Related papers: Flow-Based Algorithms for Local Graph Clustering
We introduce a new approach to computing an approximately maximum s-t flow in a capacitated, undirected graph. This flow is computed by solving a sequence of electrical flow problems. Each electrical flow is given by the solution of a…
Hypergraph-based machine learning methods are now widely recognized as important for modeling and using higher-order and multiway relationships between data objects. Local hypergraph clustering and semi-supervised learning specifically…
Given a graph $G=(V,E)$ with two distinguished vertices $s,t\in V$ and an integer parameter $L>0$, an {\em $L$-bounded cut} is a subset $F$ of edges (vertices) such that the every path between $s$ and $t$ in $G\setminus F$ has length more…
We present an $\tilde{O}\left(m^{\frac{10}{7}}U^{\frac{1}{7}}\right)$-time algorithm for the maximum $s$-$t$ flow problem and the minimum $s$-$t$ cut problem in directed graphs with $m$ arcs and largest integer capacity $U$. This matches…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
Given a directed graph $G$, a transitive reduction $G^t$ of $G$ (first studied by Aho, Garey, Ullman [SICOMP `72]) is a minimal subgraph of $G$ that preserves the reachability relation between every two vertices in $G$. In this paper, we…
Local clustering aims at extracting a local structure inside a graph without the necessity of knowing the entire graph structure. As the local structure is usually small in size compared to the entire graph, one can think of it as a…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to compute some global structural feature of the graph. Such algorithms use only local information available at nodes to determine local aspects of the…
We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…
Finding sparse cuts is an important tool in analyzing large-scale distributed networks such as the Internet and Peer-to-Peer networks, as well as large-scale graphs such as the web graph, online social communities, and VLSI circuits. In…
Finding locally optimal solutions for max-cut and max-$k$-cut are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in…
Given a graph $G$ of degree $k$ over $n$ vertices, we consider the problem of computing a near maximum cut or a near minimum bisection in polynomial time. For graphs of girth $2L$, we develop a local message passing algorithm whose…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
While in many graph mining applications it is crucial to handle a stream of updates efficiently in terms of {\em both} time and space, not much was known about achieving such type of algorithm. In this paper we study this issue for a…
This paper presents a unified analysis framework that captures recent advances in the study of local-optimality characterizations for codes on graphs. These local-optimality characterizations are based on combinatorial structures embedded…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…
We investigate the locality number, a recently introduced structural parameter for strings (with applications in pattern matching with variables), and its connection to two important graph-parameters, cutwidth and pathwidth. These…
Recently, Brandt et al. [STOC'16] proved a lower bound for the distributed Lov\'asz Local Lemma, which has been conjectured to be tight for sufficiently relaxed LLL criteria by Chang and Pettie [FOCS'17]. At the heart of their result lies a…
Graph based semi-supervised learning is the problem of learning a labeling function for the graph nodes given a few example nodes, often called seeds, usually under the assumption that the graph's edges indicate similarity of labels. This…