Related papers: Distributed Reductions for the Maximum Weight Inde…
Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For $n$-vertex and $m$-edge graphs, the best known algorithms run in…
There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even…
The problem of finding the densest subgraph in a given graph has several applications in graph mining, particularly in areas like social network analysis, protein and gene analyses etc. Depending on the application, finding dense subgraphs…
The Generalized Independent Set (GIS) problem extends the classical maximum independent set problem by incorporating profits for vertices and penalties for edges. This generalized problem has been identified in diverse applications in…
We study stochastic graph optimization problems in a novel distributed setting. As in the standard centralized setting, a random subgraph $G^*$ of a known base graph $G$ is realized by including each edge $e$ independently with a known…
Finding a maximum-weight matching is a classical and well-studied problem in computer science, solvable in cubic time in general graphs. We consider the specialization called assignment problem where the input is a bipartite graph, and…
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…
One of the biggest huddles faced by researchers studying algorithms for massive graphs is the lack of large input graphs that are essential for the development and test of the graph algorithms. This paper proposes two efficient and highly…
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…
On an evolving graph that is continuously updated by a high-velocity stream of edges, how can one efficiently maintain if two vertices are connected? This is the connectivity problem, a fundamental and widely studied problem on graphs. We…
Many real-world systems, such as social networks, rely on mining efficiently large graphs, with hundreds of millions of vertices and edges. This volume of information requires partitioning the graph across multiple nodes in a distributed…
Distributed optimization for resource allocation problems is investigated and a sub-optimal continuous-time algorithm is proposed. Our algorithm has lower order dynamics than others to reduce burdens of computation and communication, and is…
The (\textsc{Weighted}) \textsc{Subset Feedback Vertex Set} problem is a generalization of the classical \textsc{Feedback Vertex Set} problem and asks for a vertex set of minimum (weighted) size that intersects all cycles containing a…
We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks. The method exhibits a roughly linear runtime scaling over real-world networks…
Maximal Clique Enumeration (MCE) is a fundamental graph mining problem, and is useful as a primitive in identifying dense structures in a graph. Due to the high computational cost of MCE, parallel methods are imperative for dealing with…
Distributed systems that manage and process graph-structured data internally solve a graph partitioning problem to minimize their communication overhead and query run-time. Besides computational complexity -- optimal graph partitioning is…
The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in…
This paper presents a fast and simple new 2-approximation algorithm for minimum weighted vertex cover. The unweighted version of this algorithm is equivalent to a well-known greedy maximal independent set algorithm. We prove that this…
Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…
In algorithmic graph theory, a classic open question is to determine the complexity of the Maximum Independent Set problem on $P_t$-free graphs, that is, on graphs not containing any induced path on $t$ vertices. So far, polynomial-time…