Showing papers on "Static routing published in 1986"

The Torus Routing Chip

Abstract: The torus routing chip (TRC) is a self-timed chip that performs deadlock-free cut-through routing in k-ary n-cube multiprocessor interconnection networks using a new method of deadlock avoidance called virtual channels. A prototype TRC with byte wide self-timed communication channels achieved on first silicon a throughput of 64Mbits/s in each dimension, about an order of magnitude better performance than the communication networks used by machines such as the Caltech Cosmic Cube or Intel iPSC. The latency of the cut-through routing of only 150ns per routing step largely eliminates message locality considerations in the concurrent programs for such machines. The design and testing of the TRC as a self-timed chip was no more difficult than it would have been for a synchronous chip.

Alternate routing arrangement

Abstract: Improved alternate routing in a packet switching system is provided by inserting alternate routing control information into each packet and by storing alternate routing information at each network node. The stored information at each node includes a list of the available paths extending from the node towards all other nodes together with a list of available algorithms that can be used to select one of the available routes. The alternate routing control information in each packet contains postage information specifying the maximum number of nodes through which the packet is to travel. The alternate routing control information also includes a destination node index code identifying the destination node. The destination node index is used as address information by each node receiving a packet to read out the stored information at the node identifying the available paths and the algorithm to be used in selecting one of these paths for use in transmitting the packet towards the destination node. The identified algorithm is then executed to select the path to be used.

Torus routing chip

Abstract: A deadlock-free routing system for a plurality of computers ("nodes") is disclosed wherein each physical communication channel in a unidirectional multi-cycle network is split into a group of virtual channels, each channel of which has its own queue, one at each end. Packets of information traversing the same physical channel are assigned a priority as a function of the channel on which a packet arrives and the node to which the packet is destined. The packet's priority is always increasing as it moves closer and closer to its destination. Instead of reading an entire packet into an intermediate processing node before starting transmission to the next node, the routing of this invention forwards every flow control unit (flit) of the packet to the next node as soon as it arrives. The system's network is represented as a dependency graph, which graph is re-ordered to be cycle free. The resulting routing function of the cycle free channel dependency graph is rendered deadlock-free, and the system's cut-through routing results in a reduced message latency when compared under the same conditions to store-and-forward routing.

Distributed asynchronous optimal routing in data networks

Abstract: In this paper we study the performance of a class of distributed optimal routing algorithms of the gradient projection type under weaker and more realistic assumptions than those considered thus far. In particular, we show convergence to an optimal routing without assuming synchronization of computation at all nodes and measurement of link lengths at all links, while taking into account the possibility of link flow transients caused by routing updates. This demonstrates the robustness of these algorithms in a realistic distributed operating environment.

Near-Optimal n-Layer Channel Routing

Abstract: In this paper we present two n-layer channel routing algorithms that guarantee successful routing of the channel for n greater than three. The first is linear and optimal given a VHV...HV assignment of layers. The second, using an HVH...VH layer assignment, is quasilinear and performs optimally on examples from the literature. Except in pathological cases, we expect the latter router to perform within one row of optimal. For comparison with published examples we implemented the second router in five and three layers. The five-layer implementation routed all examples optimally while the three-layer implementation routed the examples with the same or fewer rows than the published examples. With its n-layer capability this channel router will allow channel routing to be used when more than three layers are available. This router can also be used to evaluate the utility of additional layers.

State-dependent routing for telephone traffic: Theory and results

Abstract: In the modern telephone network, it has become feasible to consider sophisticated call-routing schemes in order to minimize network blocking --- in particular, routing schemes which select a route for a call on the basis of the network 'state' at the time of call-arrival. In this paper, we construct an analytical model for such state-dependent routing in the framework of Markov decision processes, and derive a simple state-dependent routing scheme called 'separable' routing. The performance of this routing scheme in two network designs for a metropolitan network model is compared over a range of loads, by means of call-by-call simulations of traffic flow, with that of two other schemes: the 'sequential' routing used in the Dynamic Non-Hierarchical Routing (DNHR) network, and the 'Least-Loaded Routing' (LLR) proposed for the Trunk Status Map. In one case, separable routing achieves lower network blocking than the other schemes at normal load and overloads, while, in the other case, the improvement occurs only above a certain level of overload. However, a modified version of separable routing (to be presented in a future paper) achieves better performance than the other schemes in both networks over the entire range of loads.

Solution Improvement Heuristics for the Vehicle Routing and Scheduling Problem with Time Window Constraints

Abstract: SYNOPTIC ABSTRACTBranch exchange techniques, such as the well-known 2-opt and 3-opt procedures, are among the most powerful heuristics available for the solution of the classic vehicle routing problem. The imposition of time window constraints on customer delivery time within the vehicle routing problem, however, introduces several complexities that can reduce the power of these techniques. In this paper, two test data sets for the vehicle routing and scheduling problem with time window constraints are studied. Initial solutions are obtained using a variety of heuristics. These solutions are then improved using branch exchange procedures modified to incorporate the time window constraints.

Traffic routing and automatic network management system for telecommunication networks

Abstract: An adaptive, tariff dependent traffic routing system, which controls routing of traffic and performs management of network resources in multi-node telecommunication networks, where the cast for a communication depends on the type of service provided and on the distance between the originating node and the destination. Each node can originate traffic, receive and/or transmit traffic over inter-node trunks. The system is realized by means of a central computer, which has connections to the Stored Program Control (SPC) nodes of the network over two-way data links. The computer has access to data stored in the computer's memory, containing the actual distance- and service sensitive tariffs applied in the network. By freqent scanning of the network, the computer has a global view of the actual out-of-service and traffic load status in the nodes and in the different trunk groups. Based on the tariffs and on the global network status view the system determines the policy for routing traffic in the network, such that the revenue is maximized. When determining the routing decisions, the out-of-service and overloaded network equipment is automatically by-passed. Similarly, traffic to out-of-service, overloaded, or hard-to-reach destinations is not allowed to enter the network. The same applies to traffic destined to access-restricted nodes. The routing policy is transmitted to the SPC nodes in terms of routing instructions, specific for each originating node and each destination as well as specific for each type of services. Since new instructions are issued after each network scanning, these will vary with the actual traffic and out-of-service situation in the network. In this way an adaptive, revenue maximizing traffic routing and network management system is achieved.

Mighty: a rip-up and reroute detailed router

Abstract: For the macro-cell design style and for routing problems where the routing regions are irregular, two dimensional routers are often necessary. In this paper a new routing technique that can be applied for general two-layer detailed routing problems including switch boxes, channels and partially routed areas, is presented. The routing regions that can be handled are very general: the boundaries can be described by any rectilinear chains and the pins can be on the boundaries of the region or inside it, the obstructions can be of any shape and size. The technique is based on an algorithm that routes incrementally and intelligently the nets in the routing region and allows modifications and rip-up of nets that may impede the complete routing of other nets. The modification steps (also called weak modification) push some segments of nets already routed to make room for a blocked net. The rip-up and re-route steps (called strong modification), remove segments of nets already routed to make room for a blocked connection and is invoked only if weak modification fails. The algorithm is rigorously proven to complete in finite time and its complexity is analyzed. Many test cases have been run and on all the examples known in the literature the router has performed as well or better than existing algorithms. In particular, the Burstein's difficult switch box example has been routed using one less column than the original data. In addition, the router has routed difficult channels such as Deutsch's in density and has performed better than or as well as YACR-II in all the channels available to us. REFERENCES

Computer Networks with Compact Routing Tables

Abstract: The routing problem in computer networks is traditionally solved by providing detailed routing information for all destinations at every node We consider the problem of routing messages with only a small amount of information at every node For example, for every connected N-node network a scheme can be devised such that every message can be routed within O(√N) routing decisions Improving on an observation of Santoro & Khatib [3] for trees we derive a general method of routing messages in arbitrary networks using tables of a size corresponding to the number of links at a node, while utilizing all links in the network

WEAVER: A Knowledge-Based Routing Expert

Abstract: WEAVER, a channel/switchbox knowledge-based routing program, simultaneously considers all the important routing metrics including 100 percent routability, minimum routing area, minimum wire length, and the minimum number of vias. It allows prerouted nets and user interaction throughout the entire routing process, while relaxing the unnecessary contraints of assigning different directions?constraints imposed by all of the current channel and switchbox routers. A grid-based router using two interconnection layers, WEAVER can be easily expanded to route any shape routing area such as T or +. Implemented in OPSS, a production system language, WEAVER routinely produces routings requiring less area than routers that focus on a single routing metric.

Near-optimaln-layer channel routing

Abstract: In this paper we present two n-layer channel routing algorithms that guarantee successful routing of the channel for n greater than three. The first is linear and optimal given a VHV...HV assignment of layers. The second, using an HVH...VH layer assignment, is quasilinear and performs optimally on examples from the literature. Except in pathological cases, we expect the latter router to perform within one row of optimal. For comparison with published examples we implemented the second router in five and three layers. The five-layer implementation routed all examples optimally while the three-layer implementation routed the examples with the same or fewer rows than the published examples. With its n-layer capability this channel router will allow channel routing to be used when more than three layers are available. This router can also be used to evaluate the utility of additional layers.

Vehicle Routing with Time-Window Constraints

Abstract: (1986). Vehicle Routing with Time-Window Constraints. American Journal of Mathematical and Management Sciences: Vol. 6, Vehicle Routing with Time-Window Constraints: Algorithmic Solutions, pp. 251-260.

Reducing Routing Overhead in a Growing DDN

Abstract: The Defense Data Network (DDN), based on ARPANET technology, is expanding rapidly. One segment of the DDN, the MILNET, will include 250 packet switching nodes by the end of 1987 and as many as 700 by 1991. One obstacle that must be overcome to allow this growth is the overhead associated with the current ARPANET dynamic routing mechanism. Both link utilization due to routing updates and routing computational load are roughly proportional to network size. This paper presents three approaches to reducing routing overhead and includes both modifications to the existing routing scheme and a design for a hierarchical extension.

The Routing Problem in Computer Networks

Abstract: Few problems in the field of computer communication networks have received as early and extensive attention as the routing problem. The reason for this is twofold. First there have been numerous studies of flow problems in network theory that provide a basis for modeling the routing problem in a mathematically tractable way and, second, routing has proved to be a necessary and fundamental design choice for the operation of message- or packet- switched networks. In its simplest form the statement of the routing problem is as follows. Consider, as in Figure 12.1, a node that receives messages from an incoming link and has a choice of forwarding them via one of two outgoing links.

Optimal message routing without complete routing tables

Abstract: 1. I n t r o d u c t i o n A basic activity in a distributed network is the routing of messages between pairs of nodes. Assuming a cost function on the edges of the network, it is desirable that the routing of each message be along a shortest path. A straightforward approach is to maintain a complete routing table at each of the n nodes, which gives for each potential destination the name of the next node on a shortest path to the destination. This approach * This research was supported in part by the National Science Foundation under grant DCR-8320124. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specfic permission. requires that n 1 items of routing information be stored at each node in the network, with each item being a node name. If the network is dense and of irregular topology, then one would not expect to be able to do appreciably better spacewise than using complete routing tables. However, for sparse networks, is it possible to maintain o(n 2) items of routing information in the network and still achieve shortest path routings? We examine this question in the context of being free to assign logn-bit names to the nodes. We present a node naming and routing scheme that can handle broad classes of networks with arbitrary nonnegative costs on the edges. The scheme groups networks, starting with the class of outerplanar networks, into a natural hierarchy based on the amount of space devoted to storing routing information. Shortest path routing schemes for tree and unit-cost ring networks have been presented in [SKI and later in [vLT1]. The nodes are assigned names from 1 to n, and the end of every edge {v, w} incident with any node v is labelled with a subinterval of [1,hi. The interval represents the set R.,~ of nodes such that there is a shortest path from v to each node in Rv,w with the first edge on this path being {v, w}. In [vLW2] interval labelling schemes are also given for certain highly regular networks with edges of unit cost, including complete graphs, complete bipartite graphs, and grids. We first give an interval labelling scheme for outerplanar networks with arbitrary nonnegative costs on the edges. The scheme stores just d + 1 items of routing information at every node v, of degree d. Thus O(n) items of routing information are stored in total. For arbitrary nonnegative © 1986 ACM 0-89791-198-9/86/0800-0088 75¢ as edge costs, we show that the outerplanar graphs are precisely the graphs for which such an interval property holds. Furthermore we establish a very nice 'reflection' property of outerplanar graphs. Using this property we are able to generate an optimal algorithm for determining the labels of all edges. In [vLT2] a k-interval labelling scheme is proposed, in which each edge is labeled with up to k intervals. It is shown in [vLT2] that a grid with rowand column-wraparound and unit costs has an optimal 2-interval labelling. We present an incomparable but still stronger result, in that it is applicable to graphs with arbitrary nonnegative edge costs. We show that k-interval labelling schemes, for k > 1, can handle classes of graphs much richer than the class of outerplanar graphs. In particular, we establish that any graph that can be embedded in the plane such that all but q of the vertices are on p faces has a [(3p + q)/2J-interval property. Alternatively, the number of items of routing information required at a node of degree d is at most 3p+q+d-2. If the p faces form s connected components, we show that the graph has a [(2p + s + q)/2J-interval labelling, with a total of at most 2p+ s + q+ d 2 intervals at any node. Our approach can also be applied to graphs that can be embedded on a surface of positive genus g. We show that such graphs possess a [ (2p+ s + q + 4g)/2J-interval labelling, and use a total of at most 2p + s + q + 4g + d 2 intervals at any node. In addition, our labelling scheme can be adapted naturally to planar graphs in which we wish to route messages to vertices on only a selected subset of the faces. This technique can then be applied in a scheme for near-shortest path routings in general planar graphs IF J]. 2. R o u t i n g in o u t e r p l a n a r n e t w o r k s We first summarize the interval routing method presented in [SKI for trees and rings. Assume that the nodes are named in an appropriate manner with the integers from 1 to n. Let v be any node, and let the degree of v be d. Each edge incident with v is labelled by an interval, with the intervals from all edges incident with v forming a partition of [1, hi v. Wraparound is allowed in the intervals. For instance, the interval [ i , j ) , i > j , contains { i , i+ 1, . . . ,n, 1 , . . . , j 1}. Denote the intervals by [li, l~+x), for i = 1, 2 , . . . , d, where ld+l = v. Without loss of generality, assume that interval [/,,/,+1) labels edge {v,w,}. The values li, i = 1 ,2 , . . . ,d, are stored in a table at node v, each with a pointer to associated edge {v, wi). When a message arrives at node v, if its destination u is not equal to v, then the table is searched for the entry li such that li _< u < li+l. The message is then sent out on edge {v, wi). Since the values li, i = 1, 2 , . . . , d + 1 form a rota ted list [MS, F2], the table can be searched in O(log d) time using a modified binary search. The interval labelling method also works for outerplanar networks if the nodes are named appropriately. An outerplanar network is a network that can be embedded in the plane such that all nodes lie on one face [H]. Throughout the paper, we consider outerplanar networks in the context of such an embedding, called an outerplane embedding. We assign as names to the nodes the integers from 1 to n in consecutive order starting at an arbi trary node and proceeding clockwise around the exterior face. If any node v is visited more than once in this traversal, i.e., v is an articulation point of the network, then v may be named on any one of the visits. We call such a naming of the nodes a suitable node naming. An outerplanar network with a suitable node naming is shown in Figure 1. We first show that for any assignment of costs to edges, each end of every edge can be labelled with an interval such that routing is along shortest paths. Such a labelling of the edges of the network of Figure 1 is shown

An optimal adaptive routing algorithm

Abstract: An adaptive routing algorithm for packet-switched networks is proposed. This algorithm updates both the estimate of external traffic input and the routing assignments at each iteration. The routing assignments determine the proportions of the traffic destined for node j to be sent from node i through the outgoing links of i . The algorithm maintains the loop freedom of the routing assignment at each iteration. It also achieves the minimum delay of the network as the limit of its successive updating procedure. The additional features of the algorithm are that it allows at any iteration some routing assignments which theoretically induce infinite delay and that it may utilize variable scaling factors to speed up the convergence.

Proposed Routing Algorithms for the U.S. Army Mobile Subscriber Equipment (MSE) Network

Abstract: The US Army Mobile Subscriber Equipment (MSE) Network consists of a large number of geographically dispersed, mobile radio terminals which require secure communications The network is also subject to attacks by the enemy In this paper, we propose and analyze alternative network routing algorithms for the MSE

Continuous routing and batch routing on the hypercube

Abstract: In this paper we study two related routing problems on the n-dimensional hypercube: continuous routing, referring to the infinite routing process in which one new permutation is generated every constant r time steps, and batch routing, in which n permutations axe to be routed at the same time. We show that continuous routing with suitable value of r is feasible by giving a probabilistic routing algorithm that guarantees an 0 (n) completion time for any given permutation with overwhelming probability. The proof relies heavily on a probabilistic batch routing algorithm that has an 0 (n) completion time - an improvement over Valiant's classical 2-phase probabilistic routing algorithm when routing n permutations at the same time.

Optimal routing in circuit-switched communication networks

Abstract: We consider the optimal circuit routing problem. The problem consists of accommodating a given circuit demand in an existing circuit-switched network. The objective is to find a circuit accommodation providing the maximum residual capacity over the network under the total circuit cost constraints. Practical considerations require a solution which is robust to the variations in circuit demand and cost. The objective function for the circuit routing problem is not a smooth one. In order to overcome the difficulties of nonsmooth optimization, a sequence of smooth convex optimization problems is considered. The optimal algorithm for the circuit routing problem is obtained as a limiting case of the sequence of the optimal routing strategies for the corresponding smooth optimization problems. The proof of its convergence to the optimal solution is given. This optimization algorithm is capable of efficiently handling networks with a large number of commodities. It also satisfies the above-mentioned robustness requirements. Numerical results are discussed.

An Industrial World Channel Router for Non-Rectangular Channels

Abstract: In this paper, we discuss a number of important issues that we faced designing a router in the industrial environment. We present a channel router that addresses these issues. It can route rectilinear channels with variable channel height, and it can handle channels with pre-routed buses. Pins can come in from all four sides of the channel and the sequence of the side pins is maintained after routing. Usually, it uses two routing layers and it can use a third routing layer if needed. The basic algorithm is simple but effective to give good results. It routed the Deutsch Difficult Example in density. In routing uneven channels, it routed them with the number of tracks smaller than the channel density. The number of vias used and the total wire length are comparable with the best results in the literature. The router is fully functional and has been used in routing a number of real world integrated circuits.

Control and management of large and dynamic networks

Abstract: Dynamic networks are computer networks whose links and nodes could fail and recover frequently. The nodes may also be mobile. Large dynamic networks are dynamic networks of large size and they are clustered as hierarchical networks. The objective of this research task is to design a mechanism to support nodes to communicate with each other. To communicate with each other, the nodes would first have to know the names of other nodes, then their addresses, and finally the routes. Thus, the network should provide two mechanisms to supports the communications: binding of names of nodes with their addresses, and binding of address of nodes to the routes dynamically. The first problem, i.e. bind the names of nodes with their addresses, is usually called the naming or addressing problem. The second problem, i.e. binding the addresses with the corresponding routes, is conventionally called the routing problem. In this dissertation, we will discuss techniques to handle both problems. We first discuss techniques for the routing problem. As the network is assumed to be very large and dynamic, we concentrate our effort in developing hierarchical routing algorithms. A new adaptive hierarchical routing algorithm is proposed. The algorithm is based on the extension of the new Arpanet algorithm. The algorithm is good for both updating and initialization the routing tables. Based on the data structure stored at each node, we proposed a classification of adaptive hierarchical routing algorithms. We further evaluate all the adaptive hierarchical routing algorithms based on the proposed classification. We then proposed techniques to dynamically bind the names of nodes with their addresses. It is expected the techniques proposed in this dissertation would be very useful to assists nodes in large and dynamic computer networks to communicate reliably. (Abstract shortened with permission of author.)

Deterministic Routing to Buffered Channels

Abstract: Consider n exponential transmission channels which transmit information with different rates. Every channel has a buffer which is capable of storing an unlimited number of messages. A new message first arrives at the controller, which immediately routes it to one of the channels according to an infinite deterministic routing sequence. A cost per unit of staying time is charged in each of the channels (channel dependent cost), and the long-run average staying cost is taken as the cost criterion. For every n and a Poisson arrival process, a lower bound to the cost is found and a new routing policy, the golden ratio policy, is presented and its cost is evaluated. It is shown that for a variety of system parameters, the golden ratio routing policy has a cost close to the lower bound.

A New Routing Algorithm and Its Hardware Implementation

Abstract: Presented is a new parallel processing wire routing algorithm that can control path quality in two point connections and find a quasi-minimum Steiner tree for multi-point connections. A parallel rip-up technique for finding a candidate path which blocks an unconnected net is also presented. These routing algorithms are implemented on a two-dimensional array processor, the AAP-1. It is experimentally shown that the average AAP-1 execution time per net using the routing algorithm is 100 msec in a 256X256 grid.

Algorithms for Global Routing

Abstract: This paper presents several algorithms for global routing, including a very fast shortest path connection algorithm based on wave propagation and diffraction, a heuristic minimum tree algorithm using 'Common Edge' analysis, an overflow control method, and global rerouting treatment. These algorithms have been implemented in C and very good experimental results have been obtained.