gil Kalai which outlines the inherent bias in stable matching algorithms quantitatively. In the traditional loyd shapeley algorithm for $n$ men and $n$ women, given randomly ...
-1
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1answer
83 views

When is extra vertex required in arbitrage detection using Bellman Ford?

I am studying applications of shortest path, in particular arbitrage. Specifically, I was reading these two resources: https://stackoverflow.com/questions/2282427/interesting-problem-currency-...
1
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1answer
76 views

Pulling a graph across a partition

I am looking for the name for a particular graph property, if it has been studied, and efficient algorithms for computing it, if they exist. I realise that this may be a well known property that I am ...
2
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0answers
119 views

Crime prevention using graph theory and machine learning

I am looking for a way to the model the incidence of crime among a network of individuals. Part of it will use machine learning, and part of it will have to resort to some graph theoretic ...
1
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1answer
44 views

Problem property name where an optimal solution in a graph can be used as a solution in any subgraph

Suppose one is given a graph optimization problem where the optimal solution $S$ for the problem on graph $G$ can be used as a solution for any subgraph of $G$. In other words, given $S$ is an optimal ...
5
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1answer
108 views

Counting/Enumerating Minimal Edge Covers

A Minimal Edge Cover is an Edge Cover such that no other Edge Cover is a proper subset of it. Questions Which is the complexity of counting Minimal Edge Covers? Do we know any non-trivial ...
1
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1answer
68 views

Color shifting in a bipartite graph

Assume that we have a directed bipartite graph $G = \langle L\dot\cup R, E\rangle $. Where $E$ contains directed edges only from $L$ to $R$, that is, $E\subseteq L\times R$. Assume further that the ...
2
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0answers
85 views

Counting the maximum number of paths of length $n$ that differ in at least $k$ edges

What is known about the complexity of solving (or approximately solving) the following problem? INPUT: Graph $G=(V,E)$ and constants $L$ and $K$. OUTPUT: The maximum size of any set $S$ of simple ...
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0answers
51 views

Reduction of irregular graphs, to regular graphs, while preserving hamiltonicity

I am wondering if this is a topic that has had research done... If I could reduce irregular graphs to regular graphs (including replacing redundant node clusters with dummy nodes), while ensuring ...
8
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1answer
184 views

Could chromatic number be easy to calculate when colouring is hard for some graph class?

Similar question was asked before, but there was an error in it so it was left unanswered Graph class with easy chromatic number, but NP-hard coloring Is there any infinite set of graphs $C$ such as: ...
2
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0answers
145 views

A variant of the Maximum Weight Clique problem

I am trying to solve a problem that I could reduce to the following: Given a graph $G=(V,E)$ with both edge and vertex weights, all weights being non-negative, find a clique $Q\subseteq V$ s.t. $\sum_{...
3
votes
2answers
167 views

Finding a set which dominates the Minimum Dominating Set

Given an unweighted, undirected graph, a dominating set $S$ is a set of nodes such that every node is in $S$ or adjacent to a node in $S$. The dominating set problem is NP-hard, but I am considering ...
4
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2answers
137 views

Max cut problem between two connected subgraphs

Let $G$ be a connected graph. Consider the problem of finding a partition $G = A \cup B$ into connected subgraphs, so that the cut between $A$ and $B$ is maximized. Is there anything which is known ...
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1answer
101 views

Finding Cheapest n-Path [closed]

Given a weighted directed acyclic graph, how can I find the cheapest path from an Origin Vertex to a Destination Vertex which ...
2
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0answers
39 views

Min cut problem on unbalanced partitions for planar graphs with unit capacity edges

The question is: given a planar graph $G$ with unit capacity edge weights and a fixed positive integer $k$, what is an approximation algorithm for finding the minimum size of a cut $(A,B)$ with $|A|=k$...
5
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1answer
95 views

Exact algorithm or parameterized algorithm for Maximum Edge Biclique Problem?

The Maximum Edge Biclique(MEB) problem is to find a biclique with as many edges as possible in a bipartite graph. It was proved to be NP-complete by Peeters in 2003, and then the inapproximability ...
4
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1answer
177 views

Fast algorithm to find a maximum connected subgraph of k vertices

Given an undirected graph $G = (V, E)$ and a function $f: 2^V \to \mathbb{R}^+,$ where $2^V$ is the set of all subsets of $V$. Find a connected subgraph $T = (V_T, E_T)$ of k vertices such that $f(V_T)...
3
votes
1answer
108 views

Finding a “lowest” path in a graph

I have an undirected graph $G = (E,V)$, $|V|=n$, where each node $v_i$ has a natural number weight. Think of these weights as heights $h_i$. Given two nodes $s$ and $t$, I'd like to find a lowest ...
4
votes
2answers
142 views

Check if graph stays connected after edge swap

Checking whether a (simple, undirected) graph is connected can be done in linear time in the number of edges. What I am looking for is a more efficient way of checking whether it stays connected after ...
3
votes
1answer
199 views

What exactly is Lawler's modification to Yen's algorithm and how does it work?

I recently read about Yen's algorithm, I understand the algorithm and it seems correct, however Wikipedia mentions that there exists "Lawler's modification" to the algorithm, which is described as ...
4
votes
1answer
379 views

Minimum Union-Sum Cost Path

I have a minimum cost path selection problem that is different from the usual shortest path in that each type of cost is accounted only once in the total cost of the path if multiple edges on the path ...
1
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0answers
53 views

k-center 2.0: A stronger k-center condition

Given an unweighted, undirected graph, we can use the classical 2-appx for $k$-center to select a set $S$ of centers such that every vertex is within a distance of 2 of some center in $S$. Note that ...
3
votes
1answer
47 views

Complexity of distributively verifying that the diameter is small

Consider a graph $G=(V,E)$ and an integer parameter $k$. I'm interested in the round complexity, in the CONGEST model, of checking if the diameter of the graph is "much larger" or "much smaller" than ...
6
votes
1answer
240 views

Computing topological sort while keeping edges “short”

Motivation: I want to compute a topological sort order in which the connected vertices are close to each other. Problem statement: Given a DAG $G(V,E)$ with $n$ vertices, compute a topological sort ...
0
votes
1answer
51 views

What is the deterministic complexity of counting the number of global minimum cuts on an unweighted undirected graph?

I know as a consequence of Karger's algorithm that the number of minimum cuts is bounded by $\binom{n}{2}$. In the comments of Counting the number of distinct s-t cuts in a oriented graph It says ...
6
votes
1answer
134 views

Partition edges into edge disjoint walks

Consider an undirected graph $G=(V,E)$ and two sequences of $k$ vertices $S=s_1,\ldots,s_k$ and $T=t_1,\ldots,t_k$. A set of $k$ walks is called a $(S,T)$-walk partition if the walks form a ...
3
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0answers
116 views

Is 3-coloring bounded degree graphs subexponential: $O(\exp{(\sqrt{n}\log^2{n})})$? [closed]

We got an argument that 3-coloring bounded degree graphs is subexponential with complexity $O(\exp{(\sqrt{n}\log^2{n})})$. The treewidth of a planar graphs on $n$ vertices is $O(\sqrt{n})$ and 3-...
5
votes
1answer
153 views

“Smallest” path that visits a given set of vertices

I use smallest rather than shortest to distinguish between the shortest path problem. The problem is as follows: Given a directed graph $G=(V,E)$, two vertices $s$ and $t$, and a set of $p$ ...
1
vote
1answer
86 views

What is the best and easy (regarding implementation) way of computing three edge independent trees in a 3-connected graph?

I am searching for an implementation of an algorithm that constructs three edge independent spanning trees from a 3-edge connected graph. Any response will be appreciated. Thanks in Advance.
8
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2answers
400 views

Counterexample to max-flow algorithms with irrational weights?

It is known that Ford-Fulkerson or Edmonds-Karp with the fat pipe heuristic (two algorithms for max-flow) need not halt if some of the weights are irrational. In fact, they can even converge on the ...
13
votes
1answer
340 views

What are the obstructions to extending $L=SL$ to $L=NL$?

Omer Reingold's proof that $L=SL$ gives an algorithm for USTCON (In an Undirected graph with special vertices $s$ and $t$, are they Connected?) using only logspace. The basic idea is to build an ...
1
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2answers
191 views

Is perfect matching for bipartite graph with no cycles unique?

Given a balanced bipartite graph that satisfies Hall's theorem (is non singular) then it shown that it has at least one perfect matching. My question is if the balanced bipartite graph is also ...
-1
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1answer
301 views

Closeness Centrality for Weighted Graphs

In order to determine the Closeness Centrality for a vertex u in a graph, you compute the shortest path between u and all other vertices in the graph. The centrality is then given by: $C(u) = \frac{1}...
6
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0answers
72 views

Complexity of bounded degree full contraction

This paper defines the problem $\mathrm{B{\scriptsize OUNDED} \ D{\scriptsize EGREE}\ C{\scriptsize ONTRACTION}}$ as follows: Instance: A graph $G$ and two integers $d$ and $k$. Question: Is there a ...
5
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0answers
167 views

Find a pair of nodes with maximum sum of distances in k given trees

For k edge-weighted trees $T_1,T_2...T_k$ which contain the same set of nodes $\{1,2,... n \}$, I want to find a pair of nodes $(x,y)$ which maxifies $$\sum_{i=1}^k d_i(x,y)$$ where $d_i(x,y)$ ...
3
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0answers
101 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
398 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
114 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 ...
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0answers
98 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 ...
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votes
1answer
37 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
224 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
67 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 $O(n^3)$ ...
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0answers
26 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, ...