Awards and Grants

Clustered Elias-Fano Indexes

Giulio Ermanno Pibiri and Rossano Venturini
ACM Transactions on Information Systems (TOIS), 2017 Journal Paper
    author      = {Giulio Ermanno Pibiri and Rossano Venturini},
    title       = {{C}lustered {E}lias-{F}ano {I}ndexes},
    journal     = {{ACM} {T}ransactions on {I}nformation {S}ystems ({TOIS})},
    volume      = {36},
    number      = {1},
    year        = {2017},
    issn        = {1046-8188},
    pages       = {2:1--2:33},
    articleno   = {2},
    numpages    = {33},
    url         = {},
    doi         = {10.1145/3052773},
    acmid       = {3052773},
    publisher   = {ACM},
    address     = {New York, NY, USA}


State-of-the-art encoders for inverted indexes compress each posting list individually. Encoding clusters of posting lists offers the possibility of reducing the redundancy of the lists while maintaining a noticeable query processing speed.
In this paper we propose a new index representation based on clustering the collection of posting lists and, for each created cluster, building an ad-hoc reference list with respect to which all lists in the cluster are encoded with Elias-Fano. We describe a posting lists clustering algorithm tailored for our encoder and two methods for building the reference list for a cluster. Both approaches are heuristic and differ in the way postings are added to the reference list: or according to their frequency in the cluster or according to the number of bits necessary for their representation.
The extensive experimental analysis indicates that significant space reductions are indeed possible, beating the best state-of-the-art encoders.

Dynamic Elias-Fano Representation

Giulio Ermanno Pibiri and Rossano Venturini
Annual Symposium on Combinatorial Pattern Matching (CPM), 2017 Conference Paper
    author      = {Giulio Ermanno Pibiri and Rossano Venturini},
    title       = {{D}ynamic {E}lias-{F}ano {R}epresentation},
    booktitle   = {{C}ombinatorial {P}attern {M}atching ({CPM})},
    year        = {2017}


We show that it is possible to store a dynamic ordered set $\mathcal{S}(n,u)$ of $n$ integers drawn from a bounded universe of size $u$ in space close to the information-theoretic lower bound and yet preserve the asymptotic time optimality of the operations. Our results leverage on the Elias-Fano representation of $\mathcal{S}(n, u)$ which takes $\textsf{EF}(\mathcal{S}(n, u)) = n\lceil \log\frac{u}{n}\rceil + 2n$ bits of space and can be shown to be less than half a bit per element away from the information-theoretic minimum.
Considering a RAM model with memory words of $\Theta(\log u)$ bits, we focus on the case in which the integers of $\mathcal{S}$ are drawn from a polynomial universe of size $u = n^\gamma$, for any $\gamma = \Theta(1)$. We represent $\mathcal{S}(n,u)$ with $\textsf{EF}(\mathcal{S}(n, u)) + o(n)$ bits of space and:
1. support static predecessor/successor queries in $\mathcal{O}\min\{1+\log\frac{u}{n}, \log\log n\})$;
2. make $\mathcal{S}$ grow in an append-only fashion by spending $\mathcal{O}(1)$ per inserted element;
3. support random access in $\mathcal{O}(\frac{\log n}{\log\log n})$ worst-case, insertions/deletions in $\mathcal{O}(\frac{\log n}{\log\log n})$ amortized and predecessor/successor queries in $\mathcal{O}(\min\{1+\log\frac{u}{n}, \log\log n\})$ worst-case time. These time bounds are optimal.

Efficient Data Structures for Massive N-Gram Datasets

Giulio Ermanno Pibiri and Rossano Venturini
ACM Conference on Research and Development in Information Retrieval (SIGIR), 2017 Conference Paper
    author      = {Giulio Ermanno Pibiri and Rossano Venturini},
    title       = {{E}fficient {D}ata {S}tructures for {M}assive {N}-{G}ram {D}atasets},
    booktitle   = {{C}onference on {R}esearch and {D}evelopment in {I}nformation {R}etrieval ({SIGIR})},
    year        = {2017}


The efficient indexing of large and sparse $N$-gram datasets is crucial in several applications in Information Retrieval, Natural Language Processing and Machine Learning. Because of the stringent efficiency requirements, dealing with billions of $N$-grams poses the challenge of introducing a compressed representation that preserves the query processing speed.
In this paper we study the problem of reducing the space required by the representation of such datasets, maintaining the capability of looking up for a given $N$-gram within micro seconds. For this purpose we describe compressed, exact and lossless data structures that achieve, at the same time, high space reductions and no time degradation with respect to state-of-the-art software packages. In particular, we present a trie data structure in which each word following a context of fixed length $k$, i.e., its preceding $k$ words, is encoded as an integer whose value is proportional to the number of words that follow such context. Since the number of words following a given context is typically very small in natural languages, we are able to lower the space of representation to compression levels that were never achieved before. Despite the significant savings in space, we show that our technique introduces a negligible penalty at query time.

The slides of the talk presenting my Ph.D. Thesis proposal are available here.

The slides of the seminar I gave about Elias-Fano are available here.