相关论文: Augmenting graphs to minimize the diameter
We study the problem of finding a minimum-distortion embedding of the shortest path metric of an unweighted graph into a "simpler" metric $X$. Computing such an embedding (exactly or approximately) is a non-trivial task even when $X$ is the…
We consider network design problems in which we are given a graph and seek a min-size $2$-connected subgraph that satisfies a prescribed property. $\bullet$ In the 1-Connectivity Augmentation problem the goal is to augment a connected graph…
We study the problem of searching for a hidden target in an environment that is modeled by an edge-weighted graph. A sequence of edges is chosen starting from a given root vertex such that each edge is adjacent to a previously chosen edge.…
A linear arrangement (LA) is an assignment of distinct integers to the vertices of a graph. The cost of an LA is the sum of lengths of the edges of the graph, where the length of an edge is defined as the absolute value of the difference of…
We present a parameterized dichotomy for the \textsc{$k$-Sparsest Cut} problem in weighted and unweighted versions. In particular, we show that the weighted \textsc{$k$-Sparsest Cut} problem is NP-hard for every $k\geq 3$ even on graphs…
We investigate problems addressing combined connectivity augmentation and orientations settings. We give a polynomial-time 6-approximation algorithm for finding a minimum cost subgraph of an undirected graph $G$ that admits an orientation…
One of the first application of the recently introduced technique of \emph{flow-augmentation} [Kim et al., STOC 2022] is a fixed-parameter algorithm for the weighted version of \textsc{Directed Feedback Vertex Set}, a landmark problem in…
The paper considers the NP-hard graph vertex coloring problem, which differs from traditional problems in which it is required to color vertices with a given (or minimal) number of colors so that adjacent vertices have different colors. In…
Motivated by the landmark resolution of the 1-2-3 Conjecture, we initiate the study of the parameterized complexity of the Vertex-Coloring {0,1}-Edge-Weighting problem and its generalization, Vertex-Coloring Pre-edge-Weighting, under…
The problems of computing eccentricity, radius, and diameter are fundamental to graph theory. These parameters are intrinsically defined based on the distance metric of the graph. In this work, we propose quantum algorithms for the diameter…
The girth of a graph is the length of its shortest cycle. Due to its relevance in graph theory, network analysis and practical fields such as distributed computing, girth-related problems have been object of attention in both past and…
Graph pattern matching is a fundamental problem encountered by many common graph mining tasks and the basic building block of several graph mining systems. This paper explores for the first time how to proactively prune graphs to speed up…
In this paper we consider the fundamental problem of approximating the diameter $D$ of directed or undirected graphs. In a seminal paper, Aingworth, Chekuri, Indyk and Motwani [SIAM J. Comput. 1999] presented an algorithm that computes in…
We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence, where the aim is to obtain a graph with a given degree sequence \sigma by at most k vertex or edge deletions…
Graph modification problems, which aim to find a small set of modifications to a graph so that it satisfies a desired property, have been studied for several special graph classes. The literature is rather rich in NP-completeness results…
In this paper, we study two examples of minimum weight random graphs with edge constraints. First we consider the complete graph on ${n}$ vertices equipped with uniformly heavy edge weights and use iteration methods to obtain deviation…
We study {\sc Cluster Edge Modification} problems with constraints on the size of the clusters. A graph $G$ is a cluster graph if every connected component of $G$ is a clique. In a typical {\sc Cluster Edge Modification} problem such as the…
Let G=(V,E) be a graph with f:V\to Z_+ a function assigning degree bounds to vertices. We present the first efficient algebraic algorithm to find an f-factor. The time is \tilde{O}(f(V)^{\omega}). More generally for graphs with integral…
Data augmentation plays a critical role in improving model performance across various domains, but it becomes challenging with graph data due to their complex and irregular structure. To address this issue, we propose EPIC (Edit Path…
A minimum dominating set in a graph is a minimum set of vertices such that every vertex of the graph either belongs to it, or is adjacent to one vertex of this set. This mathematical object is of high relevance in a number of applications…