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Dynamic Connectivity is a fundamental algorithmic graph problem, motivated by a wide range of applications to social and communication networks and used as a building block in various other algorithms, such as the bi-connectivity and the…
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
Most graphs in real life keep changing with time. These changes can be in the form of insertion or deletion of edges or vertices. Such rapidly changing graphs motivate us to study dynamic graph algorithms. However, three important graph…
In this paper, we introduce a new model for sublinear algorithms called \emph{dynamic sketching}. In this model, the underlying data is partitioned into a large \emph{static} part and a small \emph{dynamic} part and the goal is to compute a…
In the non-uniform sparsest cut problem, we are given a supply graph G and a demand graph D, both with the same set of nodes V. The goal is to find a cut of V that minimizes the ratio of the total capacity on the edges of G crossing the cut…
Highly dynamic networks are characterized by frequent changes in the availability of communication links. These networks are often partitioned into several components, which split and merge unpredictably. We present a distributed algorithm…
In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…
There has been a surge of interest in spectral hypergraph sparsification, a natural generalization of spectral sparsification for graphs. In this paper, we present a simple fully dynamic algorithm for maintaining spectral hypergraph…
Spanning tree modulus is a generalization of effective resistance that is closely related to graph strength and fractional arboricity. The optimal edge density associated with spanning tree modulus is known to produce two hierarchical…
Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general…
As the development of distributed systems progresses, more and more challenges arise and the need for developing optimized systems and for optimizing existing systems from multiple perspectives becomes more stringent. In this paper I…
We study the problem of deleting the smallest set $S$ of vertices (resp. edges) from a given graph $G$ such that the induced subgraph (resp. subgraph) $G \setminus S$ belongs to some class $\mathcal{H}$. We consider the case where graphs in…
The Massively Parallel Computation (MPC) model is an emerging model which distills core aspects of distributed and parallel computation. It has been developed as a tool to solve (typically graph) problems in systems where the input is…
We consider a variant of treewidth that we call clique-partitioned treewidth in which each bag is partitioned into cliques. This is motivated by the recent development of FPT-algorithms based on similar parameters for various problems. With…
Given a query graph that represents a pattern of interest, the emerging pattern detection problem can be viewed as a continuous query problem on a dynamic graph. We present an incremental algorithm for continuous query processing on dynamic…
Recent years have seen extensive research on directed graph sparsification. In this work, we initiate the study of fast fully dynamic spectral and cut sparsification algorithms for directed graphs. We introduce a new notion of spectral…
The classic technique of Baker [J. ACM '94] is the most fundamental approach for designing approximation schemes on planar, or more generally topologically-constrained graphs, and it has been applied in a myriad of different variants and…
Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy…
For a graph $G$, let $\Pi(G)$ denote the set of all potential maximal cliques of $G$. For each subset $\Pi$ of $\Pi(G)$, let $\tw(G, \Pi)$ denote the smallest $k$ such that there is a tree-decomposition of $G$ of width $k$ whose bags all…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…