Related papers: Data reduction for directed feedback vertex set on…

We investigate polynomial-time preprocessing for the problem of hitting forbidden minors in a graph, using the framework of kernelization. For a fixed finite set of connected graphs F, the F-Deletion problem is the following: given a graph…

We give a first polynomial-time algorithm for (Weighted) Feedback Vertex Set on graphs of bounded maximum induced matching width (mim-width). Explicitly, given a branch decomposition of mim-width $w$, we give an $n^{\mathcal{O}(w)}$-time…

For microprocessors used in real-time embedded systems, minimizing power consumption is difficult due to the timing constraints. Dynamic voltage scaling (DVS) has been incorporated into modern microprocessors as a promising technique for…

A {\em quasi-kernel} of a digraph $D$ is an independent set $Q\subseteq V(D)$ such that for every vertex $v\in V(D)\backslash Q$, there exists a directed path with one or two arcs from $v$ to a vertex $u\in Q$. In 1974, Chv\'{a}tal and…

We propose to study unweighted graphs of constant distance VC-dimension as a broad generalization of many graph classes for which we can compute the diameter in truly subquadratic-time. In particular for any fixed $H$, the class of…

Graph neural network training is mainly categorized into mini-batch and full-batch training methods. The mini-batch training method samples subgraphs from the original graph in each iteration. This sampling operation introduces extra…

In $d$-Scattered Set we are given an (edge-weighted) graph and are asked to select at least $k$ vertices, so that the distance between any pair is at least $d$, thus generalizing Independent Set. We provide upper and lower bounds on the…

Research of cycles through specific vertices is a central topic in graph theory. In this context, we focus on a well-studied computational problem, \textsc{$T$-Cycle}: given an undirected $n$-vertex graph $G$ and a set of $k$ vertices…

A tournament is a directed graph T such that every pair of vertices are connected by an arc. A feedback vertex set is a set S of vertices in T such that T - S is acyclic. In this article we consider the Feedback Vertex Set problem in…

For the Kautz digraph $K(d,D)$, let $\rho_k(d,D)$ be the number of oriented edges whose shortest directed cycle has length $k+1$, and define $\Delta_k(d,D) = \rho_k(d,D) - \rho_k(d,D-1)$. We give an exact, finite-dimensional matrix product…

Depth first search (DFS) tree is a fundamental data structure for solving graph problems. The classical algorithm [SiComp74] for building a DFS tree requires $O(m+n)$ time for a given graph $G$ having $n$ vertices and $m$ edges. Recently,…

Let fvs$(G)$ and cfvs(G) denote the cardinalities of a minimum feedback vertex set and a minimum connected feedback vertex set of a graph $G$, respectively. The price of connectivity for feedback vertex set (poc-fvs) for a class of graphs…

Let $\mathcal{D}$ be a set of $n$ disks in the plane. The disk graph $G_\mathcal{D}$ for $\mathcal{D}$ is the undirected graph with vertex set $\mathcal{D}$ in which two disks are joined by an edge if and only if they intersect. The…

In this work, we propose an unsupervised method for learning dense correspondences between shapes using a recent deep functional map framework. Instead of depending on ground-truth correspondences or the computationally expensive geodesic…

Let $D$ be a strongly connected oriented graph with vertex-set $V$ and arc-set $A$. The distance from a vertex $u$ to another vertex $v$, $d(u,v)$ is the minimum length of oriented paths from $u$ to $v$. Suppose $B=\{b_1,b_2,b_3,...b_k\}$…

The Strongly Connected Steiner Subgraph (SCSS) problem is a well-studied network design problem that asks for a minimum subgraph that strongly connects a given set of terminals. In this paper, we present several new algorithmic and…

We develop new $(1+\epsilon)$-approximation algorithms for finding the global minimum edge-cut in a directed edge-weighted graph, and for finding the global minimum vertex-cut in a directed vertex-weighted graph. Our algorithms are…

Can neural networks learn to compare graphs without feature engineering? In this paper, we show that it is possible to learn representations for graph similarity with neither domain knowledge nor supervision (i.e.\ feature engineering or…

We study the existence of polynomial kernels, for parameterized problems without a polynomial kernel on general graphs, when restricted to graphs of bounded twin-width. Our main result is that a polynomial kernel for $k$-Dominating Set on…

Vertex deletion to hereditary graph class is well-studied in parameterized complexity. Vertex deletion to the scattered graph classes has gained attention in recent years. In this paper, we consider (Proper-Interval, Tree)-Vertex Deletion,…