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Edge computing enables data processing and storage closer to where the data are created. Given the largely distributed compute environment and the significantly dispersed data distribution, there are increasing demands of data sharing and collaborative processing on the edge. Since data shuffling can dominate the overall execution time of collaborative processing jobs, considering the limited power supply and bandwidth resource in edge environments, it is crucial and valuable to reduce the communication overhead across edge devices. Compared with data compression, compact data structures (CDS) seem to be more suitable in this case, for the capability of allowing data to be queried, navigated, and manipulated directly in a compact form. However, the relevant work about applying CDS to edge computing generally focuses on the intuitive benefit from reduced data size, while few discussions about the challenges are given, not to mention empirical investigations into real-world edge use cases. This research highlights the challenges, opportunities, and potential scenarios of CDS implementation in edge computing. Driven by the use case of shuffling-intensive data analytics, we proposed a three-layer architecture for CDS-aided data processing and particularly studied the feasibility and efficiency of the CDS layer. We expect this research to foster conjoint research efforts on CDS-aided edge data analytics and to make wider practical impacts.

We show that any embedding of a planar graph can be encoded succinctly while efficiently answering a number of topological queries near-optimally. More precisely, we build on a succinct representation that encodes an embedding of $m$ edges within $4m$ bits, which is close to the information-theoretic lower bound of about $3.58m$. With $4m+o(m)$ bits of space, we show how to answer a number of topological queries relating nodes, edges, and faces, most of them in any time in $\omega(1)$. Further, we show that with $O(m)$ bits of space we can solve all those operations in $O(1)$ time., Comment: This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Actions H2020-MSCA-RISE-2015 BIRDS GA No. 690941. Conference version presented at SPIRE 2019

In the field of algorithms and data structures analysis and design, most of the researchers focus only on the space/time trade-off, and little attention has been paid to energy consumption. Moreover, most of the efforts in the field of Green Computing have been devoted to hardware-related issues, being green software in its infancy. Optimizing the usage of computing resources, minimizing power consumption or increasing battery life are some of the goals of this field of research. As an attempt to address the most recent sustainability challenges, we must incorporate the energy consumption as a first-class constraint when designing new compact data structures. Thus, as a preliminary work to reach that goal, we first need to understand the factors that impact on the energy consumption and their relation with compression. In this work, we study the energy consumption required by several integer vector representations. We execute typical operations over datasets of different nature. We can see that, as commonly believed, energy consumption is highly related to the time required by the process, but not always. We analyze other parameters, such as number of instructions, number of CPU cycles, memory loads, among others., Comment: This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie Actions H2020-MSCA-RISE-2015 BIRDS GA No. 690941

Given a string of length $n$ that is composed of $r$ runs of letters from the alphabet $\{0,1,\ldots,\sigma{-}1\}$ such that $2 \le \sigma \le r$, we describe a data structure that, provided $r \le n / \log^{\omega(1)} n$, stores the string in $r\log\frac{n\sigma}{r} + o(r\log\frac{n\sigma}{r})$ bits and supports select and access queries in $O(\log\frac{\log(n/r)}{\log\log n})$ time and rank queries in $O(\log\frac{\log(n\sigma/r)}{\log\log n})$ time. We show that $r\log\frac{n(\sigma-1)}{r} - O(\log\frac{n}{r})$ bits are necessary for any such data structure and, thus, our solution is succinct. We also describe a data structure that uses $(1 + \epsilon)r\log\frac{n\sigma}{r} + O(r)$ bits, where $\epsilon > 0$ is an arbitrary constant, with the same query times but without the restriction $r \le n / \log^{\omega(1)} n$. By simple reductions to the colored predecessor problem, we show that the query times are optimal in the important case $r \ge 2^{\log^\delta n}$, for an arbitrary constant $\delta > 0$. We implement our solution and compare it with the state of the art, showing that the closest competitors consume 31-46% more space., Comment: This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Actions H2020-MSCA-RISE-2015 BIRDS GA No. 690941. 10 pages, 1 figure, 4 tables; published in DCC'2018

The sheer sizes of modern datasets are forcing data-structure designers to consider seriously both parallel construction and compactness. To achieve those goals we need to design a parallel algorithm with good scalability and with low memory consumption. An algorithm with good scalability improves its performance when the number of available cores increases, and an algorithm with low memory consumption uses memory proportional to the space used by the dataset in uncompact form. In this work, we discuss the engineering of a parallel algorithm with linear work and logarithmic span for the construction of the compact representation of planar embeddings. We also provide an experimental study of our implementation and prove experimentally that it has good scalability and low memory consumption. Additionally, we describe and test experimentally queries supported by the compact representation.

The wavelet tree has become a very useful data structure to efficiently represent and query large volumes of data in many different domains, from bioinformatics to geographic information systems. One problem with wavelet trees is their construction time. In this paper, we introduce two algorithms that reduce the time complexity of a wavelet tree's construction by taking advantage of nowadays ubiquitous multicore machines. Our first algorithm constructs all the levels of the wavelet in parallel in $O(n)$ time and $O(n\lg\sigma + \sigma\lg n)$ bits of working space, where $n$ is the size of the input sequence and $\sigma$ is the size of the alphabet. Our second algorithm constructs the wavelet tree in a domain-decomposition fashion, using our first algorithm in each segment, reaching $O(\lg n)$ time and $O(n\lg\sigma + p\sigma\lg n/\lg\sigma)$ bits of extra space, where $p$ is the number of available cores. Both algorithms are practical and report good speedup for large real datasets., Comment: This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie Actions H2020-MSCA-RISE-2015 BIRDS GA No. 690941

Succinct trees, such as wavelet trees and those based on, for instance, range Min-Max trees (RMMTs), are a family of practical data structures that store information close to their information-theoretic space lower bound. These structures are often static; meaning that once they are built, nodes cannot be added, deleted or modified. This read-only property simplifies concurrency. However, newer versions of these data structures allow for a fair degree of dynamism. Parallel programming using Hardware Transactional Memory(HTM), has been available in mainstream microprocessors since a few years ago. One limitation of HTM is still on the size of each transaction. This is why HTM's use, for the moment, is limited to operations that involve few memory addresses that need to be updated atomically, or where the level of concurrency is low. We provide the first available implementation of a concurrent, dynamic RMMT based on HTM, and we compare empirically how well HTM performs compared to a naive implementation using locks. We have shown that because of the formal properties of RMMTs, HTM is a good fit for adding concurrency to otherwise slow lock-based alternatives. We have also shown that HTM performs better than locks when the number of write operations increase, making it a practical structure to use in several write-intensive contexts. This is, as far as we know, the only practical implementation of RMMTs thoroughly tested using HTM., Comment: 5 pages, 2 figures