离散数学
The Grundy number of a graph is the maximum number of colours used by the "First-Fit" greedy colouring algorithm over all vertex orderings. Given a vertex ordering $\sigma= v_1,\dots,v_n$, the "First-Fit" greedy colouring algorithm colours…
The concept of d-separation holds a pivotal role in causality theory, serving as a fundamental tool for deriving conditional independence properties from causal graphs. Pearl defined the d-separation of two subsets conditionally on a third…
We enumerate several classes of pattern-avoiding rectangulations. We establish new bijective links with pattern-avoiding permutations, prove that their generating functions are algebraic, and confirm several conjectures by Merino and…
Identification of attractors, that is, stable states and sustained oscillations, is an important step in the analysis of Boolean models and exploration of potential variants. We describe an approach to the search for asynchronous cyclic…
Graph labeling is a technique that assigns unique labels or weights to the vertices or edges of a graph, often used to analyze and solve various graph-related problems. There are few methods with certain limitations conducted by researchers…
To simplify the analysis of Boolean networks, a reduction in the number of components is often considered. A popular reduction method consists in eliminating components that are not autoregulated, using variable substitution. In this work,…
Our goal in this paper is the robust design of filters acting on signals observed over graphs subject to small perturbations of their edges. The focus is on developing a method to identify spectral and polynomial graph filters that can…
The Maximum Common Subgraph (MCS) problem plays a crucial role across various domains, bridging theoretical exploration and practical applications in fields like bioinformatics and social network analysis. Despite its wide applicability,…
We propose an algebraic model of computation which formally relates symbolic listings, complexity of Boolean functions, and low depth arithmetic circuit complexity. In this model algorithms are arithmetic formula expressing symbolic…
We study a natural generalization of the classical $\epsilon$-net problem (Haussler--Welzl 1987), which we call the "$\epsilon$-$t$-net problem": Given a hypergraph on $n$ vertices and parameters $t$ and $\epsilon\geq \frac t n$, find a…
We explore the Ziv-Lempel and Crochemore factorizations of some classical automatic sequences making an extensive use of the theorem prover Walnut.
Minimum spanning trees and forests are powerful sparsification techniques that remove cycles from weighted graphs to minimize total edge weight while preserving node connectivity. They have applications in computer science, network science,…
This article focuses on comparing the notions of home spaces and invariants, in Transition Systems and more particularly, in Petri Nets as well as a variety of derived Petri Nets. After recalling basic notions of Petri Nets and semiflows,…
We show that any bounded integral function $f : A \times B \mapsto \{0,1, \dots, \Delta\}$ with rank $r$ has deterministic communication complexity $\Delta^{O(\Delta)} \cdot \sqrt{r} \cdot \log r$, where the rank of $f$ is defined to be the…
In the distributional Twenty Questions game, Bob chooses a number $x$ from $1$ to $n$ according to a distribution $\mu$, and Alice (who knows $\mu$) attempts to identify $x$ using Yes/No questions, which Bob answers truthfully. Her goal is…
We introduce efficient algorithms for approximate sampling from symmetric Gibbs distributions on the sparse random (hyper)graph. The examples we consider include (but are not restricted to) important distributions on spin systems and…
In this paper, we demonstrate gap amplification for reconfiguration problems. In particular, we prove an explicit factor of PSPACE-hardness of approximation for three popular reconfiguration problems only assuming the Reconfiguration…
In this paper, we introduce and study the problem of \textit{binary stretch embedding} of edge-weighted graph. This problem is closely related to the well-known \textit{addressing problem} of Graham and Pollak. Addressing problem is the…
Spin-glasses are Gibbs distributions that have been studied in CS for many decades. Recently, they have gained renewed attention as they emerge naturally in learning, inference, optimisation etc. We consider the Edwards-Anderson (EA)…
In dimension $d$, Mutually Unbiased Bases (MUBs) are a collection of orthonormal bases over $\mathbb{C}^d$ such that for any two vectors $v_1, v_2$ belonging to different bases, the scalar product $|\braket{v_1|v_2}| = \frac{1}{\sqrt{d}}$.…