Route Planning in Transportation Networks

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.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

Linear-Space Approximate Distance Oracles for Planar, Bounded-Genus, and Minor-Free Graphs

A (1 + eps)-approximate distance oracle for a graph is a data structure that supports approximate point-to-point shortest-path-distance queries. The most relevant measures for a distance-oracle construction are: space, query time, and preprocessing time. There are strong distance-oracle constructions known for planar graphs (Thorup, JACM'04) and, subsequently, minor-excluded graphs (Abraham and Gavoille, PODC'06). However, these require Omega(eps^{-1} n lg n) space for n-node graphs. We argue that a very low space requirement is essential. Since modern computer architectures involve hierarchical memory (caches, primary memory, secondary memory), a high memory requirement in effect may greatly increase the actual running time. Moreover, we would like data structures that can be deployed on small mobile devices, such as handhelds, which have relatively small primary memory. In this paper, for planar graphs, bounded-genus graphs, and minor-excluded graphs we give distance-oracle constructions that require only O(n) space. The big O hides only a fixed constant, independent of \epsilon and independent of genus or size of an excluded minor. The preprocessing times for our distance oracle are also faster than those for the previously known constructions. For planar graphs, the preprocessing time is O(n lg^2 n). However, our constructions have slower query times. For planar graphs, the query time is O(eps^{-2} lg^2 n). For our linear-space results, we can in fact ensure, for any delta > 0, that the space required is only 1 + delta times the space required just to represent the graph itself

Sampling-based Algorithms for Optimal Motion Planning

During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g., showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.Comment: 76 pages, 26 figures, to appear in International Journal of Robotics Researc

INTELLIGENT VISION-BASED NAVIGATION SYSTEM

This thesis presents a complete vision-based navigation system that can plan and follow an obstacle-avoiding path to a desired destination on the basis of an internal map updated with information gathered from its visual sensor. For vision-based self-localization, the system uses new floor-edges-specific filters for detecting floor edges and their pose, a new algorithm for determining the orientation of the robot, and a new procedure for selecting the initial positions in the self-localization procedure. Self-localization is based on matching visually detected features with those stored in a prior map. For planning, the system demonstrates for the first time a real-world application of the neural-resistive grid method to robot navigation. The neural-resistive grid is modified with a new connectivity scheme that allows the representation of the collision-free space of a robot with finite dimensions via divergent connections between the spatial memory layer and the neuro-resistive grid layer. A new control system is proposed. It uses a Smith Predictor architecture that has been modified for navigation applications and for intermittent delayed feedback typical of artificial vision. A receding horizon control strategy is implemented using Normalised Radial Basis Function nets as path encoders, to ensure continuous motion during the delay between measurements. The system is tested in a simplified environment where an obstacle placed anywhere is detected visually and is integrated in the path planning process. The results show the validity of the control concept and the crucial importance of a robust vision-based self-localization process

Lowest common ancestor interconnection networks

Lowest Common Ancestor (LCA) networks are built using switches capable of connecting u + d inputs/outputs in a permutation pattern. For n source nodes and I stages of switches, n/d switches are used in stage l - n/d - u/d in stage l - 2, and in general , n-u^l-i-l/d^l-i switches in stage i. The resulting hierarchical structure possesses interesting connectivity and permutational properties. A full characterization of LCA networks is presented together with a permutation routing algorithm for a family of LCA networks. The algorithm uses the network itself to collect and disseminate information about the permutation. A schedule of O(dp log_d/u n) passes is obtained with a switch set-up cost factor of O(log_d/u n) (p is the minimum number of passes that an algorithm with global knowledge schedules)

Re-designing Dynamic Content Delivery in the Light of a Virtualized Infrastructure

We explore the opportunities and design options enabled by novel SDN and NFV technologies, by re-designing a dynamic Content Delivery Network (CDN) service. Our system, named MOSTO, provides performance levels comparable to that of a regular CDN, but does not require the deployment of a large distributed infrastructure. In the process of designing the system, we identify relevant functions that could be integrated in the future Internet infrastructure. Such functions greatly simplify the design and effectiveness of services such as MOSTO. We demonstrate our system using a mixture of simulation, emulation, testbed experiments and by realizing a proof-of-concept deployment in a planet-wide commercial cloud system.Comment: Extended version of the paper accepted for publication in JSAC special issue on Emerging Technologies in Software-Driven Communication - November 201

Traffic Engineering in G-MPLS networks with QoS guarantees

In this paper a new Traffic Engineering (TE) scheme to efficiently route sub-wavelength requests with different QoS requirements is proposed for G-MPLS networks. In most previous studies on TE based on dynamic traffic grooming, the objectives were to minimize the rejection probability by respecting the constraints of the optical node architecture, but without considering service differentiation. In practice, some high-priority (HP) connections can instead be characterized by specific constraints on the maximum tolerable end-to-end delay and packet-loss ratio. The proposed solution consists of a distributed two-stage scheme: each time a new request arrives, an on-line dynamic grooming scheme finds a route which fulfills the QoS requirements. If a HP request is blocked at the ingress router, a preemption algorithm is executed locally in order to create room for this traffic. The proposed preemption mechanism minimizes the network disruption, both in term of number of rerouted low-priority connections and new set-up lightpaths, and the signaling complexity. Extensive simulation experiments are performed to demonstrate the efficiency of our scheme

Gozar: NAT-friendly Peer Sampling with One-Hop Distributed NAT Traversal

Gossip-based peer sampling protocols have been widely used as a building block for many large-scale distributed applications. However, Network Address Translation gateways (NATs) cause most existing gossiping protocols to break down, as nodes cannot establish direct connections to nodes behind NATs (private nodes). In addition, most of the existing NAT traversal algorithms for establishing connectivity to private nodes rely on third party servers running at a well-known, public IP addresses. In this paper, we present Gozar, a gossip-based peer sampling service that: (i) provides uniform random samples in the presence of NATs, and (ii) enables direct connectivity to sampled nodes using a fully distributed NAT traversal service, where connection messages require only a single hop to connect to private nodes. We show in simulation that Gozar preserves the randomness properties of a gossip-based peer sampling service. We show the robustness of Gozar when a large fraction of nodes reside behind NATs and also in catastrophic failure scenarios. For example, if 80% of nodes are behind NATs, and 80% of the nodes fail, more than 92% of the remaining nodes stay connected. In addition, we compare Gozar with existing NAT-friendly gossip-based peer sampling services, Nylon and ARRG. We show that Gozar is the only system that supports one-hop NAT traversal, and its overhead is roughly half of Nylon’s