Related papers: Subgraph Enumeration in Massive Graphs
We study the parameterized complexity of the Cograph Deletion problem, which asks whether one can delete at most $k$ edges from a graph to make it $P_4$-free. This is a well-known graph modification problem with applications in computation…
To understand the structure of a network, it can be useful to break it down into its constituent pieces. This is the approach taken in a multitude of successful network analysis methods, such as motif analysis. These methods require one to…
There are many methods to find a maximum (or maximal) clique in large networks. Due to the nature of combinatorics, computation becomes exponentially expensive as the number of vertices in a graph increases. Thus, there is a need for…
We initiate the study of computational problems on $k$-mers (strings of length $k$) in labeled graphs. As a starting point, we consider the problem of counting the number of distinct $k$-mers found on the walks of a graph. We establish that…
Cutwidth is one of the classic layout parameters for graphs. It measures how well one can order the vertices of a graph in a linear manner, so that the maximum number of edges between any prefix and its complement suffix is minimized. As…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
We study deterministic algorithms for computing graph cuts, with focus on two fundamental problems: balanced sparse cut and $k$-vertex connectivity for small $k$ ($k=O(\polylog n)$). Both problems can be solved in near-linear time with…
Subexponential parameterized algorithms are known for a wide range of natural problems on planar graphs, but the techniques are usually highly problem specific. The goal of this paper is to introduce a framework for obtaining…
Motivated by applications in network epidemiology, we consider the problem of determining whether it is possible to delete at most $k$ edges from a given input graph (of small treewidth) so that the resulting graph avoids a set…
We show that the VC-dimension of a graph can be computed in time $n^{\log d+1} d^{O(d)}$, where $d$ is the degeneracy of the input graph. The core idea of our algorithm is a data structure to efficiently query the number of vertices that…
The maximal clique enumeration (MCE) problem has numerous applications in biology, chemistry, sociology, and graph modeling. Though this problem is well studied, most current research focuses on finding solutions in large sparse graphs or…
In an $m$-edge host graph $G$, all triangles can be listed in time $O(m^{1.5})$ [Itai, Rodeh '78], and all $k$-cycles can be listed in time $O(m^{2-1/{\lceil k/2 \rceil}} + t)$ where $t$ is the output size [Alon, Yuster, Zwick '97]. These…
This paper is about: (1) bounds on the number of cliques in a graph in a particular class, and (2) algorithms for listing all cliques in a graph. We present a simple algorithm that lists all cliques in an $n$-vertex graph in O(n) time per…
In a finite undirected simple graph, a {\it chordless cycle} is an induced subgraph which is a cycle. We propose two algorithms to enumerate all chordless cycles of such a graph. Compared to other similar algorithms, the proposed algorithms…
We consider the maximum matching problem in the semi-streaming model formalized by Feigenbaum, Kannan, McGregor, Suri, and Zhang that is inspired by giant graphs of today. As our main result, we give a two-pass $(1/2 + 1/16)$-approximation…
In the graph stream model of computation, an algorithm processes the edges of an input graph in one or more sequential passes while using a memory sublinear in the input size. This model poses significant challenges for constructing long…
We study the problem of finding and monitoring fixed-size subgraphs in a continually changing large-scale graph. We present the first approach that (i) performs worst-case optimal computation and communication, (ii) maintains a total memory…
Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation graphs…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
A solution to a problem of Erd\H{o}s, Rubin and Taylor is obtained by showing that if a graph $G$ is $(a:b)$-choosable, and $c/d > a/b$, then $G$ is not necessarily $(c:d)$-choosable. The simplest case of another problem, stated by the same…