Showing papers on "Static routing published in 1989"

A unified approach to loop-free routing using distance vectors or link states

Abstract: We present a unified approach for the dynamic computation of shortest paths in a computer network using either distance vectors or link states. We describe a distributed algorithm that provides loop-free paths at every instant and extends or improves algorithms introduced previously by Chandy and Misra, Jaffe and Moss, Merlin and Segall, and the author. Our approach treats the problem of distributed shortest-path routing as one of diffusing computations, which was first proposed by Dijkstra and Scholten. We verify the loop-freedom of the new algorithm, and also demonstrate that it converges to the correct routing entries a finite time after an arbitrary sequence of topological changes. We analyze the complexity of the new algorithm when distance vectors and link states are used, and show that using distance vectors is better insofar as routing overhead is concerned.

Comparison of deflection and store-and-forward techniques in the Manhattan Street and Shuffle-Exchange Networks

Abstract: The Manhattan Street Network (MS-Net) and Shuffle-Exchange Network (SX-Net) are two-connected networks with significantly different topologies. Fixed-size packets are transmitted between nodes in these networks. The nodes are synchronized so that all of the packets that are received by a node within a slot transmission time arrive at a switching point simultaneously. Instead of storing large numbers of packets at intermediate nodes, a deflection strategy similar to hot-potato routing is used. There are characteristics of the MS-Net that make it well suited for deflection routing. With no buffer, 55-70% of the throughput with an infinite number of buffers has been obtained; with a single buffer per node, the throughput increases to 80-90%. With uniform load the throughput does not decrease significantly as the network utilization increases. Therefore, additional flow control mechanisms are not required to achieve the highest network throughput. The SX-Net does not have the above characteristics of the MS-Net. However, deflection routing still provides a significant portion of the available throughput. In the SX-Net, more buffers are required than in the MS-Net, and a flow control mechanism must be used to achieve the greatest throughput. >

Compact distributed data structures for adaptive routing

Abstract: In designing a routing scheme for a communication network it is desirable to use as short as possible paths for routing messages, while keeping the routing information stored in the processors' local memory as succinct as possible. The efficiency of a routing scheme is measured in terms of its stretch factor - the maximum ratio between the cost of a route computed by the scheme and that of a cheapest path connecting the same pair of vertices.This paper presents a family of adaptive routing schemes for general networks. The hierarchical schemes H Sk (for every fixed k ≥ 1) guarantee a stretch factor of O (k2 · 3k) and require storing at most O (knk log n) bits of routing information per vertex. The new important features, that make the schemes appropriate for adaptive use, are applicability to networks with arbitrary edge costs;name-independence, i.e., usage of original names;a balanced distribution of the memory;an efficient on-line distributed preprocessing.

High Performance Communications In Processor Networks

Abstract: In order to provide an arbitrary and fully dynamic connectivity in a network of processors, transport mechanisms must be implemented, which provide the propagation of data from processor to processor, based on addresses contained within a packet of data. Such data transport mechanisms must satisfy a number of requirements - deadlock and livelock freedom, good hot-spot performance, high throughput and low latency. This paper proposes a solution to these problems, which allows deadlock free, adaptive, high throughput packet routing to be implemented on networks of processors. Examples are given which illustrate the technique for 2-D array and toroidal networks. An implementation of this scheme on arrays of transputers is described. The scheme also serves as a basis for a very low latency routing strategy named the mad postman, a detailed implementation of which is described here as well.

Expanders might be practical: fast algorithms for routing around faults on multibutterflies

Abstract: Simple deterministic O(log N)-step algorithms for routing packets on a multibutterfly are described. The algorithms are shown to be robust against faults, even in the worst case, and to be efficient from a practical point of view. As a consequence, the multibutterfly is shown to be an excellent candidate for a high-bandwidth, low-diameter switching network underlying a distributed-memory machine. >

Method and apparatus for providing a local area network bridge

Abstract: A communication bridge interconnecting two or more local area networks. Input buffers forward packet headers of received data packets through to a routing engine. The routing engine contains one or more routing tables each having a plurality of table locations containing table data in the form of station addresses and routing data. The table is accessed by applying a hashing algorithm to a received destination address contained in the data packet to determine the table location and then checking that the station address retrieved from the table location corresponds with the destination address in the received data packet.

An adaptive hierarchical routing protocol

Abstract: An adaptive hierarchical routing protocol based on the extension of the new Arpanet scheme is proposed and its simulated performance is presented. The protocol can adapt to rapidly changing environments and works for arbitrarily large networks. A number of existing schemes as well as the proposed scheme are simulated under many different environments and clustering structures. The proposed protocol is found to be superior to the other protocols tested in many different types of network traffic and topological configurations. The results indicate that intercluster links must be reliable, because (1) the failure of these links can significantly degrade the routing performance, even though the protocol does not degrade as badly as the existing scheme and (2) hierarchical routing protocols usually prefer small clusters, which means that there will be many intercluster links. The tradeoff between two conflicting performance criteria, response speed and communication overhead, is shown. >

An optimal shortest-path routing policy for network computers with regular mesh-connected topologies

Abstract: A probabilistic routing policy, the Z/sup 2/ (zigzag) routing policy, is presented within the class of nonadaptive, shortest-path routing policies for regular mesh-connected topologies such as n-dimensional toroids and hypercubes. The focus of the research is routing in networks of computers in a distributed computing environment, where constituent subcomputers are organized in a mesh-connected topology and communication among individual computers takes places by some form of message exchange. The authors prove the optimality of this policy with respect to two criteria: (1) maximizing the probability of reaching the destination from a given source without delays at intermediate nodes; and (2) minimizing the expected lifetime of a message. >

Compact distributed data structures for adaptive routing

Abstract: In designing a routing scheme for a communication network it is desirable to use as short as possible paths for routing messages, while keeping the routing information stored in the processors' local memory as succinct as possible. The efficiency of a routing scheme is measured in terms of its stretch factor - the maximum ratio between the cost of a route computed by the scheme and that of a cheapest path connecting the same pair of vertices.This paper presents a family of adaptive routing schemes for general networks. The hierarchical schemes H Sk (for every fixed k ≥ 1) guarantee a stretch factor of O (k2 · 3k) and require storing at most O (knk log n) bits of routing information per vertex. The new important features, that make the schemes appropriate for adaptive use, are applicability to networks with arbitrary edge costs;name-independence, i.e., usage of original names;a balanced distribution of the memory;an efficient on-line distributed preprocessing.

The Arc Oriented Location Routing Problem

Abstract: The location routing problem is concerned with locating depots and creating routes to service customers. In particular, location-allocation-routing (LAR) algorithms are designed to locate facilities, allocate customers to facilities and design the routes through these customers. In the literature, the typical location routing problem is a node oriented problem, where depots and customers are all represented by nodes and the routing is a node routing problem. In this paper, an Arc Oriented Location Routing Problem (AOLRP) is described, where the customers to be serviced are represented by arcs. Therefore, the allocation of customers to depots is an arc oriented problem as well as the resulting routing problem. An algorithm is presented for solving the AOLRP and computational results are given regarding parameter settings and performance of this algorithm.

Randomized Routing on Fat-Trees

Abstract: Fat-trees are a class of routing networks for hardwareefficient parallel computation. This paper presents a randomized algorithm for routing messages on a fat-tree. The quality of the algorithm is measured in terms of the load factor of a set of messages to be routed, which is a lower bound on the time required to deliver the messages. We show that if a set of messages has load factor λ = Ω(lg n lg lg n) on a fat-tree with n processors, the number of delivery cycles (routing attempts) that the algorithm requires is O(λ) with probability 1-O(1/n). The best previous bound was O(λ lg n) for the off-line problem where switch settings can be determined in advance. In a VLSI-like model where hardware cost is equated with physical volume, we use the routing algorithm to demonstrate that fat-trees are universal routing networks in the sense that any routing network can be efficiently simulated by a fat-tree of comparable hardware cost.

Excellerator: custom CMOS leaf cell layout generator

Abstract: A description is given of a program, Excellerator, which automatically generates full-custom symbolic CMOS cell layouts. The input is a transistor-level netlist with optimal constraints on layout shape and I/O port positions. The output is a high-quality virtual-grid-based layout suitable for use in a two-dimensional tiling methodology. I/O port locations can be optimized. Versatile support for different layout shapes and port locations makes this system ideal for use in a top-down, fully automatic physical design system. Transistor routing is provided by a novel, recursive version of the A-Star search procedure. This technique reduces the frequency and seriousness of routing blockages by finding near-optimal compromises between new connections and reroutes of previous connections. Routing occurs in two metal layers plus polysilicon and diffusion, and is easily extendable to any number of routing layers. Routing priority can be given to critical nodes. >

DTR: A Defect-Tolerant Routing Algorithm

Abstract: A new channel routing algorithm called DTR (Defect-Tolerant Routing) is investigated. This algorithm minimizes the total area and simultaneously maximizes the performance by reducing the critical area which can potentially be the source of logical faults caused by the bridging effects of spot defects. Experimental results show DTR produces less critical area than Yoshimura & Kuh's algorithm [1].

Linear complexity algorithms for hierarchical routing

Abstract: A hierarchical procedure for net routing on l*m*n grid-graphs, where l is the number of layers, m is the number of rows, and n is the number of columns, is presented. The hierarchy reduces the overall problem to a sequence of subproblems, where each subproblem works on an l*m'*n portion of the overall grid. For each subproblem, an initial constructive placement (CP) of as many nets as possible is used; then a generalized dynamic programming (DP) algorithm to solve the Steiner problem of an l*2*n grid-graph is used for any remaining nets. The CP procedure uses simplistic routing assumptions to route quickly as many nets as possible. If all nets are routed, the subproblem solution is (locally) optimal and the corresponding branch of the binary recursion tree generated by the hierarchy is pruned. For any unrouted nets, the generalized DP procedure is called to route each net, one at a time, with a run time complexity of O(K*n) where n is the number of columns and K is a function of the grid cross section and layer/wiring restrictions. There are no a priori layer restrictions or limitations on the number of layers used; three-layer cases and even some four-layer cases are feasible for the PYRAMID 90-X. >

Robust design and planning of a worldwide intelligent network

Abstract: The authors describe the structure of the worldwide intelligent network (WIN), describe methods for its design and planning, investigate the adequacy of decentralized control for problem-free worldwide call completion, explore the feasibility of adaptive routing and control concepts, discuss network robustness/reliability objectives, and describe a strategy for achieving these objectives for all cooperating international carriers. Several decentralized adaptive routing policies that are particularly attractive in the WIN environment and network performance improvements that can be achieved with the introduction of flexible routing capabilities are characterized. It is shown by example that network integration coupled with flexible routing and bandwidth allocation for preferential treatment of new services provides an effective approach for robust and economical new service provisioning. >

Administrative Domains and Routing Domains: A model for routing in the Internet

Abstract: This RFC proposes a model for describing routing within the Internet. The model is an adaptation of the "OSI Routeing Framework". This memo does not specify an Internet standard.

Upper and lower bounds for routing schemes in dynamic networks

Abstract: An algorithm and two lower bounds are presented for the problem of constructing and maintaining routing schemes in dynamic networks. The algorithm distributively assigns addresses to nodes and constructs routing tables in a dynamically growing tree. The resulting scheme routes data messages over the shortest path between any source and destination, assigns addresses of O(log/sup 2/n) bits to each node, and uses in its routing table O(log/sup 3/n) bits of memory per incident link, where n is the final number of nodes in the tree. The amortized communication cost of the algorithm is O(log n) messages per node. Also given are two lower bounds on the tradeoff between the quality of routing schemes (i.e. their stretch factor) and their amortized communication cost in general dynamic networks. >

On Global Wire Ordering for Macro-Cell Routing

Abstract: In an automatic routing system for macro-cell layout the wiring area is decomposed into a number of smaller regions These regions are routed separately by a detailed router such as a channel router or a switch-box router The position of the pins at the junction between two adjacent regions is usually determined by the detailed router The locality of this 'bottom-up' ordering disregards the global topologies of the nets which usually span several routing regions This may result in twisted wires, unnecessary vias and waste of area An algorithm to prevent twisted wires during detailed routing is presented A consistent order is determined for the junction pins which ensures that no unnecessary wire twisting is introduced If wires have to cross their intersection will preferably be placed in such a position that the chip area is least affected

A distributed routing algorithm for mobile radio networks

Abstract: The authors present a distributed routing protocol intended for use in networks where the rate of topological change is not so fast as to make 'flooding' the only possible routing method but not so slow as to make one of the existing protocols for a static topology applicable. The routing algorithm adapts asynchronously in a distributed fashion to arbitrary changes in topology in the absence of global topological knowledge. The protocol maintains a set of loop-free routes to each destination from any node that desires a route. The protocol's performance, measured in terms of end-to-end packet delay and throughput, is compared with that of pure flooding and an alternative algorithm that is well suited to the medium-rate topological change environment envisioned here. The results show that, when the rate of topological change becomes very high, flooding is preferable to the other alternatives. For lower rate of change, it appears that, when the effects of channel access are accounted for, the performance of the new algorithm is encouraging in that it has been generally superior to that of the alternative protocols. >

Optimal routing in circuit switched communication networks

Abstract: Consideration is given to the optimal circuit routing problem in an existing circuit-switched network. The objective is to find circuit routing which accommodates a given circuit demand while maximizing the residual capacity of the network. In addition, the cost of accommodating the circuit demand should not exceed a given amount. Practical considerations require that a solution be robust to the variations in circuit demand and cost. The objective function for the optimal circuit routing problem is not a smooth one. In order to overcome the difficulties of nonsmooth optimization, the objective function is approximated by smooth concave functions. The optimization algorithm for the circuit routing problem is obtained as a limiting case of the sequence of optimal routing strategies for the corresponding smooth convex optimization problems, and the proof of its convergence to the optimal solution is given. An approach to calculating the optimal multicommodity flow is presented. The optimization algorithm efficiently handles networks with a large number of commodities, satisfies the robustness requirements, and can be used to solve circuit routing problems for large networks. >

Distributed routing for load balancing

Abstract: Some open-loop and closed-loop control algorithms are discussed for an example of a discrete-event system, namely, the routing of arriving tasks from different arrival streams among several possible service stations. It is shown that it is possible to design open-loop policies that give good performance in a way which is very robust with respect to large changes in the arrival rates. This is possible even though it is assumed that there is no online coordination between the routing algorithms for the different arrival streams. Some further improvements of the performance are possible when a simple feedback policy, namely, overflow routing, is implemented. This also gives reasonable robustness of performance with respect to changes in the service rates. >

Robust algorithms for packet routing in a mesh

Abstract: This paper considers the problem of permutation packet routing on a √n×√n mesh-connected array of processors. Each node in the array is assumed to be independently faulty with a probability bounded above by a valuep. This paper gives a routing algorithm which, ifp⩽ 0.29, will with very high probability route every packet that can be routed inO(√n logn) steps with queue lengths that areO(log2n). Extensions to higher-dimensional meshes are given.

Multi-packet-routing on mesh connected arrays

Abstract: In this paper we study the problem of routing packets on an r-dimensional mesh-connected array of processors. The focus of this paper lies on routing with each processor containing exactly k packets, k > 2, initially and finally (so-called k-k-routing). For two-dimensional n x n grids the number of transport steps is at most ~kn + O(kn/f(n)) with a buffersize of O(kf(n)). In the special case of a sequence of k permutation routing problems this step count can be reduced to kn + O(kn/f(n)). For an r-dimensional cube, r > 3, with side length n the same technique yields an algorithm with step count [~] ( 2 r 2)n + O(kn/f(n) 1/(r-1)) and a buffer size of O(kf(n)). Furthermore it is shown that splitting large packets into smaller ones has benefits for permutation routing problems. 1 I n t r o d u c t i o n The performance of parallel computation is heavily influenced by the existence of fast data movement algorithms [AJP86]. In this area especially mesh connected processor arrays have drawn attention because of their simple interconnection and their easy scalability. A nl x . . . x n~ mesh connected array is a set mesh(n1,..., n~)of N = n l . . . n~ identical processors where each processor P = (pl,...,p~),O _< Pi _< ni 1, is directly connected to all its nearPermission 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 /o r specific permission. @ t989 A C M 0 8 9 7 9 1 3 2 3 X / 8 9 / 0 0 0 6 / 0 3 3 6 $1.50 est neighbours only. A processor Q = ( q l , . . . , q r ) is called nearest neighbour of P iff the manhattan distance between P and Q is 1 (d(P,Q) = Eir=l IPi -qi[)" The control structure of the grid of processors is assumed to be of the MIMD type (Multiple Instruction Multiple Data). That is, each processor has its own program memory, different processors can perform different instructions at the same clock period, there is a global clock, and each processor can send data only to its nearest neighbours during one clock period. Bidirectional communication can occur with all nearest neighbours in one clock cycle. Furthermore, each processor has only a limited number of registers for data (e.g. the buffer size is constant or log N). D e f i n i t i o n I (k -k p a c k e t r o u t i n g ) A k-k pakket routing problem is the problem of transporting k packets from each processor in the mesh to k destination processors. Each processor in the mesh sends and finally receives k packets. More formally a k-k routing problem is described by a (k+l) tuple (mesh, address],..., addressk ) where each addressi is a map from mesh to mesh and for all processors P in the mesh we have k Ei=~ ]address~-l(P)l = k. All the packets in address~-l(mesh) are said to lie in layer i. In the case of k = 1 address1 is a bijective func tion by definition and the problem is then called a permutation routing problem. This basic problem has been extensively studied in the literature. For n × n meshes some algorithms based on sorting only need 3n+O(low order) steps and a buffer*This research was supported by SIEMENS AG, Mfinchen, and by the Deutsche Forschungsgemeinschaft, Grant No. Ku 658/1-1.

A new responsive distributed shortest-path rounting algorithm

Abstract: Distributed shortest-path routing algorithms based on the Ford-Fulkerson method are simple to implement but they suffer from the cost-dependent looping problem: when link costs increase, routing table loops may form and convergence to correct paths may be too slow, depending on link costs. This problem can be eliminated if constraints are imposed on the order in which routing tables are updated at different nodes but the resulting internode protocols tend to be relatively complex. Furthermore, update constraints may restrict a node's ability to obtain alternate paths quickly in an environment where topology changes are frequent. In this paper, a new distributed shortest-path routing scheme based on the Ford-Fulkerson method is presented. Under the new scheme, each node uses partial topology information to eliminate the cost-dependent looping problem. No update constraints are imposed and no assumptions are made regarding link costs. In the worst case, the new scheme responds to link cost changes in O(D) update steps, where D is the diameter of the network after the occurrence of the changes.

Routing management in computer networks

Abstract: A communication system includes a plurality of machines 21-24, 30, 33-35, etc) having unique identifiers and interconnected by a network of message switching nodes (10-14, 40, etc). Each node includes a dynamic routing table containing a plurality of machine identifiers and, for each, the next place in the network where a message to that machine should be directed to. The system includes a Directory Information Base (DIB) which includes a machine listing. For each machine, the listing has an entry including attributes of the machine. The attributes include updating and routing information. The former identifies the parts of the system need to be be updated to maintain consistency if some part of the entry is changed, including in particular information as to which nodes require their dynamic routing tables to be updated in response to a change in that entry (as if the routing tables were part of the DIB). The latter gives node identifications and routes from those nodes to the potential receiving machines. The DIB includes updating means which, on a change in an entry, use the updating attribute of that entry to transmit updating information to the rest of the DIB, in a format defined for the whole of the DIB. Such information is thus also sent to the relevant nodes. Each node includes means for updating the routing table in response to such transmissions from the updating means, including format conversion means for converting such transmissions to the format of the routing table.

Convergence of gradient projection routing methods in an asynchronous stochastic quasi-static virtual circuit network

Abstract: The convergence of the gradient projection algorithms for optimal routing in virtual circuit data networks proposed by D.P. Bertsekas (1982) is studied. The routing model explicitly takes into account stochastic generation and termination of virtual circuits, distributed asynchronous routing updates, inaccurate flow measurement, and delays in forwarding control packets. The problem of assigning paths for incoming sessions (or virtual circuits) to implement the gradient projection algorithms is also studied. A metering rule based on deficiency in a desired number of virtual circuits is proposed and analyzed. It is shown that the proposed metering rule is better than a randomized rule in some sense. The gradient projection routing algorithms implemented either by the metering rule or the randomized rule are shown to converge to a neighborhood of a long-term optimal routing. >

Method for accessing data in a table and its application to the routing of data between remote stations

Abstract: The present invention relates to the accessing data in tables and its application to apparatus for providing a communication bridge interconnecting two or more local area networks (LAN). A LAN (1) is connected to another LAN 2 by means of a bridge generally designated by the numeral (3). Input buffers (11, 21) forward packet headers of received data packets through to a routing engine (5). The routing engine (5) contains one or more routing tables each having a plurality of table locations containing table data in the form of station addresses and routing data. The table is accessed by applying a hashing algorithm to a received destination address contained in the data packet to determine the table location and then checking that the station address retrieved from the table location corresponds with the destination address in the received data packet. If the table location is empty or the destination address does not match the station address, the data packet is forwarded to all interconnected LANs. Otherwise, the data packet is forwarded according to the retrieved routing data. Embodiments are described wherein the table locations are over-written by applying the hashing algorithm to the source address of a received data packet and writing in at the resultant table location the source address and routing information of the received data packet. A time stamp can also be written at this time so that obsolete data entries are not employed for routing.

Internet routing

Abstract: Comprising an estimated 60,000 hosts, the DARPA Internet is the largest existing internet. This paper traces the routing information protocols used by Internet gateways to build routing tables that define the paths datagrams traverse as they travel between end systems. We articulate the weaknesses and limitations of the most commonly used routing protocols, including RIP, GGP, and HELLO and examine how the protocols interact with each other and with EGP. Finally, we trace the evolution of routing as the Internet has grown from a single backbone (ARPANET) to its present inclusion of the ARPANET, Milnet, and NSFnet cross-country networks.