Related papers: Simple Counting and Sampling Algorithms for Graphs…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
Online social network services provide a platform for human social interactions. Nowadays, many kinds of online interactions generate large-scale social network data. Network analysis helps to mine knowledge and pattern from the…
{\sc Vertex $(s, t)$-Cut} and {\sc Vertex Multiway Cut} are two fundamental graph separation problems in algorithmic graph theory. We study matroidal generalizations of these problems, where in addition to the usual input, we are given a…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
We study the design of sampling trajectories for stable sampling and the reconstruction of bandlimited spatial fields using mobile sensors. The spectrum is assumed to be a symmetric convex set. As a performance metric we use the path…
Triangle counting and sampling are two fundamental problems for streaming algorithms. Arguably, designing sampling algorithms is more challenging than their counting variants. It may be noted that triangle counting has received far greater…
We study the well-established problem of finding an optimal routing of unsplittable flows in a graph. While by now there is an extensive body of work targeting the problem on graph classes such as paths and trees, we aim at using the…
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…
Scatterplot selection is an effective approach to represent essential portions of multidimensional data in a limited display space. Various metrics for evaluation of scatterplots such as scagnostics have been presented and applied to…
We study the problem of sampling a uniformly random directed rooted spanning tree, also known as an arborescence, from a possibly weighted directed graph. Classically, this problem has long been known to be polynomial-time solvable; the…
We study the weighted improper coloring problem, a generalization of defective coloring. We present some hardness results and in particular we show that weighted improper coloring is not fixed-parameter tractable when parameterized by…
Although it has been claimed in two different papers that the maximum cardinality cut problem is polynomial-time solvable for proper interval graphs, both of them turned out to be erroneous. In this paper, we give FPT algorithms for the…
In Path Set Packing, the input is an undirected graph $G$, a collection $\calp$ of simple paths in $G$, and a positive integer $k$. The problem is to decide whether there exist $k$ edge-disjoint paths in $\calp$. We study the parameterized…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications…
A central theme in sublinear graph algorithms is the relationship between counting and sampling: can the ability to approximately count a combinatorial structure be leveraged to sample it nearly uniformly at essentially the same cost? We…
We study a generalization of the classic Spanning Tree problem that allows for a non-uniform failure model. More precisely, edges are either \emph{safe} or \emph{unsafe} and we assume that failures only affect unsafe edges. In Unweighted…
In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…
The splitting number of a graph $G=(V,E)$ is the minimum number of vertex splits required to turn $G$ into a planar graph, where a vertex split removes a vertex $v \in V$, introduces two new vertices $v_1, v_2$, and distributes the edges…
A mixed dominating set is a collection of vertices and edges that dominates all vertices and edges of a graph. We study the complexity of exact and parameterized algorithms for \textsc{Mixed Dominating Set}, resolving some open questions.…