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In this paper, we propose a paradigm for processing in parallel graph joins in road networks. The methodology we present can be used for distance join processing among the elements of two disjoint sets R,S of nodes from the road network, with R preceding S, and we are in search for the pairs of vertices (u,v), where u in R and v in S, such that dist(u,v) < {\theta}. Another variation of the problem would involve retrieving the k closest pairs (u,v) in the road network with u in R and v in S, such that dist(u,v) <= dist(w,y), where w,y do not belong in the result. We reckon that this is an extremely useful paradigm with many practical applications. A typical example of usage of our methods would be to find the pairs of restaurants and bars (in that order) from which to select for a night out, that either fall within walking distance for example, or just the k closest pairs, depending on the parameters. Another entirely different scenario would involve finding the points of two distinct trajectories that are within a certain distance predicate, or the k closest such points. For example, we would like to transfer from one train to another a few tones of freight, and hence, we want to minimize the distance we have to cover for moving the cargo from the carrying train to the other. We reckon that this endeavor of ours covers exactly those needs for processing such queries efficiently. Moreover, for the specific purposes of this paper, we also propose a novel heuristic graph partitioning scheme. It resembles a recursive bisection method, and is tailored to the requirements of the problem, targeting at establishing well separated partitions, so as to allow computations to be performed simultaneously and independently within each partition, unlike hitherto work that aims at minimizing either the number of edges among different partitions, or the number of nodes thereof.

This work is pertaining to the diversified ranking of web-resources and interconnected documents that rely on a network-like structure, e.g. web-pages. A practical example of this would be a query for the k most relevant web-pages that are also in the same time as dissimilar with each other as possible. Relevance and dissimilarity are quantified using an aggregation of network distance and context similarity. For example, for a specific configuration of the problem, we might be interested in web-pages that are similar with the query in terms of their textual description but distant from each other in terms of the web-graph, e.g. many clicks away. In retrospect, a dearth of work can be found in the literature addressing this problem taking the network structure formed by the document links into consideration. In this work, we propose a hill-climbing approach that is seeded with a document collection which is generated using greedy heuristics to diversify initially. More importantly, we tackle the problem in the context of web-pages where there is an underlying network structure connecting the available documents and resources. This is a significant difference to the majority of works that tackle the problem in terms of either content definitions, or the graph structure of the data, but never addressing both aspects simultaneously. To the best of our knowledge, this is the very first effort that can be found to combine both aspects of this important problem in an elegant fashion by also allowing a great degree of flexibility on how to configure the trade-offs of (i) document relevance over result-items' dissimilarity, and (ii) network distance over content relevance or dissimilarity. Last but not least, we present an extensive evaluation of our methods that demonstrate the effectiveness and efficiency thereof., Comment: 12 pages of unpublished work

In this paper we consider a set of travelers, starting from likely different locations towards a common destination within a road network, and propose solutions to find the optimal connecting points for them. A connecting point is a vertex of the network where a subset of the travelers meet and continue traveling together towards the next connecting point or the destination. The notion of optimality is with regard to a given aggregated travel cost, e.g., travel distance or shared fuel cost. This problem by itself is new and we make it even more interesting (and complex) by considering affinity factors among the users, i.e., how much a user likes to travel together with another one. This plays a fundamental role in determining where the connecting points are and how subsets of travelers are formed. We propose three methods for addressing this problem, one that relies on a fast and greedy approach that finds a sub-optimal solution, and two others that yield globally optimal solution. We evaluate all proposed approaches through experiments, where collections of real datasets are used to assess the trade-offs, behavior and characteristics of each method., Comment: This submission has been withdrawn by arXiv administrators due to disputed authorship