# Parallel Search with no Coordination

2 GANG - Networks, Graphs and Algorithms
IRIF - Institut de Recherche en Informatique Fondamentale, Inria de Paris
Abstract : We consider a parallel version of a classical Bayesian search problem. $k$ agents are looking for a treasure that is placed in one of the boxes indexed by $N+$ according to a known distribution $p$. The aim is to minimize the expected time until the first agent finds it. Searchers run in parallel where at each time step each searcher can peek'' into a box. A basic family of algorithms which are inherently robust is \emph{non-coordinating} algorithms. Such algorithms act independently at each searcher, differing only by their probabilistic choices. We are interested in the price incurred by employing such algorithms when compared with the case of full coordination. We first show that there exists a non-coordination algorithm, that knowing only the relative likelihood of boxes according to $p$, has expected running time of at most $10+4(1+\frac{1}{k})^2 T$, where $T$ is the expected running time of the best fully coordinated algorithm. This result is obtained by applying a refined version of the main algorithm suggested by Fraigniaud, Korman and Rodeh in STOC'16, which was designed for the context of linear parallel search. We then describe an optimal non-coordinating algorithm for the case where the distribution $p$ is known. The running time of this algorithm is difficult to analyse in general, but we calculate it for several examples. In the case where $p$ is uniform over a finite set of boxes, then the algorithm just checks boxes uniformly at random among all non-checked boxes and is essentially $2$ times worse than the coordinating algorithm. We also show simple algorithms for Pareto distributions over $M$ boxes. That is, in the case where $p(x) \sim 1/x^b$ for $0< b < 1$, we suggest the following algorithm: at step $t$ choose uniformly from the boxes unchecked in ${1, . . . ,min(M, ⌊t/σ⌋)}$,, where $σ = b/(b + k − 1)$. It turns out this algorithm is asymptotically optimal, and runs about $2+b$ times worse than the case of full coordination.
Keywords :
Type de document :
Communication dans un congrès
24th International Colloquium on Structural Information and Communication Complexity (SIROCCO), Jun 2017, Porquerolles, France

Littérature citée [21 références]

https://hal.inria.fr/hal-01523506
Contributeur : Amos Korman <>
Soumis le : mardi 16 mai 2017 - 15:35:18
Dernière modification le : jeudi 11 janvier 2018 - 06:28:03
Document(s) archivé(s) le : vendredi 18 août 2017 - 00:34:03

### Fichiers

sirocco.pdf
Fichiers produits par l'(les) auteur(s)

### Identifiants

• HAL Id : hal-01523506, version 1
• ARXIV : 1705.05704

### Citation

Amos Korman, Yoav Rodeh. Parallel Search with no Coordination. 24th International Colloquium on Structural Information and Communication Complexity (SIROCCO), Jun 2017, Porquerolles, France. 〈hal-01523506〉

### Métriques

Consultations de la notice

## 115

Téléchargements de fichiers