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We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main…
We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…
We give almost-linear-time algorithms for approximating rooted minimum cut and maximum arborescence packing in directed graphs, two problems that are dual to each other [Edm73]. More specifically, for an $n$-vertex, $m$-edge directed graph…
We consider the maximum vertex-weighted matching problem (MVM), in which non-negative weights are assigned to the vertices of a graph, the weight of a matching is the sum of the weights of the matched vertices, and we are required to…
We study partial and budgeted versions of the well studied connected dominating set problem. In the partial connected dominating set problem, we are given an undirected graph G = (V,E) and an integer n', and the goal is to find a minimum…
A 2-packing set for an undirected graph $G=(V,E)$ is a subset $\mathcal{S} \subset V$ such that any two vertices $v_1,v_2 \in \mathcal{S}$ have no common neighbors. Finding a 2-packing set of maximum cardinality is a NP-hard problem. We…
The 1-median problem (1MP) on undirected weighted graphs seeks to find a facility location minimizing the total weighted distance to all customer nodes. Although the 1MP can be solved exactly by computing the single-source shortest paths…
This paper presents a graph bundling algorithm that agglomerates edges taking into account both spatial proximity as well as user-defined criteria in order to reveal patterns that were not perceivable with previous bundling techniques. Each…
A dominating set of a graph $G=(V,E)$ is a subset of vertices $S\subseteq V$ such that every vertex $v\in V\setminus S$ has at least one neighbor in set $S$. The corresponding optimization problem is known to be NP-hard. The best known…
Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a class of novel Distributed-Approx Newton algorithms that approximate the standard Newton optimization method. We first develop the…
Matching nodes in a graph G = (V, E) is a well-studied algorithmic problem with many applications. The b-matching problem is a generalizati on that allows to match a node with up to b neighbors. This allows more flexible connectivity…
We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…
Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…
A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…
We study the approximability of two related problems on graphs with $n$ nodes and $m$ edges: $n$-Pairs Shortest Paths ($n$-PSP), where the goal is to find a shortest path between $O(n)$ prespecified pairs, and All Node Shortest Cycles…
In the graph label selection problem, one is given an $n$-vertex graph and a budget $k$, and seeks to select $k$ vertices whose labels enable accurate prediction of the labels on the remaining vertices. This problem formalizes distilling a…
We consider the problem of embedding unweighted, directed k-nearest neighbor graphs in low-dimensional Euclidean space. The k-nearest neighbors of each vertex provides ordinal information on the distances between points, but not the…
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…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…