Related papers: The Fine-Grained Complexity of Boolean Conjunctive…
Is detecting a $k$-clique in $k$-partite regular (hyper-)graphs as hard as in the general case? Intuition suggests yes, but proving this -- especially for hypergraphs -- poses notable challenges. Concretely, we consider a strong notion of…
Given a large data matrix $A\in\mathbb{R}^{n\times n}$, we consider the problem of determining whether its entries are i.i.d. with some known marginal distribution $A_{ij}\sim P_0$, or instead $A$ contains a principal submatrix $A_{{\sf…
In the last decade, algorithmic frameworks based on a structural graph parameter called mim-width have been developed to solve generally NP-hard problems. However, it is known that the frameworks cannot be applied to the Clique problem, and…
Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…
The class of quasi-chain graphs is an extension of the well-studied class of chain graphs. This latter class enjoys many nice and important properties, such as bounded clique-width, implicit representation, well-quasi-ordering by induced…
The hypergraph transversal problem has been intensively studied, from both a theoretical and a practical point of view. In particular , its incremental complexity is known to be quasi-polynomial in general and polynomial for bounded…
We prove that with high probability over the choice of a random graph $G$ from the Erd\H{o}s-R\'enyi distribution $G(n,1/2)$, the $n^{O(d)}$-time degree $d$ Sum-of-Squares semidefinite programming relaxation for the clique problem will give…
We introduce $k$-robust clique complexes, a family of simplicial complexes that generalizes the traditional clique complex. Here, a subset of vertices forms a simplex provided it does not contain an independent set of size $k$. We…
Quasi-cliques are dense incomplete subgraphs of a graph that generalize the notion of cliques. Enumerating quasi-cliques from a graph is a robust way to detect densely connected structures with applications to bio-informatics and social…
We study the problem of approximating the number of $k$-cliques in a graph when given query access to the graph. We consider the standard query model for general graphs via (1) degree queries, (2) neighbor queries and (3) pair queries. Let…
It is well-known that the graph isomorphism problem can be posed as an equivalent problem of determining whether an auxiliary graph structure contains a clique of specific order. However, the algorithms that have been developed so far for…
We investigate computational problems involving large weights through the lens of kernelization, which is a framework of polynomial-time preprocessing aimed at compressing the instance size. Our main focus is the weighted Clique problem,…
We propose a simple, powerful, and flexible machine learning framework for (i) reducing the search space of computationally difficult enumeration variants of subset problems and (ii) augmenting existing state-of-the-art solvers with…
Recently, Daligault, Rao and Thomass\'e asked in [3] if every hereditary class which is well-quasi-ordered by the induced subgraph relation is of bounded clique-width. There are two reasons why this questions is interesting. First, it…
Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…
Automata networks are a versatile model of finite discrete dynamical systems composed of interacting entities (the automata), able to embed any directed graph as a dynamics on its space of configurations (the set of vertices, representing…
We study the deterministic query complexity of Boolean functions on slices of the hypercube. The $k^{th}$ slice $\binom{[n]}{k}$ of the hypercube $\{0,1\}^n$ is the set of all $n$-bit strings with Hamming weight $k$. We show that there…
The subset sum problem is one of the simplest and most fundamental NP-hard problems in combinatorial optimization. We consider two extensions of this problem: The subset sum problem with digraph constraint (SSG) and subset sum problem with…
We study the problem of conjunctive query evaluation relative to a class of queries; this problem is formulated here as the relational homomorphism problem relative to a class of structures A, wherein each instance must be a pair of…
The generic homomorphism problem, which asks whether an input graph $G$ admits a homomorphism into a fixed target graph $H$, has been widely studied in the literature. In this article, we provide a fine-grained complexity classification of…