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The goal of the thesis is to leverage fast graph algorithms and modern algorithmic techniques for problems in model checking and synthesis on graphs, MDPs, and game graphs. The results include symbolic algorithms, a well-known class of…
Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
We propose a consistent polynomial-time method for the unseeded node matching problem for networks with smooth underlying structures. Despite widely conjectured by the research community that the structured graph matching problem to be…
The graph alignment problem, which considers the optimal node correspondence across networks, has recently gained significant attention due to its wide applications. There are graph alignment methods suited for various network types, but we…
Matching, a task to optimally assign limited resources under constraints, is a fundamental technology for society. The task potentially has various objectives, conditions, and constraints; however, the efficient neural network architecture…
It is known that a better than $2$-approximation algorithm for the girth in dense directed unweighted graphs needs $n^{3-o(1)}$ time unless one uses fast matrix multiplication. Meanwhile, the best known approximation factor for a…
We present a $(1- \varepsilon)$-approximation algorithms for maximum cardinality matchings in disk intersection graphs -- all with near linear running time. We also present estimation algorithm that returns $(1\pm…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for…
We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with…
In this letter, we propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix under the assumption that the observed signals vary smoothly over the nodes of the graph. The proposed algorithm is based on the…
Graph pattern matching, which aims to discover structural patterns in graphs, is considered one of the most fundamental graph mining problems in many real applications. Despite previous efforts, existing systems face two main challenges.…
We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex. For two Erd\H{o}s-R\'enyi graphs $\mathcal{G}(n,q)$ whose edges are…
In the distributed backup-placement problem each node of a network has to select one neighbor, such that the maximum number of nodes that make the same selection is minimized. This is a natural relaxation of the perfect matching problem, in…
Hypergraphs are generalisation of graphs in which a hyperedge can connect any number of vertices. It can describe n-ary relationships and high-order information among entities compared to conventional graphs. In this paper, we study the…
Given a bipartite graph, the maximum balanced biclique (\textsf{MBB}) problem, discovering a mutually connected while equal-sized disjoint sets with the maximum cardinality, plays a significant role for mining the bipartite graph and has…
Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…
We present a novel approach for finding multiple noisily embedded template graphs in a very large background graph. Our method builds upon the graph-matching-matched-filter technique proposed in Sussman et al., with the discovery of…
Near ubiquitous mobile computing has led to intense interest in dynamic graph theory. This provides a new and challenging setting for algorithmics and complexity theory. For any graph-based problem, the rapid evolution of a (possibly…