Jeffrey M. Jaffe

Algorithms for finding paths with multiple constraints

Let G = (V, E) be a graph with weight function w:E rightarrow Z+ and length function l:E /rightarrow Z+. The problem of determining for v1, V2 /in V whether there is a path from v1 to v2 with weight at most W and length at most L is NP-complete. This paper gives two approaches to meeting or approximating the length and weight constraints. The first approach is to use a pseudopolynomial-time algorithm which determines whether a path meets the constraints. Its running time is O (n5b log nb) where n = |V| and b is the largest length or weight. If tables with O (n3b) entries are kept then all instances of multiple constraints may be decided. Table size may be substantially decreased if one is willing to tolerate incorrect answers to rare instances. The algorithm is suitable for distributed execution. In the second approach, an objective function is defined which evaluates a paths distance from meeting the constraints. Polynomial-time algorithms attempt to find good paths in terms of the objective function. One algorithm is at most 1.62 times worst than optimal. A notion of “average worst-case behavior” is defined. The algorithms “average” behavior is 1.51 times worse than optimal.

A Responsive Distributed Routing Algorithm for Computer Networks

A new distributed algorithm is presented for dynamically determining weighted shortest paths used for message routing in computer networks. The major features of the algorithm are that the paths defined do not form transient loops when weights change and the number of steps required to find new shortest paths when network links fail is less than for previous algorithms. Specifically, the worst case recovery time is proportional to the largest number of hops h in any of the weighted shortest paths. For previous loop-free distributed algorithms this recovery time is proportional to h2.

Point-To-Multipoint Communication Over Broadcast Links

In this paper we study some link control protocols for use in point-to-multipoint communication over broadcast links. We concentrate on automatic repeat request protocols of the go-back- N type and define, analyze, and compare three such protocols. A major contribution of this paper is a relatively simple protocol which is easy to implement and performs very well under a wide range of conditions. Our analytical models show that this protocol performs considerably better than the other go-back- N protocols, particularly in environments with a large number of receivers.

Algorithms for Scheduling Tasks on Unrelated Processors

Several algorithms are presented for the nonpreemptlve assignment of n independent tasks to m unrelated processors One algorithm requires polynomial Ume in n and m and IS at most 2x/~ times worse than optimal in the worst case This is the best polynomial-time algorithm known for scheduling such sets of tasks. An algorithm with slightly better worst case performance requires polynomial time in n but exponential ume in m This 1s the best algorithm known that requires time O(nlogn) for every fixed value of m

SNA Networks of Small Systems

This paper discusses SNA/LEN, a possible extension of Systems Network Architecture intended to allow peer, dynamic, and easy to use networking functions for a variety of node sizes down to and including the new generation of personal computers. After reviewing the special requirements posed by small systems and the need for including them as equal partners in networks, the LEN architecture is described. This is done by following a sequence of steps that begin when a logical resource at some node that may not yet be part of the connectivity of an existing network requests a session with a remote logical resource of unknown location. After connectivity with the preexisiting network is established, directory services locates the remote object, route selection services determines the preferred path, a session is activated, and deadlock-free flow control assures a useful flow of data. Preliminary quantitative results from an LEN prototype are presented.

Establishing virtual circuits in large computer networks

Abstract Network routing algorithms generally attempt to provide communication between two nodes by sending data messages along the best or shortest path between them. Unfortunately, in large networks it is difficult to maintain knowledge of such path due to the cost in storage, computation, and communication bandwidth. In an attempt to solve this problem the technique of clustering has been proposed. Clustering generally reduces the cost of routing of by sacrificing optimality. Kamoun has shown that this sacrifice is asymptotically negligible under certain strong assumptions. In this paper we propose a new clustering technique which permits us to obtain optimal paths. However, determining these paths requires some effort and thus the methodology is appropriate only if the paths are then used for many messages in virtual circuit fashion. An application to planar networks gives a quantitative demonstration of obtaining optimal paths with reduced path determination cost.

Subtle design issues in the implementation of distributed, dynamic routing algorithms

Abstract The design of distributed, dynamic routing procedures is highly complex, due to the fact that it relies on cooperation among a number of independent processors located at the nodes of communication networks and the fact that a network may face arbitrary topological changes. As a result, many simple, intuitive, concepts that seem, at first glance, that they should result in correct algorithms do not work. This paper evaluates this theme by exploring a number of examples of this phenomenon. The conclusion is that one must be careful both in the overall design of a distributed algorithm, and in its detailed implementation. This also illustrates the importance of careful formal validation of such protocols, rather than informal, intuitive arguments.

SNA routing: past, present, and possible future

This paper reviews the evolution of routing mechanisms in IBMs Systems Network Architecture (SNA) since its inception in 1974 to the present. Routing mechanisms are related to changes in the application and communications environment. Also discussed are possible evolutionary paths that may be taken in the future to address the problems of large heterogeneous networks.

Local Distributed Deadlock Detection by Cycle Detection and Clusterng

A distributed algorithm for the detection of deadlocks in store-and-forward communication networks is presented. At first, we focus on a static environment and develop an efficient knot detection algorithm for general graphs. The knot detection algorithm uses at most O(n2+ m) messages and O(log (n)) bits of memory to detect all deadlocked nodes in the static network. Using the knot detection algorithm as a building block, a deadlock detection algorithm in a dynamic environment is developed. This algorithm has the following properties: It detects all the nodes which cause the deadlock. The algorithm is triggered only when there is a potential for deadlock and only those nodes which are potentially deadlocked perform the algorithm. The algorithm does not affect other processes at the nodes.

Route Setup with Local Indentifiers

The paper introduces a reliable distributed procedure for establishing and cancelling routes in a circuit-switched data network that uses local path identifiers (LPID). The procedure ensures that the route is set up properly unless a failure is encountered, data messages are delivered to their destinations unless they encounter a cancellation process and the route is cancelled, and all LPID entries are released after a failure or session completion.