Related papers: Hardness of Token Swapping on Trees
Many popular algorithms for searching the space of leaf-labelled trees are based on tree rearrangement operations. Under any such operation, the problem is reduced to searching a graph where vertices are trees and (undirected) edges are…
Let $G$ be a complete edge-weighted graph on $n$ vertices. To each subset of vertices of $G$ assign the cost of the minimum spanning tree of the subset as its weight. Suppose that $n$ is a multiple of some fixed positive integer $k$. The…
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…
Minimum Spanning Tree (MST) is an important graph algorithm that has wide ranging applications in the areas of computer networks, VLSI routing, wireless communications among others. Today virtually every computer is built out of multi-core…
Message passing-based graph neural networks (GNNs) have achieved great success in many real-world applications. For a sampled mini-batch of target nodes, the message passing process is divided into two parts: message passing between nodes…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
In comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance, that is, the minimum number of transpositions needed to transform a genome into another, is,…
In recent years many algorithms have been developed for finding patterns in graphs and networks. A disadvantage of these algorithms is that they use subgraph isomorphism to determine the support of a graph pattern; subgraph isomorphism is a…
Pedigree graphs, or family trees, are typically constructed by an expensive process of examining genealogical records to determine which pairs of individuals are parent and child. New methods to automate this process take as input genetic…
We consider discrete, iterative load balancing via matchings on arbitrary graphs. Initially each node holds a certain number of tokens, defining the load of the node, and the objective is to redistribute the tokens such that eventually each…
Let $G$ be a planar graph and $I_s$ and $I_t$ be two independent sets in $G$, each of size $k$. We begin with a "token" on each vertex of $I_s$ and seek to move all tokens to $I_t$, by repeated "token jumping", removing a single token from…
Vertex splitting is a graph modification operation in which a vertex is replaced by multiple vertices such that the union of their neighborhoods equals the neighborhood of the original vertex. We introduce and study vertex splitting as a…
In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several…
Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs…
We consider the $k$-prize-collecting Steiner tree problem. An instance is composed of an integer $k$ and a graph $G$ with costs on edges and penalties on vertices. The objective is to find a tree spanning at least $k$ vertices which…
A central problem in graph mining is finding dense subgraphs, with several applications in different fields, a notable example being identifying communities. While a lot of effort has been put on the problem of finding a single dense…
Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete…
We consider the problem of finding a subgraph of a given graph which maximizes a given function evaluated at its degree sequence. While the problem is intractable already for convex functions, we show that it can be solved in polynomial…
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…
A forbidden transition graph is a graph defined together with a set of permitted transitions i.e. unordered pair of adjacent edges that one may use consecutively in a walk in the graph. In this paper, we look for the smallest set of…