Showing papers on "Destination-Sequenced Distance Vector routing published in 1982"

Routing, merging and sorting on parallel models of computation

Abstract: A variety of models have been proposed for the study of synchronous parallel computation. We review these models and study further some prototype problems. We distinguish two classes of models, fixed connection networks and models based on a shared memory. Routing is the prototype problem for the networks. In particular, routing provides the basis for simulating the more powerful shared memory models. We show that a simple but important class of deterministic strategies (oblivious routing) is necessarily inefficient with respect to worst case analysis. Routing can be viewed as a special case of sorting and the existence of a deterministic O(logn) routing or sorting algorithm for an n processor fixed connection network remains open. However, if we consider the more powerful class of shared memory models, we are -&-ldquo;almost-&-rdquo; able to achieve such an efficient sort via Valiant's parallel merging algorithm. Within a spectrum of models, we show that log log n - log log r is asymptotically optimal for rn processors to merge two sorted lists of n elements.

An optimal control approach to dynamic routing in networks

Abstract: This paper explores the application of optimal control theory to the problem of dynamic routing in networks. The approach derives from a continuous state space model for dynamic routing and an associated linear optimal control problem with linear state and control variable inequality constraints. The conceptual form of an algorithm is presented for finding a feedback solution to the optimal control problem when the inputs are assumed to be constant in time. The algorithm employs a combination of necessary conditions, dynamic programming, and linear programming to construct a set of convex polyhedral cones which cover the admissible state space with optimal controls. An implementable form of the algorithm, along with a simple example, is presented for a special class of single destination networks.

A Distributed Routing Design for a Broadcast Environment

Abstract: In this paper, we will present the need for distributed network control in a packet radio environment, the criteria used for its evaluation, and an overview of the network algorithms chosen to maintain routing information and to route user traffic The routing algorithm, known as tiered rings, functions by building a distributed tree of shortest path routes to each packet radio in the network The information kept by each node grows only linearly as the network expands The design uses the radio channel efficiently by providing shortest path routing and by taking advantage of the information available in a broadcast environment

On Routing Two-Point Nets Across a Channel

Abstract: Many problems that arise in general channel routing manifest themselves in simpler situations. We consider connecting a set of n terminals on a line to another set on a parallel line across a rectangular channel. We show that in any solution to the problem that (almost) minimizes the width of the channel (i.e. the distance between the lines the terminals reside on), (i) a net may require as many as O(vn) jogs, (ii) no net routed from top to bottom need ever turn upward in the middle. We also present an efficient algorithm to obtain minimal jogging in river routing, and provide necessary and sufficient conditions for conflict cycle resolution. These and other results are presented in the context of a general survey on routing from a combinatorial complexity point of view.

A New Two-Dimensional Routing Algorithm

Abstract: A new heuristic algorithm for two-dimensional routing utilizing two distinct layers is described. It is assumed that all terminals are on the boundary of a rectilinear routing region with or without cutout sections. Terminals on vertical boundary segments are assumed to be on one layer and those on horizontal boundary segments are on the other layer. This algorithm finds all possible paths with minimum corners for a net and then chooses one of those paths by considering path length, the likelihood of blocking nets not yet routed, the usage of vacant tracks, and the necessity of going through an area expected to be congested. A dynamic data structure is maintained. If h and v are the numbers of horizontal and vertical tracks, n is the number of nets, and t is the number of terminals, then the storage requirement is o(hv) and the time complexity is o((t-n)hv). For h=23, v=64, n=47, and t=130 the storage required is 60K bytes and cpu time is 16 seconds. This algorithm is implemented in the C language on a VAX 11/780 under the Berkeley Unix (FOOTNOTE: Unix is a trademark of Bell Laboratories.) Operating system, as part of the LTX layout system of the layout aids group at Bell Laboratories, Murray Hill.

Optimal dynamic routing in communication networks with continuous traffic

Abstract: New characterizations of optimal state-dependent routing strategies are obtained for the continuous traffic network model proposed by A. Segall for linear cost with unity weighting at each node and for constant inputs. The concept of flow relaxation is introduced and is used to transform the optimal routing problem into an initial flow optimization problem with convex cost and linear constraints. Three algorithms are given for open-loop computation of the optimal initial flow. The first is a simple iterative algorithm based on gradient descent with bending and it is well suited for decentralized computation. The second algorithm reduces the problem to a series of max-flow problems and it computes the exact optimal initial flow in O(|N|4) computations where |N| is the number of nodes in the network. The third algorithm is based on a search for successive bottlenecks in the network.

On Routing for Custom Integrated Circuits

Abstract: This paper presents a novel and effective strategy for routing custom integrated circuits as well as solutions to subproblems associated with this strategy. Given an initial placement of rectangular blocks, the routing strategy includes the following major steps: construction of a channel graph, estimation of channel widths (based on a statistical model for signal nets and topological routing of power and ground nets), placement modification to include the estimated channel widths, topological routing for signal nets, and finally track assignment. Besides presenting an overview of our strategy, the following topics will be discussed in some detail: (1) necessary and sufficient conditions and a simple algorithm for single layer topological routing of power and ground nets, (2) a quadratic programming formulation for the placement modification problem, and (3) a fast algorithm for obtaining topological routes for signal nets.

Distributed multi-destination routing: The constraints of local information

Abstract: In computer networks, message routing is often accomplished by network nodes using local information. The unavailability of global information intuitively makes hard routing problems virtually impossible. This paper formalizes this intuition by examining a hard (NP-complete) routing problem, the problem of multi-destination routing. It is shown that with only limited information it is impossible to optimize network utilization for the multi-destination routing problem. Moreover, it is impossible to even approximate optimality to within a specified tolerance. Several versions of this result are proved; the versions differ in terms of the amount of information available at a node, and the extent to which the problem cannot be approximated.

A Minimum-Impact Routing Algorithm

Abstract: A routing heuristic is presented that routes two-terminal nets one at a time, for each net choosing the path so as to avoid adversely impacting the nets not yet routed. An algorithm is presented and proved to correctly implement this heuristic; the computational complexity of that algorithm is shown to be polynomially bounded, but perhaps still too great to be of practical use. Another, speedier algorithm is presented that seems to approximate the heuristic rather closely. Strong evidence is given that the Lee routing algorithm is in some sense inadequate to implement this heuristic. The heuristic has been applied, with very encouraging results, to a specific routing problem: the routing of a channel in which all four sides of the channel may contain terminals. This problem arises in the layout of custom VLSI.

An Analytical Method for Compacting Routing Area in Integrated Circuits

Abstract: An analytical method is proposed for solving a routing area compaction problem in building block integrated circuits. Related minimization is performed with a linear programming technique. Minimum channel dimensions are calculated for a preliminary routing; these dimensions are used to construct routing constraints. Placement constraints are added for the interrelations between placement and routing. This combined set of constraints leads to a least overestimation of routing area and under certain conditions guarantees routing feasibility. Computational complexity and existence of a solution are discussed.

The 1-2-3 routing algorithm or the single channel 2-step router on 3 interconnection layers

Abstract: In this paper an algorithm is presented for the single channel routing on 3 interconnection layers. First some general characteristics of routing on 3 interconnection layers are presented. Then the specifications are introduced of the routing problem on 3 interconnection layers that will be considered. Pins will be allowed to come out on both the diffusion/poly layer and the second metal layer with the routing done on both the first and second metal layer. If only the first metal layer was to be used horizontally then the routing problem could be solved by a simple left-edge channel algorithm. However the 1-2-3 algorithm presented here will solve identical problems with a smaller number of tracks and via's since it makes use of some specific characteristics of routing on 3 interconnection layers.

Two-Dimensional Channel Routing and Channel Intersection Problems

Abstract: A two-dimensional channel routing program for hierarchical IC layout with orthogonal building blocks of variable size and shape is presented. A two dimensional channel model and a one layer channel router are used. A detailed description of the routing scheme which avoids the generation of "switch box" problems is given. The behavior of the two-dimensional routing algorithm to single and coupled channel intersections is demonstrated.

Routing of telephone traffic to minimize network blocking

Abstract: The problem of optimum routing of telephone traffic to minimize network blocking is formulated for a class of routing schemes. The necessary conditions for minimum-blocking routing are shown to be analogous to conditions for minimum-delay routing in a store-and-forward data network. A method is described for calculating an optimum routing on the basis of centralized computational for the network. Owing to its computational complexity, however, the method is more useful for off-line studies than for real-time adaptive routing.

Distributed routing in computer communication networks

Abstract: This paper considers a class of simple distributed shortest-path routing algorithms first introduced in the ARPA Network with convergence for fixed cost functions proven by W.D. Tajibnapis. The basic algorithm has since been implemented in somewhat modified form by a number of operating networks as well as in some computer communication architectures. The basic algorithm, although simple to implement, is prone to loops and utilizes O(n3) control packets during its convergence mode. A so-called Predecessor algorithm is described that retains simplicity of implementation yet reduces the incidence of loops and the number of control packets generated. Comparative theoretical studies of the two algorithms are presented for full-duplex loop networks. Comparative performance results of the two algorithms for large networks, using computer experimentation, are presented as well.

A hierarchical scheme for multiobjective adaptive routing in large communication networks

Abstract: A novel two-level scheme for designing protocols for optimal traffic routing in large communication networks is presented. Major strong points of the scheme are: (i) it is adaptive to changes in load and network topology, (ii) permits consideration of multiple objective functions in performance optimization, and (iii) combines elements of flow control and routing for an effective control of traffic congestion.

A routing scheme for integrated networks

Abstract: A routing scheme using delay, bandwidth and reliability measures is presented, and flow control is partially included in the method. Decisions are distributed, and the routing tables at each node contain lists of non-dominated best paths to all other nodes. Two algorithms are presented for constructing the tables, and simulation results show that their overheads are comparable to those of existing algorithms. The routing scheme is suitable for integrated packet switched and circuit switched computer networks.