相关论文: Arboricity, h-Index, and Dynamic Algorithms

We show two results related to the Hamiltonicity and $k$-Path algorithms in undirected graphs by Bj\"orklund [FOCS'10], and Bj\"orklund et al., [arXiv'10]. First, we demonstrate that the technique used can be generalized to finding some…

Hyperbolicity is a graph parameter related to how much a graph resembles a tree with respect to distances. Its computation is challenging as the main approaches consist in scanning all quadruples of the graph or using fast matrix…

We introduce the class of interval $H$-graphs, which is the generalization of interval graphs, particularly interval bigraphs. For a fixed graph $H$ with vertices $a_1,a_2,\dots,a_k$, we say that an input graph $G$ with given partition…

Graph algorithms applied in many applications, including social networks, communication networks, VLSI design, graphics, and several others, require dynamic modifications -- addition and removal of vertices and/or edges -- in the graph.…

We present a polynomial-time algorithm for the cluster vertex deletion problem on chordal graphs, resolving an open question posed in different contexts by Cao et al. [Theoretical Computer Science, 2018], Aprile et al. [Mathematical…

We present a framework for dynamically maintaining $k$-edge-connectivity of an undirected simple graph $G$ under edge insertions and deletions, where $k$ is a fixed constant. After an edge insertion, the algorithm identifies and removes a…

The notion of directed treewidth was introduced by Johnson, Robertson, Seymour and Thomas [Journal of Combinatorial Theory, Series B, Vol 82, 2001] as a first step towards an algorithmic metatheory for digraphs. They showed that some…

In this paper, the dynamics of heuristic algorithms for constructing small vertex covers (or independent sets) of finite-connectivity random graphs is analysed. In every algorithmic step, a vertex is chosen with respect to its vertex…

Identifying dense bipartite subgraphs is a common graph data mining task. Many applications focus on the enumeration of all maximal bicliques (MBs), though sometimes the stricter variant of maximal induced bicliques (MIBs) is of interest.…

We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…

Predicting the nodes of a given graph is a fascinating theoretical problem with applications in several domains. Since graph sparsification via spanning trees retains enough information while making the task much easier, trees are an…

We investigate a relaxation of the notion of fractional treewidth-fragility, namely fractional tree-independence-number-fragility. In particular, we obtain polynomial-time approximation schemes for meta-problems such as finding a…

Let H be a connected bipartite graph with n nodes and m edges. We give an O(nm) time algorithm to decide whether H is an interval bigraph. The best known algorithm has time complexity O(nm^6(m + n) \log n) and it was developed in 1997 [18].…

We consider the task of estimating a high-dimensional directed acyclic graph, given observations from a linear structural equation model with arbitrary noise distribution. By exploiting properties of common random graphs, we develop a new…

This study introduces a new metric called ''DynamicScore'' to evaluate the dynamics of graphs. It can be applied to both vertices and edges. Unlike traditional metrics, DynamicScore not only measures changes in the number of vertices or…

The Havel-Hakimi algorithm iteratively reduces the degree sequence of a graph to a list of zeroes. As shown by Favaron, Mah\'eo, and Sacl\'e, the number of zeroes produced, known as the residue, is a lower bound on the independence number…

Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network…

In the deletion version of the list homomorphism problem, we are given graphs G and H, a list L(v) that is a subset of V(H) for each vertex v of G, and an integer k. The task is to decide whether there exists a subset W of V(G) of size at…

In this paper we propose a new method called ND-Tree-based update (or shortly ND-Tree) for the dynamic non-dominance problem, i.e. the problem of online update of a Pareto archive composed of mutually non-dominated points. It uses a new…

In this work, we introduce TreeWidzard, an engine for developing dynamic programming algorithms that decide graph-theoretic properties parameterized by treewidth and pathwidth. Besides providing a unified framework for algorithms deciding…