Finding k-Dissimilar Paths with Minimum Collective Length

Shortest path computation is a fundamental problem in road networks. However, in many real-world scenarios, determining solely the shortest path is not enough. In this paper, we study the problem of finding k-Dissimilar Paths with Minimum Collective Length (kDPwML), which aims at computing a set of paths from a source s to a target t such that all paths are pairwise dissimilar by at least \theta and the sum of the path lengths is minimal. We introduce an exact algorithm for the kDPwML problem, which iterates over all possible s-t paths while employing two pruning techniques to reduce the prohibitively expensive computational cost. To achieve scalability, we also define the much smaller set of the simple single-via paths, and we adapt two algorithms for kDPwML queries to iterate over this set. Our experimental analysis on real road networks shows that iterating over all paths is impractical, while iterating over the set of simple single-via paths can lead to scalable solutions with only a small trade-off in the quality of the results.Comment: Extended version of the SIGSPATIAL'18 paper under the same titl

Defining Equitable Geographic Districts in Road Networks via Stable Matching

We introduce a novel method for defining geographic districts in road networks using stable matching. In this approach, each geographic district is defined in terms of a center, which identifies a location of interest, such as a post office or polling place, and all other network vertices must be labeled with the center to which they are associated. We focus on defining geographic districts that are equitable, in that every district has the same number of vertices and the assignment is stable in terms of geographic distance. That is, there is no unassigned vertex-center pair such that both would prefer each other over their current assignments. We solve this problem using a version of the classic stable matching problem, called symmetric stable matching, in which the preferences of the elements in both sets obey a certain symmetry. In our case, we study a graph-based version of stable matching in which nodes are stably matched to a subset of nodes denoted as centers, prioritized by their shortest-path distances, so that each center is apportioned a certain number of nodes. We show that, for a planar graph or road network with $n$ nodes and $k$ centers, the problem can be solved in $O(n\sqrt{n}\log n)$ time, which improves upon the $O(nk)$ runtime of using the classic Gale-Shapley stable matching algorithm when $k$ is large. Finally, we provide experimental results on road networks for these algorithms and a heuristic algorithm that performs better than the Gale-Shapley algorithm for any range of values of $k$.Comment: 9 pages, 4 figures, to appear in 25th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL 2017) November 7-10, 2017, Redondo Beach, California, US

Location- and keyword-based querying of geo-textual data: a survey

With the broad adoption of mobile devices, notably smartphones, keyword-based search for content has seen increasing use by mobile users, who are often interested in content related to their geographical location. We have also witnessed a proliferation of geo-textual content that encompasses both textual and geographical information. Examples include geo-tagged microblog posts, yellow pages, and web pages related to entities with physical locations. Over the past decade, substantial research has been conducted on integrating location into keyword-based querying of geo-textual content in settings where the underlying data is assumed to be either relatively static or is assumed to stream into a system that maintains a set of continuous queries. This paper offers a survey of both the research problems studied and the solutions proposed in these two settings. As such, it aims to offer the reader a first understanding of key concepts and techniques, and it serves as an “index” for researchers who are interested in exploring the concepts and techniques underlying proposed solutions to the querying of geo-textual data.Agency for Science, Technology and Research (A*STAR)Ministry of Education (MOE)Nanyang Technological UniversityThis research was supported in part by MOE Tier-2 Grant MOE2019-T2-2-181, MOE Tier-1 Grant RG114/19, an NTU ACE Grant, and the Singtel Cognitive and Artificial Intelligence Lab for Enterprises (SCALE@NTU), which is a collaboration between Singapore Telecommunications Limited (Singtel) and Nanyang Technological University (NTU) that is funded by the Singapore Government through the Industry Alignment Fund Industry Collaboration Projects Grant, and by the Innovation Fund Denmark centre, DIREC