Related papers: Worst-Case and Average-Case Hardness of Hypercycle…
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…
In recent years it has become popular to study dynamic problems in a sensitivity setting: Instead of allowing for an arbitrary sequence of updates, the sensitivity model only allows to apply batch updates of small size to the original input…
A large number of applications such as querying sensor networks, and analyzing protein-protein interaction (PPI) networks, rely on mining uncertain graph and hypergraph databases. In this work we study the following problem: given an…
Computing a dense subgraph is a fundamental problem in graph mining, with a diverse set of applications ranging from electronic commerce to community detection in social networks. In many of these applications, the underlying context is…
In recent years, the expander decomposition method was used to develop many graph algorithms, resulting in major improvements to longstanding complexity barriers. This powerful hammer has led the community to (1) believe that most problems…
Hypergraph is a data structure that enables us to model higher-order associations among data entities. Conventional graph-structured data can represent pairwise relationships only, whereas hypergraph enables us to associate any number of…
We present a new technique for efficiently removing almost all short cycles in a graph without unintentionally removing its triangles. Consequently, triangle finding problems do not become easy even in almost $k$-cycle free graphs, for any…
We consider the problem of counting $k$-cliques in $s$-uniform Erdos-Renyi hypergraphs $G(n,c,s)$ with edge density $c$, and show that its fine-grained average-case complexity can be based on its worst-case complexity. We prove the…
We consider two extremal problems for set systems without long Berge cycles. First we give Dirac-type minimum degree conditions that force long Berge cycles. Next we give an upper bound for the number of hyperedges in a hypergraph with…
We propose a unifying framework for the automated computer-assisted worst-case analysis of cyclic block coordinate algorithms in the unconstrained smooth convex optimization setup. We compute exact worst-case bounds for the cyclic…
We prove tight bounds on the site percolation threshold for $k$-uniform hypergraphs of maximum degree $\Delta$ and for $k$-uniform hypergraphs of maximum degree $\Delta$ in which any pair of edges overlaps in at most $r$ vertices. The…
In this paper we focus on the problem of finding (small) subhypergraphs in a (large) hypergraph. We use this problem to illustrate that reducing hypergraph problems to graph problems by working with the 2-section is not always a reasonable…
A drawback of the classic approach for complexity analysis of distributed graph problems is that it mostly informs about the complexity of notorious classes of ``worst case'' graphs. Algorithms that are used to prove a tight (existential)…
In this thesis, we design algorithms for several NP-hard problems in both worst and beyond worst case settings. In the first part of the thesis, we apply the traditional worst case methodology and design approximation algorithms for the Hub…
This work addresses the well-known Maximum Independent Set problem in the context of hypergraphs. While this problem has been extensively studied on graphs, we focus on its strong extension to hypergraphs, where edges may connect any number…
MapReduce (and its open source implementation Hadoop) has become the de facto platform for processing large data sets. MapReduce offers a streamlined computational framework by interleaving sequential and parallel computation while hiding…
The problem of finding the longest simple cycle in a directed graph is NP-hard, with critical applications in computational biology, scheduling, and network analysis. Existing approaches include exact algorithms with exponential runtimes,…
Studying the computational complexity of problems is one of the - if not the - fundamental questions in computer science. Yet, surprisingly little is known about the computational complexity of many central problems in data mining. In this…
Worst-case to average-case reductions are a cornerstone of complexity theory, providing a bridge between worst-case hardness and average-case computational difficulty. While recent works have demonstrated such reductions for fundamental…
Subgraph detection has recently been one of the most studied problems in the CONGEST model of distributed computing. In this work, we study the distributed complexity of problems closely related to subgraph detection, mainly focusing on…