Related papers: Arboricity, h-Index, and Dynamic Algorithms

For any particular class of graphs, algorithms for computational problems restricted to the class often rely on structural properties that depend on the specific problem at hand. This begs the question if a large set of such results can be…

Homogeneous matroids are characterized by the property that strength equals fractional arboricity, and arise in the study of base modulus [22]. For graphic matroids, Cunningham [9] provided efficient algorithms for calculating graph…

A tree-packing is a collection of spanning trees of a graph. It has been a useful tool for computing the minimum cut in static, dynamic, and distributed settings. In particular, [Thorup, Comb. 2007] used them to obtain his dynamic min-cut…

We study homomorphism polynomials, which are polynomials that enumerate all homomorphisms from a pattern graph $H$ to $n$-vertex graphs. These polynomials have received a lot of attention recently for their crucial role in several new…

Graphs have been widely used in many applications such as social networks, collaboration networks, and biological networks. One important graph analytics is to explore cohesive subgraphs in a large graph. Among several cohesive subgraphs…

A bipartite graph is chordal bipartite if every cycle of length at least six has a chord in it. M$\ddot{\rm u}$ller \cite {muller1996Hamiltonian} has shown that the Hamiltonian cycle problem is NP-complete on chordal bipartite graphs by…

In this paper we consider the fundamental problem of finding subgraphs in highly dynamic distributed networks - networks which allow an arbitrary number of links to be inserted / deleted per round. We show that the problems of $k$-clique…

The \emph{linear vertex arboricity} of a graph is the smallest number of sets into which the vertices of a graph can be partitioned so that each of these sets induces a linear forest. Chaplick et al. [JoCG 2020] showed that, somewhat…

We develop a framework for applying treewidth-based dynamic programming on graphs with "hybrid structure", i.e., with parts that may not have small treewidth but instead possess other structural properties. Informally, this is achieved by…

Fully dynamic graph algorithms that achieve polylogarithmic or better time per operation use either a hierarchical graph decomposition or random-rank based approach. There are so far two graph properties for which efficient algorithms for…

For any finite set $\mathcal{H} = \{H_1,\ldots,H_p\}$ of graphs, a graph is $\mathcal{H}$-subgraph-free if it does not contain any of $H_1,\ldots,H_p$ as a subgraph. In recent work, meta-classifications have been studied: these show that if…

This paper presents a comprehensive study of algorithms for maintaining the number of all connected four-vertex subgraphs in a dynamic graph. Specifically, our algorithms maintain the number of paths of length three in deterministic…

Searching for high-dimensional vector data with high accuracy is an inevitable search technology for various types of data. Graph-based indexes are known to reduce the query time for high-dimensional data. To further improve the query time…

The study of structural graph width parameters like tree-width, clique-width and rank-width has been ongoing during the last five decades, and their algorithmic use has also been increasing [Cygan et al., 2015]. New width parameters…

To train good supervised and semi-supervised object classifiers, it is critical that we not waste the time of the human experts who are providing the training labels. Existing active learning strategies can have uneven performance, being…

We identify a sufficient condition, treewidth-pliability, that gives a polynomial-time algorithm for an arbitrarily good approximation of the optimal value in a large class of Max-2-CSPs parameterised by the class of allowed constraint…

The arboricity $\Gamma$ of a graph is the minimum number of forests its edge set can be partitioned into. Previous approximation schemes were nonconstructive, i.e., they only approximated the arboricity as a value without computing a…

Timeslices are often used to draw and visualize dynamic graphs. While timeslices are a natural way to think about dynamic graphs, they are routinely imposed on continuous data. Often, it is unclear how many timeslices to select: too few…

Many different classification tasks need to manage structured data, which are usually modeled as graphs. Moreover, these graphs can be dynamic, meaning that the vertices/edges of each graph may change during time. Our goal is to jointly…

The Subgraph Isomorphism problem is of considerable importance in computer science. We examine the problem when the pattern graph H is of bounded treewidth, as occurs in a variety of applications. This problem has a well-known algorithm via…