Showing papers by "Laurent Viennot published in 2023"
TL;DR: Breadth-First Depth-Next (BFDN) as mentioned in this paper was the first algorithm to achieve a 2 n/k + O(D 2 log(k ))-time guarantee.
Abstract: We consider the problem of collaborative tree exploration posed by Fraigniaud, Gasieniec, Kowalski, and Pelc [Fraigniaud et al., 2006] where a team of k agents is tasked to collectively go through all the edges of an unknown tree as fast as possible. Denoting by n the total number of nodes and by D the tree depth, the O ( n/ log( k ) + D ) algorithm of Fraigniaud et al. [2006] achieves the best-known competitive ratio with respect to the cost of offline exploration which is Θ(max { 2 n/k, 2 D } ) . Brass, Cabrera-Mora, Gasparri, and Xiao Brass et al. [2011] consider an alternative performance criterion, namely the additive overhead with respect to 2 n/k , and obtain a 2 n/k + O (( D + k ) k ) runtime guarantee. In this paper, we introduce ‘Breadth-First Depth-Next’ (BFDN), a novel and simple algorithm that performs collaborative tree exploration in time 2 n/k + O ( D 2 log( k )) , thus outperforming Brass et al. [2011] for all values of ( n, D ) and being order-optimal for all trees with depth D = o k ( √ n ) . Moreover, a recent result from Disser et al. [2017] implies that no exploration algorithm can achieve a 2 n/k + O ( D 2 − (cid:15) ) runtime guarantee. The dependency in D 2 of our bound is in this sense optimal. The proof of our result crucially relies on the analysis of an associated two-player game. We extend the guarantees of BFDN to: scenarios with limited memory and communication, adversarial setups where robots can be blocked, and exploration of classes of non-tree graphs. Finally, we provide a recursive version of BFDN with a runtime of O (cid:96) ( n/k 1 /(cid:96)
1 citations
TL;DR: The problem of assigning time labels to the edges of a digraph in order to maximize the total reachability of the resulting temporal graph was shown to be NP-hard in this article .
Abstract: A temporal graph is a graph in which edges are assigned a time label. Two nodes u and v of a temporal graph are connected one to the other if there exists a path from u to v with increasing edge time labels. We consider the problem of assigning time labels to the edges of a digraph in order to maximize the total reachability of the resulting temporal graph (that is, the number of pairs of nodes which are connected one to the other). In particular, we prove that this problem is NP-hard. We then conjecture that the problem is approximable within a constant approximation ratio. This conjecture is a consequence of the following graph theoretic conjecture: any strongly connected directed graph with n nodes admits an out-arborescence and an in-arborescence that are edge-disjoint, have the same root, and each spans $\Omega$(n) nodes.
1 citations
TL;DR: In this article , the authors introduce the notion of forbidden patterns in temporal cliques, which leads to a characterization of this class of graphs and the number of such cliques for a given number of agents.
Abstract: In this paper, we study temporal graphs arising from mobility models where some agents move in a space and where edges appear each time two agents meet. We propose a rather natural one-dimensional model. If each pair of agents meets exactly once, we get a temporal clique where each possible edge appears exactly once. By ordering the edges according to meeting times, we get a subset of the temporal cliques. We introduce the first notion of of forbidden patterns in temporal graphs, which leads to a characterization of this class of graphs. We provide, thanks to classical combinatorial results, the number of such cliques for a given number of agents. We consider specific cases where some of the nodes are frozen, and again provide a characterization by forbidden patterns. We give a forbidden pattern when we allow multiple crossings between agents, and leave open the question of a characterization in this situation.
TL;DR: In this article , it was shown that the problem of finding the maximum number of forward connected pairs in a strongly connected directed graph is in APX, as one can efficiently enumerate the vertices of the graph in order to achieve a quadratic number of pairs.
Abstract: In a directed graph $D$ on vertex set $v_1,\dots ,v_n$, a \emph{forward arc} is an arc $v_iv_j$ where $i0$ such that one can always find an enumeration realizing $c.|R|$ forward connected pairs $\{x_i,y_i\}$ (in either direction).
16 Jun 2023
TL;DR: Breadth-First Depth-Next (BFDN) as discussed by the authors is the fastest known algorithm for collaborative tree exploration with time complexity O(n/k + O(D2 log(k)) for all values of (n, D) and order-optimal for fixed k and trees with depth D = o(√n).
Abstract: We consider the problem of collaborative tree exploration posed by Fraigniaud, Gasieniec, Kowalski, and Pelc [8] where a team of k agents is tasked to collectively go through all the edges of an unknown tree as fast as possible and return to the root. Denoting by n the total number of nodes and by D the tree depth, the O(n/log(k) + D) algorithm of [8] achieves the best competitive ratio known with respect to the optimal exploration algorithm that knows the tree in advance, which takes order max {2n/k, 2D} rounds. Brass, Cabrera-Mora, Gasparri, and Xiao [1] consider an alternative performance criterion, the additive overhead with respect to 2n/k, and obtain a 2n/k + O((D + k)k) runtime guarantee. In this announcement, we present 'Breadth-First Depth-Next' (BFDN), a novel and simple algorithm that performs collaborative tree exploration in time 2n/k + O(D2 log(k)), thus outperforming [1] for all values of (n, D) and being order-optimal for fixed k and trees with depth D = o(√n). The proof of our result crucially relies on the analysis of a simple two-player game with balls in urns that could be of independent interest. We extend the guarantees of BFDN to: scenarios with limited memory and communication, adversarial setups where robots can be blocked, and exploration of classes of non-tree graphs. Finally, we provide a recursive version of BFDN with a runtime of Oℓ(n/k1/ℓ + log(k)D1+1/ℓ) for parameter ℓ ≥ 1, thereby improving performance for trees with large depth. A complete version of the paper is available online [2].
01 Jan 2023
TL;DR: In this article , the authors investigate the problem of making an artificial neural network perform hidden computations whose result can be easily retrieved from the network's output and propose a simple and efficient training procedure, which they call hidden learning, that produces two networks: (i) one that solves the original classification task with performance near to state-of-the-art; (ii) a second one that takes as input the output of the first, retrieving sensitive information to solve a second classification task.
Abstract: We investigate the problem of making an artificial neural network perform hidden computations whose result can be easily retrieved from the network’s output. In particular, we consider the following scenario. A user is provided a neural network for a classification task by a third party. The user’s input to the network contains sensitive information and the third party can only observe the output of the network. I this work, we provide a simple and efficient training procedure, which we call hidden learning, that produces two networks: (i) one that solves the original classification task with performance near to state of the art; (ii) a second one that takes as input the output of the first, retrieving sensitive information to solve a second classification task with good accuracy. Our result might expose important issues from an information security point of view, as for the use of artificial neural networks in sensible applications.