Michael N. Rice

Bio: Michael N. Rice is an academic researcher from University of California, Riverside. The author has contributed to research in topics: Shortest path problem & Travelling salesman problem. The author has an hindex of 7, co-authored 8 publications receiving 171 citations.

Graph indexing of road networks for shortest path queries with label restrictions

Abstract: The current widespread use of location-based services and GPS technologies has revived interest in very fast and scalable shortest path queries. We introduce a new shortest path query type in which dynamic constraints may be placed on the allowable set of edges that can appear on a valid shortest path (e.g., dynamically restricting the type of roads or modes of travel which may be considered in a multimodal transportation network). We formalize this problem as a specific variant of formal language constrained shortest path problems, which we call the Kleene Language Constrained Shortest Paths problem. To efficiently support this type of dynamically constrained shortest path query for large-scale datasets, we extend the hierarchical graph indexing technique known as Contraction Hierarchies. Our experimental evaluation using the North American road network dataset (with over 50 million edges) shows an average query speed and search space improvement of over 3 orders of magnitude compared to the naive adaptation of the standard Dijkstra's algorithm to support this query type. We also show an improvement of over 2 orders of magnitude compared to the only previously-existing indexing technique which could solve this problem without additional preprocessing.

Route planning with flexible edge restrictions

Abstract: In this work, we explore a new type of flexible shortest-path query, in which the query can be dynamically parameterized to constrain the type of edges that may be included in the resulting shortest path (e.g., find the shortest path in a road network that avoids toll roads and low overpasses, respective of the specified vehicle height). We extend the hierarchical preprocessing technique known as Contraction Hierarchies to efficiently support such flexible queries. We also present several effective algorithmic optimizations for further improving the overall scalability and query times of this approach, including the addition of goal-directed search techniques, search space pruning techniques, and generalizing the constraints of the local search. Experiments are presented for both the North American and the European road networks, showcasing the general effectiveness and scalability of our proposed methodology to large-scale, real-world graphs.

Parameterized algorithms for generalized traveling salesman problems in road networks

Abstract: The Generalized Traveling Salesman (Path) Problem involves finding a minimum-cost tour (or path) through exactly one location from each of a set of generalized location categories (e.g., gas stations, coffee shops). This problem type has many practical applications in personal navigation and logistics. While NP-hard in general, this problem also admits fixed-parameter tractable (FPT) algorithms with run times of the form f(k)nO(1) for some function f (independent of the problem size, n) with respect to the number of location categories, k (typically very small in practice). We present both exact and approximate FPT algorithms for this problem. Experimental results on the road network of North America (with over 50 million edges) show that we can optimally solve nationwide queries with up to 7 categories and millions of optional category locations in sub-second time. Our approximate solutions improve this even further down to millisecond query times, resulting in only negligible relative error with respect to optimality, on average.

Engineering Generalized Shortest Path queries

Abstract: Generalized Shortest Path (GSP) queries represent a variant of constrained shortest path queries in which a solution path of minimum total cost must visit at least one location from each of a set of specified location categories (e.g., gas stations, grocery stores) in a specified order. This problem type has many practical applications in logistics and personalized location-based services, and is closely related to the NP-hard Generalized Traveling Salesman Path Problem (GTSPP). In this work, we present a new dynamic programming formulation to highlight the structure of this problem. Using this formulation as our foundation, we progressively engineer a fast and scalable GSP query algorithm for use on large, real-world road networks. Our approach incorporates concepts from Contraction Hierarchies, a well-known graph indexing technique for static shortest path queries. To demonstrate the practicality of our algorithm we experimented on the North American road network (with over 50 million edges) where we achieved up to several orders of magnitude speed improvements over the previous-best algorithm, depending on the relative sizes of the location categories.

Exact graph search algorithms for generalized traveling salesman path problems

Abstract: The Generalized Traveling Salesman Path Problem (GTSPP) involves finding the shortest path from a location s to a location t that passes through at least one location from each of a set of generalized location categories (e.g., gas stations, grocery stores). This NP-hard problem type has many applications in transportation and location-based services. We present two exact algorithms for solving GTSPP instances, which rely on a unique product-graph search formulation. Our exact algorithms are exponential only in the number of categories (not in the total number of locations) and do not require the explicit construction of a cost matrix between locations, thus allowing us to efficiently solve many real-world problems to optimality. Experimental analysis on the road network of North America demonstrates that we can optimally solve large-scale, practical GTSPP instances typically in a matter of seconds, depending on the overall number and sizes of the categories.

Route Planning in Transportation Networks

Abstract: We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.

Exact Routing in Large Road Networks Using Contraction Hierarchies

Abstract: Contraction hierarchies are a simple approach for fast routing in road networks. Our algorithm calculates exact shortest paths and handles road networks of whole continents. During a preprocessing step, we exploit the inherent hierarchical structure of road networks by adding shortcut edges. A subsequent modified bidirectional Dijkstra algorithm can then find a shortest path in a fraction of a millisecond, visiting only a few hundred nodes. This small search space makes it suitable to implement it on a mobile device. We present a mobile implementation that also handles changes in the road network, like traffic jams, and that allows instantaneous routing without noticeable delay for the user. Also, an algorithm to calculate large distance tables is currently the fastest if based on contraction hierarchies.

Customizable route planning

Abstract: We present an algorithm to compute shortest paths on continental road networks with arbitrary metrics (cost functions). The approach supports turn costs, enables real-time queries, and can incorporate a new metric in a few seconds--fast enough to support real-time traffic updates and personalized optimization functions. The amount of metric-specific data is a small fraction of the graph itself, which allows us to maintain several metrics in memory simultaneously.

Customizable Route Planning in Road Networks

Abstract: We propose the first routing engine for computing driving directions in large-scale road networks that satisfies all requirements of a real-world production system. It supports arbitrary metrics (cost functions) and turn costs, enables real-time queries, and can incorporate a new metric in less than a second, which is fast enough to support real-time traffic updates and personalized cost functions. The amount of metric-specific data is a small fraction of the graph itself, which allows us to maintain several metrics in memory simultaneously. The algorithm is the core of the routing engine currently in use by Bing Maps.

Shortest path and distance queries on road networks: an experimental evaluation

Abstract: Computing the shortest path between two given locations in a road network is an important problem that finds applications in various map services and commercial navigation products. The state-of-the-art solutions for the problem can be divided into two categories: spatial-coherence-based methods and vertex-importance-based approaches. The two categories of techniques, however, have not been compared systematically under the same experimental framework, as they were developed from two independent lines of research that do not refer to each other. This renders it difficult for a practitioner to decide which technique should be adopted for a specific application. Furthermore, the experimental evaluation of the existing techniques, as presented in previous work, falls short in several aspects. Some methods were tested only on small road networks with up to one hundred thousand vertices; some approaches were evaluated using distance queries (instead of shortest path queries), namely, queries that ask only for the length of the shortest path; a state-of-the-art technique was examined based on a faulty implementation that led to incorrect query results.To address the above issues, this paper presents a comprehensive comparison of the most advanced spatial-coherence-based and vertex-importance-based approaches. Using a variety of real road networks with up to twenty million vertices, we evaluated each technique in terms of its preprocessing time, space consumption, and query efficiency (for both shortest path and distance queries). Our experimental results reveal the characteristics of different techniques, based on which we provide guidelines on selecting appropriate methods for various scenarios.