Alessandro Roncato

Efficient Parallel Graph Algorithms For Coarse Grained Multicomputers and BSP

In this paper, we present deterministic parallel algorithms for the coarse grained multicomputer (CGM) and bulk-synchronous parallel computer (BSP) models which solve the following well known graph problems: (1) list ranking, (2) Euler tour construction, (3) computing the connected components and spanning forest, (4) lowest common ancestor preprocessing, (5) tree contraction and expression tree evaluation, (6) computing an ear decomposition or open ear decomposition, (7) 2-edge connectivity and biconnectivity (testing and component computation), and (8) cordai graph recognition (finding a perfect elimination ordering). The algorithms for Problems 1–7 require O(log p) communication rounds and linear sequential work per round. Our results for Problems 1 and 2 hold for arbitrary ratios \(\frac{n}{p}\), i.e. they are fully scalable, and for Problems 3–8 it is assumed that \(\frac{n}{p} \geqslant p^ \in ,{\mathbf{ }} \in {\mathbf{ }} > 0\), which is true for all commercially available multiprocessors. We view the algorithms presented as an important step towards the final goal of O(1) communication rounds. Note that, the number of communication rounds obtained in this paper is independent of n and grows only very slowly with respect to p. Hence, for most practical purposes, the number of communication rounds can be considered as constant. The result for Problem 1 is a considerable improvement over those previously reported. The algorithms for Problems 2–7 are the first practically relevant deterministic parallel algorithms for these problems to be used for commercially available coarse grained parallel machines.

On time versus size for monotone dynamic monopolies in regular topologies

We consider a well-known distributed colouring game played on a simple connected graph: initially, each vertex is coloured black or white; at each round, each vertex simultaneously recolours itself by the colour of the simple (strong) majority of its neighbours. A set of vertices M is said to be a dynamo, if starting the game with only the vertices of M coloured black, the computation eventually reaches an all-black configuration.The importance of this game follows from the fact that it models the spread of faults in point-to-point systems with majority-based voting; in particular, dynamos correspond to those sets of initial failures which will lead the entire system to fail. Investigations on dynamos have been extensive but restricted to establishing tight bounds on the size (i.e., how small a dynamic monopoly might be).In this paper we start to study dynamos systematically with respect to both the size and the time (i.e., how many rounds are needed to reach all-black configuration) in various models and topologies.We derive tight tradeoffs between the size and the time for a number of regular graphs, including rings, complete d-ary trees, tori, wrapped butterflies, cube connected cycles and hypercubes. In addition, we determine optimal size bounds of irreversible dynamos for butterflies and shuffle-exchange using simple majority and for DeBruijn using strong majority rules. Finally, we make some observations concerning irreversible versus reversible monotone models and slow complete computations from minimal dynamos.

Spatio-temporal aggregations in trajectory data warehouses

In this paper we investigate some issues related to the design of a simple Data Warehouse (DW), storing several aggregate measures about trajectories of moving objects. First we discuss the loading phase of our DW which has to deal with overwhelming streams of trajectory observations, possibly produced at different rates, and arriving in an unpredictable and unbounded way. Then, we focus on the measure presence, the most complex measure stored in our DW. Such a measure returns the number of trajectories that lie in a spatial region during a given temporal interval. We devise a novel way to compute an approximate, but very accurate, presence aggregate function, which algebraically combines a bounded amount of measures stored in the base cells of the data cube.

Approximate Aggregations in Trajectory Data Warehouses

In this paper we discuss how data warehousing technology can be used to store aggregate information about trajectories and perform OLAP operations over them. To this end, we define a data cube with spatial and temporal dimensions, discretized according to a regular grid. We investigate in depth some issues related to the computation of a holistic aggregate function, i.e, the presence, which returns the number of distinct trajectories occurring in a given spatio-temporal area. In particular, we introduce a novel way to compute an approximate, but nevertheless very accurate, presence aggregate function, which uses only a bounded amount of measures stored in the base cells of our cuboid. We also concentrate on the loading phase of our data warehouse, which has to deal with an unbounded stream of trajectory observations. We suggest how the complexity of this phase can be reduced, and we analyse the errors that this procedure induces at the level of the sub-aggregates stored in the base cells. These errors and the accuracy of our approximate aggregate functions are carefully evaluated by means of tests performed on synthetic trajectory datasets.

A general framework for trajectory data warehousing and visual OLAP

In this paper we present a formal framework for modelling a trajectory data warehouse (TDW), namely a data warehouse aimed at storing aggregate information on trajectories of moving objects, which also offers visual OLAP operations for data analysis. The data warehouse model includes both temporal and spatial dimensions, and it is flexible and general enough to deal with objects that are either completely free or constrained in their movements (e.g., they move along a road network). In particular, the spatial dimension and the associated concept hierarchy reflect the structure of the environment in which the objects travel. Moreover, we cope with some issues related to the efficient computation of aggregate measures, as needed for implementing roll-up operations. The TDW and its visual interface allow one to investigate the behaviour of objects inside a given area as well as the movements of objects between areas in the same neighbourhood. A user can easily navigate the aggregate measures obtained from OLAP queries at different granularities, and get overall views in time and in space of the measures, as well as a focused view on specific measures, spatial areas, or temporal intervals. We discuss two application scenarios of our TDW, namely road traffic and vessel movement analysis, for which we built prototype systems. They mainly differ in the kind of information available for the moving objects under observation and their movement constraints.

T-Warehouse: Visual OLAP analysis on trajectory data

Technological advances in sensing technologies and wireless telecommunication devices enable novel research fields related to the management of trajectory data. As it usually happens in the data management world, the challenge after storing the data is the implementation of appropriate analytics for extracting useful knowledge. However, traditional data warehousing systems and techniques were not designed for analyzing trajectory data. Thus, in this work, we demonstrate a framework that transforms the traditional data cube model into a trajectory warehouse. As a proof-of-concept, we implemented T-WAREHOUSE, a system that incorporates all the required steps for Visual Trajectory Data Warehousing, from trajectory reconstruction and ETL processing to Visual OLAP analysis on mobility data.

Computing on anonymous networks with sense of direction

Sense of direction refers to a set of global consistency constraints of the local labeling of the edges of a network. Sense of direction has a large impact on the communication complexity of many distributed problems. In this paper, we study the impact that sense of direction has on computability and we focus on anonymous networks. We establish several results. In particular, we prove that with weak sense of direction, the intuitive knowledge-computability hierarchy between levels of a priori structural knowledge collapses. A powerful implication is the formal proof that shortest path routing is possible in anonymous networks with sense of direction. We prove that weak sense of direction is computationally stronger than topological awareness. We also consider several fundamental problems; for each, we provide a complete characterization of the anonymous networks on which it is computable with sense of direction.

Frequent spatio-temporal patterns in trajectory data warehouses

In this paper we present an approach for storing and aggregating spatio-temporal patterns by using a Trajectory Data Warehouse (TDW). In particular, our aim is to allow the analysts to quickly evaluate frequent patterns mined from trajectories of moving objects occurring in a specific spatial zone and during a given temporal interval. We resort to a TDW, based on a data cube model, having spatial and temporal dimensions, discretized according to a hierarchy of regular grids, and whose facts are sets of trajectories which intersect the spatio-temporal cells of the cube. The idea is to enrich such a TDW with a new measure: frequent patterns obtained from a data-mining process on trajectories. As a consequence these patterns can be analysed by the user at various levels of granularity by means of OLAP queries. The research issues discussed in this paper are (1) the extraction/mining of the patterns to be stored in each cell, which requires an adequate projection phase of trajectories before mining; (2) the spatio-temporal aggregation of patterns to answer roll-up queries, which poses many problems due to the holistic nature of the aggregation function.

Mob-Warehouse: A Semantic Approach for Mobility Analysis with a Trajectory Data Warehouse

The effective analysis and understanding of huge amount of mobility data have been a hot research topic in the last few years. In this paper, we introduce Mob-Warehouse, a Trajectory Data Warehouse which goes a step further to the state of the art on mobility analysis since it models trajectories enriched with semantics. The unit of movement is the (spatio-temporal) point endowed with several semantic dimensions including the activity, the transportation means and the mobility patterns. This model allows us to answer the classical Why, Who, When, Where, What, How questions providing an aggregated view of different aspects of the user movements, no longer limited to space and time. We briefly present an experiment of Mob-Warehouse on a real dataset.

A Semantic Model for Movement Data Warehouses

Despite recent progresses in methods for processing data about the movement of objects in the geographic space, some fundamental issues remain unresolved. One of them is how to describe movement segments (e.g., semantic trajectories, episodes like stops and moves) and diverse movement patterns (e.g., moving clusters, hotel-restaurant-shop-hotel), with formal semantic descriptions. Another issue is how to arrange descriptive data and measures in a Movement Data Warehouse (MDW) for powerful information analyses and reasonable performance. This paper introduces general definitions for movement segments, movement patterns, their categories and hierarchies. The proposed constructs are semantically enriched with references to concepts (categories) and/or instances of these concepts (objects) arranged in distinct hierarchies. Based on these constructs, we propose a semantic multidimensional model for MDW. A case study illustrates the expressiveness of the proposal for analyzing movement data collected via social media and semantically enriched with Linked Open Data (LOD).