Showing papers on "Equal-cost multi-path routing published in 1994"

Packet routing and job-shop scheduling in O (congestion+dilation) steps

Abstract: In this paper, we prove that there exists a schedule for routing any set of packets with edge-simple paths, on any network, inO(c+d) steps, wherec is the congestion of the paths in the network, andd is the length of the longest path. The result has applications to packet routing in parallel machines, network emulations, and job-shop scheduling.

Photonic packet switches: architectures and experimental implementations

Abstract: Photonic packet switches offer high speed, data rate and format transparency, and flexibility required by future computer communications and cell-based telecommunications networks. In this paper, we review experimental progress in state-of-the-art photonic packet switches with an emphasis on all-optical guided-wave systems. The term all-optical implies that the data portion of a packet remains in optical format from the source to the destination. While the data remain all-optical, both optical and optoelectronic techniques have been used to process packet routing functions based on extremely simple routing protocols. An overview of the design issues for all-optical photonic packet switching is given and contrasted with electronic packet switch implementations. Low-level functions that have been experimentally implemented include routing, contention resolution, synchronization, and header regeneration. System level demonstrations, including centralized photonic switching and distributed all-optical multihop networks, will be reviewed. >

A Necessary and Sufficient Condition for Deadlock-Free Adaptive Routing in Wormhole Networks

Abstract: Deadlock avoidance is a key issue in wormhole networks. A first approach [8] consists of removing the cyclic dependencies between channels. Although this is a necessary and sufficient condition for deadlock-free deterministic routing, it is only a sufficient condition for deadlock-free adaptive routing. A more powerful approach [12] only requires the absence of cyclic dependencies on a connected channel subset. The remaining channels can be used in almost any way. In this paper, we propose a necessary and sufficient condition for deadlock-free adaptive routing. This condition is the key for the design of maximally adaptive routing algorithms with minimum restrictions. Some examples are given, showing the application of the new theory. In particular, we propose a partially adaptive routing algorithm for k-ary n-cubes which doubles the throughput without increasing the hardware complexity significantly.

EIGRP--A Fast Routing Protocol based on Distance Vectors - eScholarship

Abstract: EIGRP{A FAST ROUTING PROTOCOL BASED ON DISTANCE VECTORS Bob Albrightson Cisco Systems Menlo Park, CA 94025 albright@cisco.com J.J. Garcia-Luna-Aceves University of California Santa Cruz, CA 95064 jj@cse.ucsc.edu Joanne Boyle Cisco Systems Menlo Park, CA 94025 boyle@cisco.com Abstract Early routing protocols were based on distance vectors; they were very simple and easy to implement but had the severe drawbacks of counting to innity and routing loops. These problems were reduced using such techniques as split horizon and hold-downs; however, for these techniques to work in practice, long convergence times are introduced. Routing protocols based on link states have been implemented to address the problem of slow convergence in distance-vector protocols, but they add complexity in conguration and troubleshooting. We present a new distance-vector protocol that converges as quickly as current link-state protocols, while maintaining loop freedom at every instant. The protocol is based on three main elements: a transport algorithm that supports the reliable exchange of messages among routers, the diusing update algorithm, which computes shortest paths distributedly, and modules that permit the operation of the new routing protocol in a multiprotocol environment. 1 INTRODUCTION Today's intradomain routing protocols can be classied as distance-vector or link-state protocols. In a distance-vector protocol, a router knows the length of the shortest path from each neighbor node to every network destination, and uses this information to compute the shortest path and next router in the path to each destination. A router sends update messages to its neighbors, who in turn process the messages and send messages of their own, if needed. Each update message contains a vector of one or more entries, each of which species, as a minimum, the distance to a given destination. In contrast, in a link-state protocol a router must receive information about the entire topology to compute the shortest path to each destination using a local shortest-path algorithm such as Dijkstra's algorithm [1]. Each router broadcasts update messages, containing the state of each of the router's adjacent links, to every other router in the network. The distance vector protocols used in the Internet thus far are based on variants of the distributed Bellman-Ford algorithm (DBF) for shortest-path computation [1]. The primary disadvantage of DBF is that incorrect entries in routing tables may form routing-table loops for one or more destinations whenever link costs increase [9]. Because a router chooses as its successor to a destination any neighbor router who appears to oer the shortest path to that destination, the router may choose paths that lead to loops for as long as those neighbor routers with viable paths to the destination oer path lengths longer than those paths leading to loops. The worst case of this problem is rather severe: when routers fail or the network partitions, a router can detect such events only after it has considered all possible path lengths to the one or more destinations that have become unreachable through any of its neighbors. Accordingly, this

Adaptive deadlock- and livelock-free routing with all minimal paths in torus networks

Abstract: This paper consists of two parts. In the first part, two new algorithms for deadlock- and livelock-free wormhole routing in the torus network are presented. The first algorithm, called Channels, is for the n-dimensional torus network. This technique is fully-adaptive minimal, that is, all paths with a minimal number of hops from source to destination are available for routing, and needs only five virtual channels per bidirectional link, the lowest channel requirement known in the literature for fully-adaptive minimal worm-hole routing. In addition, this result also yields the lowest buffer requirement known in the literature for packet-switched fully-adaptive minimal routing. The second algorithm, called 4-Classes, is for the bidimensional torus network. This technique is fully-adaptive minimal and requires only eight virtual channels per bidirectional link. Also, it allows for a highly parallel implementation of its associated routing node. In the second part of this paper, four worm-hole routing techniques for the two-dimensional torus are experimentally evaluated using a dynamic message injection model and different traffic patterns and message lengths. >

Compressionless routing: a framework for adaptive and fault-tolerant routing

Abstract: Compressionless Routing (GR) is a new adaptive routing framework which provides a unified framework for efficient deadlock-free adaptive routing and fault-tolerance. CR exploits the tight-coupling between wormhole routers for flow control to detect potential deadlock situations and recover from them. Fault-tolerant Compressionless Routing (FCR) extends Compressionless Routing to support end-to-end fault-tolerant delivery. Detailed routing algorithms, implementation complexity and performance simulation results for CR and FCR are presented.CR has the following advantages: deadlock-free adaptive routing in torus networks with no virtual channels, simple router designs, order-preserving message transmission, applicability to a wide variety of network topologies, and elimination of the need for buffer allocation messages. FCR has the following advantages: tolerates transient faults while maintaining data integrity (nonstop fault-tolerance), tolerates permanent faults, can be applied to a wide variety of network topologies, and eliminates the need for software buffering and retry for reliability. These advantages of CR and FCR not only simplify hardware support for adaptive routing and fault-tolerance, they also can simplify communication software layers.

Performance Evaluation of Adaptive Routing Algorithms for k-ary-n-cubes

Abstract: Deadlock avoidance is a key issue in wormhole networks. A first approach [9] consists in removing the cyclic dependencies between channels. Although the absence of cyclic dependencies is a necessary and sufficient condition for deadlock-free deterministic routing, it is only a sufficient condition for deadlock-free adaptive routing. A more powerful approach [12] only requires the absence of cyclic dependencies on a connected channel subset. Moreover, we proposed a necessary and sufficient condition for deadlock-free adaptive routing [15].

Efficient fully adaptive wormhole routing in n-dimensional meshes

Abstract: An efficient fully adaptive wormhole routing algorithm for n-dimensional meshes is developed. The routing algorithm provides full adaptivity at a cost of one additional virtual channel per physical channel irrespective of the number of dimensions of the network. The algorithm is based on dividing the network graph into two acyclic graphs that contain all of the physical channels in the system. Virtual channels are classified as either waiting or nonwaiting channels. Busy channels that a message waits for to become available are classified as waiting channels, otherwise they are classified as nonwaiting channels. Thus, a message considers nonwaiting channels first to reach its destination. If all non-waiting channels are busy, the message considers waiting channels. Messages acquire waiting channels in two phases. In each phase, waiting channels belonging to one acyclic network graph are traversed. This 2-phase routing algorithm could be either minimal or nonminimal. However, we concentrate on minimal routing. It is demonstrated that this adaptive routing algorithm can utilize the virtual paths (channels) between any two nodes more efficiently than any of the present algorithms with the same hardware requirement. >

Multicast routing in self-routing multistage networks

Abstract: The authors present a study on multicast routing algorithms for the self-routing multistage networks. This work is based on the use of the cube concept which consists of a group of outlets reachable in one pass through the network. A multicast connection is decomposed into associated cubes such that each cube can be self-routed through the network. The context of this work is a recursive scheme for multistage network where the outlets are fed back to the inlets through external links. Three routing algorithms are proposed. The emphasis is on evaluating the performance of those algorithms in terms of two metrics. Extensive results from analysis and simulations are given to derive insights into the performance of the proposed routing algorithms. >

MDP routing in ATM networks using virtual path concept

Abstract: The virtual path (VP) concept has been proposed to simplify traffic control and resource management in future B-ISDN. In particular, call setup processing can be significantly reduced when resources are reserved on VPs. However, this advantage is offset by a decrease in statistical multiplexing gains of the networks. The focus of this paper is on how to improve bandwidth efficiency through adaptive routing when capacity is reserved on all VPs. The authors first examine two VP capacity reservation strategies. They then design and evaluate computationally feasible Markov decision process-based routing algorithms and show that the network blocking probability can be significantly reduced by MDP routing. >

Optimum routing of multicast streams

Abstract: The authors show that the problem of optimally routing multicast streams can be formulated as an integer programming problem. They propose an efficient solution technique, composed of two parts: (i) an extension to the decomposition principle, to speed up the linear relaxation of the problem, and (ii) enhanced value-fixing rules, to prune the search space for the integer problem. They characterize the reduction in run time gained using these techniques. Finally, they compare the run times for the optimum multicast routing algorithm and for existing heuristic algorithms. >

Fast algorithms for routing around faults in multibutterflies and randomly-wired splitter networks

Abstract: Simple deterministic O(log N)-step algorithms for routing permutations of packets in multibutterflies and randomly wired splitter networks are described. The algorithms are robust against faults (even in the worst case), and are efficient from a practical point of view. As a consequence, it is found that the multibutterfly is an excellent candidate for a high-bandwidth low-diameter switching network underlying a shared-memory machine. >

Controlling alternate routing in general-mesh packet flow networks

Abstract: High-speed packet networks will begin to support services that need Quality-of-Service (QoS) guarantees. Guaranteeing QoS typically translates to reserving resources for the duration of a call. We propose a state-dependent routing scheme that builds on any base state-independent routing scheme, by routing flows which are blocked on their primary paths (as selected by the state-independent scheme) onto alternate paths in a manner that is guaranteed—under certain Poisson assumptions— to improve on the performance of the base state-independent scheme. Our scheme only requires each node to have state information of those links that are incident on it. Such a scheme is of value when either the base state-independent scheme is already in place and a complete overhaul of the routing algorithm is undesirable, or when the state (reserved flows) of a link changes fast enough that the timely update of state information is infeasible to all possible call-originators. The performance improvements due to our controlled alternate routing scheme are borne out from simulations conducted on a fully-connected 4-node network, as well as on a sparsely-connected 12-node network modeled on the NSFNet T3 Backbone.

An Efficient Zero-Skew Routing Algorithm

Abstract: A bucket algorithm is proposed for zero-skew routing with linear time complexity on the average. Our algorithm is much simpler and more efficient than the best known algorithm which uses Delaunay triangulations for segments on Manhattan distance. Experimental results show that the linearity of our algorithm is accomplished. Our algorithm generates a zero-skew routing for 3000-pin benchmark data within 5 seconds on a 90MIPS RISC workstation.

Fully adaptive minimal deadlock-free packet routing in hypercubes, meshes, and other networks: algorithms and simulations

Abstract: This paper deals with the problem of packet-switched routing in parallel machines. Several new routing algorithms for different interconnection networks are presented. While the new techniques apply to a wide variety of networks, routing algorithms will be shown for the hypercube, the two-dimensional mesh, and the shuffle-exchange. Although the new techniques are designed for packet routing, they can be used alternatively for virtual cut-through routing models. The techniques presented for hypercubes and meshes are fully-adaptive and minimal. A fully-adaptive and minimal routing is one in which all possible minimal paths between a source and a destination are of potential use at the time a message is injected into the network. Minimal paths followed by messages ultimately depend on the local congestion encountered in each node of the network. All of the new techniques are completely free of deadlock situations. >

Fault-tolerant wormhole routing in tori

Abstract: We present a method to enhance wormhole routing algorithms for deadlock-free fault-tolerant routing in tori. We consider arbitrarily-located faulty blocks and assume only local knowledge of faults. Messages are routed via shortest paths when there are no faults, and this constraint is only slightly relaxed to facilitate routing in the presence of faults. The key concept we use is that, for each fault region, a fault ring consisting of fault free nodes and physical channels can be formed around it. These fault rings can be used to route messages around fault regions. We prove that at most four additional virtual channels are sufficient to make any fully-adaptive algorithm tolerant to multiple faulty blocks in torus networks. As an example of this technique, we present simulation results for a fully-adaptive algorithm and show that good performance can be obtained with as many as 10% links faulty.

Minimising packet copies in multicast routing by exploiting geographic spread

Abstract: Routing connections in a point-to-point network is typically treated as a shortest path problem in a graph. Nodes represent switching systems, edges represent links and the edge lengths represent the costs associated with using a link. With multicast routing, one is interested in the shortest subtree of the network containing a given set of hosts. This is essentially a Steiner Tree problem in graphs and is known to be NP-complete [Karp]. Traditionally, the multicast routing algorithms proposed for packet switched networks like asynchronous transfer mode (ATM) networks have been aimed at minimising the total link cost of the Steiner tree [Waxman88], [Jaffe83] and do not take the geographical spreading of the connections into account. A dynamic point-to-multipoint routing algorithm is proposed, which takes into account the concept of geographic spread (also defined) of the connections and its performance is evaluated against the KMB near optimal heuristic algorithm for solving the Steiner tree problem [Kou].

Algorithms for a switch module routing problem

Abstract: We consider a awitch module routing problem /or aymmelric array FPGAs. The work is motivated by two applications. The firaf ia that of efficiently evaluating awitch module designs [a]. The second ia that of evaluating the routability of global routing patha for a placement on this architecture. Only an approzimate algorithm was previously known jar this problem. In thin paper, we present an optimal algorithm for the problem based on integer linear programming. Ezperimental rerulta conaistently show that our algorithm is very efficient jor practical sized switch modules. We further improve this technique, by doing some pre-processing on the given switch module. We also idenlijy interesting special cases of the problem which can be solved optimally in polynomial time.

A new global routing algorithm for FPGAs

Abstract: As in traditional ASIC technologies, FPGA routing usually consists of two steps: global routing and detailed routing. Unlike existing FPGA detailed routers, which can take full advantage of the special structures of the programmable routing resources, FPGA global routing algorithms still greatly resemble their counterparts in the traditional ASIC technologies. In particular, the routing congestion information of a switch block essentially is still measured by the numbers of available rows and columns in the switch block. Since the internal architecture of a switch block decides what can route through the block, the traditional measure of routing capacity is no longer accurate. In this paper, we present an accurate measure of switch block routing capacity. Our new measure considers the exact positions of the switches inside a switch block. Experiments with a global router based on these ideas show an average improvement of 38% in the channel width required to route some benchmark circuits using a popular switch block, compared with an algorithm based on the traditional methods for congestion control.

Single-layer global routing

Abstract: We introduce the single-layer global routing problem (SLGRP), also called homotopic routing or rubber-band-equivalent routing, and propose a technique for solving it. Given a set of nets, the proposed technique first determines the routing sequence based on the estimated congestion, the bounding-box length and priority. Then, it finds a routing path, being a sequence of tiles, for each net (one net at a time), avoiding "congested" areas. The overall goal of the algorithm is to maximize the number of routed nets. The proposed global router is the first true single-layer global router ever reported in the literature. The size of tiles, w/spl times/w, is an input parameter in our algorithm. For w=1, the proposed global router serves as an effective detailed router. An optimal postprocessing algorithm, minimizing wire length and number of bends, under homotopic transformation, is presented. The technique has been implemented and tried out for randomly generated data. The algorithm is very efficient and produces good results. >

Optimal Broadcast in All-Port Wormhole-Routed Hypercubes

Abstract: We give an optimal algorithm that broadcasts on an n-dimensional hypercube in Theta(n/ log_{2}(n+ 1)) routing steps with wormhole, e-cube routing and all-port communication. Previously, the best algorithm of McKinley and Trefftz requires [n/2] routing steps. We also give routing algorithms that achieve tight time bounds for n leqslant 7.

METRO: a router architecture for high-performance, short-haul routing networks

Abstract: The Multipath Enhanced Transit Router Organization (METRO) is a flexible routing architecture for high-performance, tightly-coupled, multiprocessors and routing hubs. A METRO router is a dilated cross-bar routing component supporting half-duplex bidirectional, pipelined, circuit-switched connections. Each METRO router is self-routing and supports dynamic message traffic. The routers works in conjunction with source-responsible network interfaces to achieve reliable end-to-end data transmission in the presence of heavy network congestion and dynamic faults. METRO separates the fundamental architectural characteristics from implementation parameters. Simplicity of routing function coupled with freedom in the implementation parameters allows METRO implementations fully exploit available technology to achieve low-latency and high-bandwidth. We illustrate the effects of this implementation freedom by summarizing the performance which various METRO configurations can extract from some modern CMOS technologies. Included in our illustrations is METROJR-ORBIT, a minimal instance of the METRO architecture we constructed in a 1.2μ gate-array technology.

Non-tree routing

Abstract: An implicit premise of existing routing methods is that the routing topology must correspond to a tree (ie it does not contain cycles) In this paper we investigate the consequences of abandoning this basic axiom, and instead allow routing topologies that correspond to arbitrary graphs (ie where cycles are admissible) We show that adding extra wires to an existing routing tree can often significantly improve signal propagation delay by exploiting a tradeoff between wire capacitance and resistance, and we propose a new routing algorithm based on this phenomenon Using SPICE to determine the efficacy of our methods, we obtain dramatic results: for example, the judicious addition of a few extra wires to an existing Steiner routing reduces the signal propagation delay by an average of up to 62%, with relatively modest total wirelength increase, depending on net size and the technology parameters Finally, we observe that non-tree routing also significantly reduces signal skew >

Storage-efficient, deadlock-free packet routing algorithms for torus networks

Abstract: We present two new packet routing algorithms for parallel computers with torus interconnection networks of arbitrary size and dimension. Both algorithms use only minimal length paths, are fully adaptive in the sense that all minimal length paths may be used to avoid congestion, and are free of deadlock, livelock and starvation. Algorithm 1 requires only three central queues per routing node. It is the first known minimal length packet routing algorithm for torus networks which requires a constant number of queues per node, regardless of the size and dimension of the torus. In fact, the requirement of three queues per node is optimal, as no such algorithm is possible when all nodes have two or fewer queues. Algorithm 2 requires only that each node have two input buffers per edge. It is the first known minimal-fully-adaptive packet routing algorithm for torus networks which does not require central queues and which does not require any node to have more than two input or two output buffers per edge. Both algorithms are simple and appear to be well-suited to VLSI implementation. They can be used with either store-and-forward or virtual cut-through routing. >

Deterministic 1 - k routing on meshes with applications to worm-hole routing

Abstract: In 1-k routing each of the n2 processing units of an n x n mesh connected computer initially holds 1 packet which must be routed such that any processor is the destination of at most k packets. This problem has great practical importance in itself and by its implications for hot-potato worm-hole routing.

Potential function analysis of greedy hot-potato routing

Abstract: We study the problem of packet routing in synchronous networks. We put forward a notion of greedy hot-potato routing algorithms and devise tech- niques for analyzing such algorithms. A greedy hot-potato routing algorithm is one where:

On the NP-completeness of regular 2-D FPGA routing architectures and a novel solution

Abstract: Several industrial FPGA routing architectures have been shown to have no efficient routing algorithms (unless P=NP). Here, we further investigate if the intractability of the routing problem on a regular 2-D FPGA routing architecture can be alleviated by adding routing switches. We show that on this routing architecture, even with a substantial increase in switching flexibility, a polynomial time, predictable routing algorithm is still not likely to exist, and there is no constant ratio bound of the detailed over global routing channel densities. We also show that a perfect routing is unachievable on this architecture even with near complete (maximum) switching flexibility.We also discuss a new, greedy routing architecture, that possesses predictable and other desired routing properties, yet requires fewer routing resources than regular architectures. This theoretical result may suggest an alternative approach in routing architecture designs.

Optimal Interval Routing

Abstract: Interval routing was introduced to reduce the size of the routing tables. This way of implementing routing functions is quite attractive but very few is known on the topological properties that should satisfy a network to admit an interval routing function satisfying particular constraints (shortest paths, limited number of intervals associated to each direction, etc). In this paper, we investigate the study of optimal interval routing functions, that is routing functions that construct shortest paths. In particular we derive practical tools that allow to determine if a network supports or not an optimal interval routing function. We describe large classes of networks that admit optimal interval routing functions. We also study the case of the usual networks that interconnect the processors of a distributed memory parallel computer.

Signaling system utilizing source routing information in a packet network

Abstract: For executing a signaling operation of a virtual channel which is used for communication between a transmission side and a reception terminal in a connection-oriented packet network, the transmission side acquires source routing information relating to a source route path between the transmission side and the reception terminal. The transmission side includes a transmission terminal and a switch between the transmission terminal and the reception terminal. With reference to the source routing information, the transmission terminal carries out a signaling operation of a setup for the virtual channel. It is preferable that the switch acquires the source routing information to transmit the source routing information to the transmission terminal. Alternatively, the transmission terminal may acquire the source routing information.