Gordon Wilfong

Bio: Gordon Wilfong is an academic researcher from Bell Labs. The author has contributed to research in topics: Graph (abstract data type) & Approximation algorithm. The author has an hindex of 40, co-authored 137 publications receiving 5687 citations. Previous affiliations of Gordon Wilfong include AT&T & Cornell University.

The stable paths problem and interdomain routing

Abstract: Dynamic routing protocols such as RIP and OSPF essentially implement distributed algorithms for solving the shortest paths problem. The border gateway protocol (BGP) is currently the only interdomain routing protocol deployed in the Internet. BGP does not solve a shortest paths problem since any interdomain protocol is required to allow policy-based metrics to override distance-based metrics and enable autonomous systems to independently define their routing policies with little or no global coordination. It is then natural to ask if BGP can be viewed as a distributed algorithm for solving some fundamental problem. We introduce the stable paths problem and show that BGP can be viewed as a distributed algorithm for solving this problem. Unlike a shortest path tree, such a solution does not represent a global optimum, but rather an equilibrium point in which each node is assigned its local optimum. We study the stable paths problem using a derived structure called a dispute wheel, representing conflicting routing policies at various nodes. We show that if no dispute wheel can be constructed, then there exists a unique solution for the stable paths problem. We define the simple path vector protocol (SPVP), a distributed algorithm for solving the stable paths problem. SPVP is intended to capture the dynamic behavior of BGP at an abstract level. If SPVP converges, then the resulting state corresponds to a stable paths solution. If there is no solution, then SPVP always diverges. In fact, SPVP can even diverge when a solution exists. We show that SPVP will converge to the unique solution of an instance of the stable paths problem if no dispute wheel exists.

Autonomous robot vehicles

Abstract: Contents: Guidance (Kinematics, Control, and Trajectory Generation.- Sensors.- Navigation (Position and Copurse Estimation).- Map Representation.- Sensing Strategies.- Motion Planning.- Systems.

An analysis of BGP convergence properties

Abstract: The Border Gateway Protocol (BGP) is the de facto inter-domain routing protocol used to exchange reachability information between Autonomous Systems in the global Internet. BGP is a path-vector protocol that allows each Autonomous System to override distance-based metrics with policy-based metrics when choosing best routes. Varadhan et al. [18] have shown that it is possible for a group of Autonomous Systems to independently define BGP policies that together lead to BGP protocol oscillations that never converge on a stable routing. One approach to addressing this problem is based on static analysis of routing policies to determine if they are safe. We explore the worst-case complexity for convergence-oriented static analysis of BGP routing policies. We present an abstract model of BGP and use it to define several global sanity conditions on routing policies that are related to BGP convergence/divergence. For each condition we show that the complexity of statically checking it is either NP-complete or NP-hard.

One-processor scheduling with symmetric earliness and tardiness penalties

Abstract: We consider one-processor scheduling problems having the following form: Tasks T1, T2,..., TN are given, with each Ti having a specified length li and a preferred starting time ai or, equivalently, a preferred completion time bi. The tasks are to be scheduled nonpreemptively i.e., a task cannot be split on a single processor to begin as close to their preferred starting times as possible. We examine two different cost measures for such schedules, the sum of the absolute discrepancies from the preferred starting times and the maximum such discrepancy. For the first of these, we show that the problem of finding minimum cost schedules is NP-complete; however, we give an efficient algorithm that finds minimum cost schedules whenever the tasks either all have the same length or are required to be executed in a given fixed sequence. For the second cost measure, we give an efficient algorithm that finds minimum cost schedules in general, with no constraints on the ordering or lengths of the tasks.

On the correctness of IBGP configuration

Abstract: The Border Gateway Protocol (BGP) has two distinct modes of operation. External BGP (EBGP) exchanges reachability information between autonomous systems, while Internal BGP (IBGP) exchanges external reachability information within an autonomous system. We study several routing anomalies that are unique to IBGP because, unlike EBGP, forwarding paths and signaling paths are not always symmetric. In particular, we focus on anomalies that can cause the protocol to diverge, and those that can cause a router's chosen forwarding path to an egress point to be deflected by another router on that path. Deflections can greatly complicate the debugging of routing problems, and in the worst case multiple deflections can combine to form persistent forwarding loops. We define a correct IBGP configuration to be one that is anomaly free for every possible set of routes sent by neighboring autonomous systems. We show that determination of IBGP configuration correctness is NP-hard. However, we give simple sufficient conditions on network configurations that guarantee correctness.

Random graphs

Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Planning Algorithms: Introductory Material

Abstract: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Voronoi diagrams—a survey of a fundamental geometric data structure

Abstract: Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer graphics, computer-aided design, robotics, pattern recognition, and operations research—give rise to problems that inherently are geometrical. This is one reason computational geometry has attracted enormous research interest in the past decade and is a well-established area today. (For standard sources, we refer to the survey article by Lee and Preparata [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner [1987bl.) Readers familiar with the literature of computational geometry will have noticed, especially in the last few years, an increasing interest in a geometrical construct called the Voronoi diagram. This trend can also be observed in combinatorial geometry and in a considerable number of articles in natural science journals that address the Voronoi diagram under different names specific to the respective area. Given some number of points in the plane, their Voronoi diagram divides the plane according to the nearest-neighbor

Exact robot navigation using artificial potential functions

Abstract: A methodology for exact robot motion planning and control that unifies the purely kinematic path planning problem with the lower level feedback controller design is presented. Complete information about a freespace and goal is encoded in the form of a special artificial potential function, called a navigation function, that connects the kinematic planning problem with the dynamic execution problem in a provably correct fashion. The navigation function automatically gives rise to a bounded-torque feedback controller for the robot's actuators that guarantees collision-free motion and convergence to the destination from almost all initial free configurations. A formula for navigation functions that guide a point-mass robot in a generalized sphere world is developed. The simplest member of this family is a space obtained by puncturing a disk by an arbitrary number of smaller disjoint disks representing obstacles. The other spaces are obtained from this model by a suitable coordinate transformation. Simulation results for planar scenarios are provided. >