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We consider the communication complexity of finding an approximate maximum matching in a graph in a multi-party message-passing communication model. The maximum matching problem is one of the most fundamental graph combinatorial problems,…
Edge-Geodetic Sets play a crucial role in network monitoring and optimization, wherein the goal is to strategically place monitoring stations on vertices of a network, represented as a graph, to ensure complete coverage of edges and…
We design and mathematically analyze sampling-based algorithms for regularized loss minimization problems that are implementable in popular computational models for large data, in which the access to the data is restricted in some way. Our…
In 1985, Chv\'{a}tal introduced the concept of star cutsets as a means to investigate the properties of perfect graphs, which inspired many researchers to study cutsets with some specific structures, for example, star cutsets, clique…
We consider the problem of clustering graph nodes over large-scale dynamic graphs, such as citation networks, images and web networks, when graph updates such as node/edge insertions/deletions are observed distributively. We propose…
In this thesis, we present new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions: - Single-Source Reachability…
We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…
To solve the combinatorial optimization problems especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of…
We study fundamental graph problems such as graph connectivity, minimum spanning forest (MSF), and approximate maximum (weight) matching in a distributed setting. In particular, we focus on the Adaptive Massively Parallel Computation (AMPC)…
We investigate graph problems in the following setting: we are given a graph $G$ and we are required to solve a problem on $G^2$. While we focus mostly on exploring this theme in the distributed CONGEST model, we show new results and…
In this paper we consider graph algorithms in models of computation where the space usage (random accessible storage, in addition to the read only input) is sublinear in the number of edges $m$ and the access to input data is constrained.…
Significant research effort has been devoted to improving the performance of join processing in the massively parallel computation model, where the goal is to evaluate a query with the minimum possible data transfer between machines.…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…
Subtrajectory clustering is an important variant of the trajectory clustering problem, where the start and endpoints of trajectory patterns within the collected trajectory data are not known in advance. We study this problem in the form of…
Max-k-Cut and correlation clustering are fundamental graph partitioning problems. For a graph with G=(V,E) with n vertices, the methods with the best approximation guarantees for Max-k-Cut and the Max-Agree variant of correlation clustering…
Communication and topology aware process mapping is a powerful approach to reduce communication time in parallel applications with known communication patterns on large, distributed memory systems. We address the problem as a quadratic…
We present $O(\log\log n)$-round algorithms in the Massively Parallel Computation (MPC) model, with $\tilde{O}(n)$ memory per machine, that compute a maximal independent set, a $1+\epsilon$ approximation of maximum matching, and a…
We present a general framework of designing efficient dynamic approximate algorithms for optimization on undirected graphs. In particular, we develop a technique that, given any problem that admits a certain notion of vertex sparsifiers,…
We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing…
In our paper, we consider the following general problems: check feasibility, count the number of feasible solutions, find an optimal solution, and count the number of optimal solutions in $P \cap Z^n$, assuming that $P$ is a polyhedron,…