arXiv subjects

Roberto Trani

Publications and source records attributed to Roberto Trani.

3 recordsLinked to original sources

arXiv2021

An Optimal Algorithm for Finding Champions in Tournament Graphs

A tournament graph is a complete directed graph, which can be used to model a round-robin tournament between $n$ players. In this paper, we address the problem of finding a champion of the tournament, also known as Copeland winner, which is a player that wins the highest number of matches. In detail, we aim to investigate algorithms that find the champion by playing a low number of matches. Solving this problem allows us to speed up several Information Retrieval and Recommender System applications, including question answering, conversational search, etc. Indeed, these applications often search for the champion inducing a round-robin tournament among the players by employing a machine learning model to estimate who wins each pairwise comparison. Our contribution, thus, allows finding the champion by performing a low number of model inferences. We prove that any deterministic or randomized algorithm finding a champion with constant success probability requires $\Omega(\ell n)$ comparisons, where $\ell$ is the number of matches lost by the champion. We then present an asymptotically-optimal deterministic algorithm matching this lower bound without knowing $\ell$, and we extend our analysis to three variants of the problem. Lastly, we conduct a comprehensive experimental assessment of the proposed algorithms on a question answering task on public data. Results show that our proposed algorithms speed up the retrieval of the champion up to $13\times$ with respect to the state-of-the-art algorithm that perform the full tournament.

cs.IR↗

arXiv2021

Parallel and External-Memory Construction of Minimal Perfect Hash Functions with PTHash

A function $f : U \to \{0,\ldots,n-1\}$ is a minimal perfect hash function for a set $S \subseteq U$ of size $n$, if $f$ bijectively maps $S$ into the first $n$ natural numbers. These functions are important for many practical applications in computing, such as search engines, computer networks, and databases. Several algorithms have been proposed to build minimal perfect hash functions that: scale well to large sets, retain fast evaluation time, and take very little space, e.g., 2 - 3 bits/key. PTHash is one such algorithm, achieving very fast evaluation in compressed space, typically several times faster than other techniques. In this work, we propose a new construction algorithm for PTHash enabling: (1) multi-threading, to either build functions more quickly or more space-efficiently, and (2) external-memory processing to scale to inputs much larger than the available internal memory. Only few other algorithms in the literature share these features, despite of their big practical impact. We conduct an extensive experimental assessment on large real-world string collections and show that, with respect to other techniques, PTHash is competitive in construction time and space consumption, but retains 2 - 6$\times$ better lookup time.

cs.DS↗

arXiv2021

PTHash: Revisiting FCH Minimal Perfect Hashing

Given a set $S$ of $n$ distinct keys, a function $f$ that bijectively maps the keys of $S$ into the range $\{0,\ldots,n-1\}$ is called a minimal perfect hash function for $S$. Algorithms that find such functions when $n$ is large and retain constant evaluation time are of practical interest; for instance, search engines and databases typically use minimal perfect hash functions to quickly assign identifiers to static sets of variable-length keys such as strings. The challenge is to design an algorithm which is efficient in three different aspects: time to find $f$ (construction time), time to evaluate $f$ on a key of $S$ (lookup time), and space of representation for $f$. Several algorithms have been proposed to trade-off between these aspects. In 1992, Fox, Chen, and Heath (FCH) presented an algorithm at SIGIR providing very fast lookup evaluation. However, the approach received little attention because of its large construction time and higher space consumption compared to other subsequent techniques. Almost thirty years later we revisit their framework and present an improved algorithm that scales well to large sets and reduces space consumption altogether, without compromising the lookup time. We conduct an extensive experimental assessment and show that the algorithm finds functions that are competitive in space with state-of-the art techniques and provide $2-4\times$ better lookup time.

cs.DS↗