# Tagged Questions

Algorithms on graphs, excluding heuristics.

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### Does there exist any distributed algorithms for the Minimum Feedback Arc Set Problem

I am wondering if there are any known distributed algorithms for the Minimum Feedback Arc Set Problem. Exact solutions, approximation algorithms, and heuristic approaches all welcome.
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### Minimum-weight feedback edge set in undirected graph - how to find it? Is it NP hard problem?

Let G = (V,E) be an undirected graph. A set F ⊆ E of edges is called a feedback-edge set if every cycle of G has at least one edge in F. Suppose that G is a weighted undirected graph with positive ...
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### Confusing running time analysis for the Divide & Conquer algorithm of Hamiltonian Path problem

In the Hamiltonian Path problem we are given a graph $G=(V,E)$ and two distinct vertices $\{s,t\}$ and we ask if there is a path from $s$ to $t$ which traverses all other vertices exactly once. ...
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### Triangular Mesh Reordering - Huddling Triangles

I am given a 3D model represented by its outside surface as a triangular mesh (hollow inside). The model is mostly 2-manifold, so that each triangle edge is shared by exactly 2 triangles. This, ...
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### Minimum vertex k-cut

Given an undirected graph $G = (V, E)$ and an integer $k$, the well-known minimum (edge) $k$-cut problem asks to find $E' \subseteq E$ with minimum $|E'|$ that the graph $(V, E \setminus E')$ has at ...
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### Constant Width Max Sum Product Multi-objective Shortest path problem

This question is a follow-up on the question I asked three days ago here. For convenience I restate it here. I am given a graph. Each edge is labelled by a vector of numbers, called weights. They ...
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### Max Sum Product Multi-objective Shortest path problem

Is anything known about the following problem: I am given a graph. Each edge is labelled by a vector of numbers, called weights. They are numbers between 0 and 1. A path is first assigned a vector, ...
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### Complexity of the homomorphism problem parameterized by treewidth

The homomorphism problem $\text{Hom}(\mathcal{G}, \mathcal{H})$ for two classes $\mathcal{G}$ and $\mathcal{H}$ of graphs is defined as follows: Input: a graph $G$ in $\mathcal{G}$, a graph $H$ in ...
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### On bandwidth of graphs

I am trying to find references on algorithms for graphs of bounded bandwidth, in the same way as it is done with treewidth for instance. I could only find research related to computing the bandwidth, ...
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### Graph Isomorphism of Strongly Regular Graph with fixed parameter

$G, H$ are strongly regular graphs with parameter $(n, r, \lambda, \mu)$ where $\lambda$ is constant. Here, $n$ is the number of total vertices. Each graph is $r$ regular. Every two adjacent ...
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### What is the best known FPT result for 3-hitting set?

My research problem involves solving a special instance of the 3-Hitting Set problem, and I was wondering whether my result is actually significant (i.e. if it is better than the best known result for ...
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### Petrank's proof for the APX-hardness of MAX k-VERTEX COVER on subcubic graphs

My question is about the following maximization problem, which is the "fixed cardinality" version of MIN VERTEX COVER. I am interested in the restriction to subcubic graphs (i.e. of maximum degree 3). ...
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### Max common sub forest on $k$ graphs

Not sure how to phrase this really, but here goes. Suppose you are given $k$ simple graphs, each having exactly $m$ edges. The edges in each graph are labeled from 1 to $m$. The problem is to find ...
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### About complexity of recovering or learning Bayesian networks

Are there complexity theoretic results about recoverability or learnability of the marginals (of the source vertices) and the conditionals (along each of the edges) of a Bayesian network from having ...
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### Enumerating all (super)orientations of an undirected graph

Given an undirected graph $G$, an orientation of $G$ is a directed graph obtained by assigning every edge a direction, a superorientation of $G$ is a directed graph obtained by orienting every edge in ...
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### Finding a minimum tree which is isomorphic to a subtree of $T_1$ but not to a subtree of $T_2$

Consider the problem that receives two trees $T_1$, $T_2$, and asks to find a minimum size tree $T$ such that there exists a subtree of $T_1$ which is isomorphic to $T$, but there is no such ...
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### How do I describe this (graph-)problem for a research paper?

I have a function f(x, y) which takes two integers and returns a scalar. My task is to find the set of (x, y) pairs, 0<x<W, 0<y<H where f(x, y)>0, which maximize the sum f(x_i, y_i) ...
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### Finding the shortest distance in a dynamic graph

I have a non-weighted directed graph G with edges E and vertices G. Edges can be added or removed, and therefore vertices can be added. For instance, if I have a graph with 4 nodes: 0, 1, 2, 3 and if ...
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### Thresholding technique for Bottleneck Optimization Problems like k-centre, k-suppliers etc

There is a well know thresholding techniques (introduced by Hochbaum and Shmoys in [1]) for bottleneck optimization problems which preprocesses the instance which is a graph whose edges satisfy the ...
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### Efficient all pair bottleneck computation for a tree

Consider a weighted tree $T = (V,E)$. The bottleneck weight for a pair of vertices $v_1,v_2 \in V$ is the highest weight of the edges on the unique path from $v_1$ to $v_2$ (if $v_1 = v_2$ it is 0). ...
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### Optimization of process duration when multiple processes interact

When you have a process composed of multiple steps (e.g., a recipe), where: each step S has a specific duration d(S) steps ...
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### Graph class with easy chromatic number, but NP-hard coloring

Is there a graph class for which the chromatic number can be computed in polynomial time, but finding an actual $k$-coloring with $k=\chi(G)$ is NP-hard? Without any further restriction the answer ...
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### The relationship between degree of vertex and size of dominating set

I was wondering is there any relationship between degree of vertex and size of dominating set. For example, if I know the number of vertices is $n$, and I could know each vertex in the graph has ...
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### Is it possible to find a non-cut vertex in O(|V|) time?

Let $G = (V, E)$ be an undirected connected graph, which is represented by an adjacency list. A vertex is called a cut vertex if removing this vertex with its incident edges from $G$ makes the graph ...
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### Does such model exists?

I have a problem on distributed graph, with the following model: 1. There is a Global Graph $G=(V,E)$ 2. There are $k$ computers. 3. Each computer $1 \leq i \leq k$ knows ALL the nodes of the graph,...
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### Generate connected induced subgraphs as the satisfying assignments to a SAT instance

I want a SAT instance (in CNF) whose set of satisfying assignments are the connected induced subgraphs of a given input graph. A general solution would be helpful, but I really only need this when the ...
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### Efficient algorithm for finding directed cycle with smallest average weight

Suppose we have a strongly connected directed graph with non-negative weights on its edges. Is there an efficient algorithm to find the directed cycle with the smallest average weight in the graph? (...
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