An m-ballot path of size n is a path on the square grid consisting of north and east unit steps, starting at (0,0), ending at (mn,n), and never going…

Consider a rooted binary tree with n nodes. Assign with the root the abscissa 0, and with the left (resp. right) child of a node of abscissa i the ab…

Consider an instance I to one-in-three-3sat and a satisfying assignment for I. We construct the collection QI of quartet trees, as well as the ternary phylogenetic tree Tσ as described in Sections 3 and 4, respectively. Clearly, constructing QI and …

We answer, in the affirmative, the following question proposed by Mike Steel as a $100 challenge: "Is the following problem NP-hard? Given a ternary …

Since the topic emerged several years ago, work on regular model checking has mostly been devoted to the verification of state reachability and safet…

From the works of Rauzy and Thurston, we know how to construct (multiple) tilings of some Euclidean space using the conjugates of a Pisot unit $\beta…

A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Inspired by sequential complexity the…

Let k≥5 be an integer. Let G be a connected graph of girth at least k and x1,…,xk be terminals of G. Then one and only one of the following holds:

For all integers $k\geq 3$, we give an $O(n^4)$ time algorithm for the problem whose instance is a graph $G$ of girth at least $k$ together with $k$ …

Let us start by fixing some notation. In a two-player game, let p be an efficiently computable correlated equilibrium that the players know and aim to generate. A typical scenario is that p is the lexicographically first correlated equilibrium that …

A correlated equilibrium is a fundamental solution concept in game theory that enjoys many desirable properties. However, it requires a trusted media…

Pavlovian Population protocols are symmetric. We just proved that they have a very limited computational power. However, assuming population protocols symmetric (not-necessarily Pavlovian) is not truly a restriction.

Population protocols have been introduced by Angluin et {al.} as a model of networks consisting of very limited mobile agents that interact in pairs …

We provide a general method to prove the existence and compute efficiently elimination orderings in graphs. Our method relies on several tools that w…

The problem of dictionary matching is a classical problem in string matching: given a set S of d strings of total length n characters over an (not ne…

" How well connected is the network? " This is one of the most fundamental questions one would ask when facing the challenge of designing a communica…

We have compared three models of randomized strategies —behavioural, mixed, and general— in the context of graph games. Depending on the sub-case, we were able to expose variations in the amount of memory needed, the existence of finite-memory strat…

Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specif…

We conclude the paper with some open questions.

We define a new class of languages of $\omega$-words, strictly extending $\omega$-regular languages. One way to present this new class is by a type…

An ancestry labeling scheme assigns labels (bit strings) to the nodes of rooted trees such that ancestry queries between any two nodes in a tree can …

Generating functions for plane overpartitions are obtained using various methods such as nonintersecting paths, RSK type algorithms and symmetric fun…

A graph is a $k$-leaf power of a tree $T$ if its vertices are leaves of $T$ and two vertices are adjacent in $T$ if and only if their distance in $T$…

In [{Structural properties and decomposition of linear balanced matrices}, {\it Mathematical Programming}, 55:129--168, 1992], Conforti and Rao conje…

We proved that predicates on counts of input agents n≥0, n=0, n≥m, where n,m are some counts of input agents, can be computed by some Pavlovian population protocols.

Population protocols have been introduced as a model of sensor networks consisting of very limited mobile agents with no control over their own movem…

Motivated by multiplication algorithms based on redundant number representations, we study representations of an integer $n$ as a sum $n=\sum_k \epsi…

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