Showing papers on "Destination-Sequenced Distance Vector routing published in 1990"
01 Jun 1990
TL;DR: In this paper, the authors present an LP relaxation of the set partitioning formulation of the VRPTW problem, which is solved by column generation, where feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming.
Abstract: The vehicle routing problem with time windows VRPTW is a generalization of the vehicle routing problem where the service of a customer can begin within the time window defined by the earliest and the latest times when the customer will permit the start of service. In this paper, we present the development of a new optimization algorithm for its solution. The LP relaxation of the set partitioning formulation of the VRPTW is solved by column generation. Feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming. The LP solution obtained generally provides an excellent lower bound that is used in a branch-and-bound algorithm to solve the integer set partitioning formulation. Our results indicate that this algorithm proved to be successful on a variety of practical sized benchmark VRPTW test problems. The algorithm was capable of optimally solving 100-customer problems. This problem size is six times larger than any reported to date by other published research.
992 citations
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TL;DR: In this paper, the authors presented a new vehicle routing problem amenable to practical applications, and demonstrated the potential for cost savings over similar “traditional” vehicle routing when implementing the model and solutions presented here.
Abstract: This article examines a relaxed version of the generic vehicle routing problem. In this version, a delivery to a demand point can be split between any number of vehicles. In spite of this relaxation the problem remains computationally hard. Since only small instances of the vehicle routing problem are known to be solved using exact methods, the vehicle route construction for this problem version is approached using heuristic rules. The main contribution of this article to the existing body of literature on vehicle routing issues in (a) is presenting a new vehicle routing problem amenable to practical applications, and (b) demonstrating the potential for cost savings over similar “traditional” vehicle routing when implementing the model and solutions presented here. The solution scheme allowing for split deliveries is compared with a solution in which no split deliveries are allowed. The comparison is conducted on six sets of 30 problems each for problems of size 75, 115, and 150 demand points (all together 540 problems). For very small demands (up to 10% of vehicle's capacity) no significant difference in solutions is evident for both solution schemes. For the other five problem sets for which point demand exceeds 10% of vehicle's capacity, very significant cost savings are realized when allowing split deliveries. The savings are significant both in the total distance and the number of vehicles required. The vehicles' routes constructed by our procedure tend to cover cohesive geographical zones and retain some properties of optimal solutions.
278 citations
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08 Jan 1990TL;DR: In this article, a message tag is used to identify the destination node of the message in the network and prioritization data which, when the message is generated, is initialized to have a value (weight) corresponding to the length (number of links) of the minimal path from the source node where the message originates to the destination.
Abstract: A communication network having a multiplicity of nodes provides efficient exchange of messages between the nodes. The messages may be originated and received by the computers of a parallel computer system, the processors and associated memories of which are connected to each node. Each node includes a routing system which results in efficient system performance for the parallel computer system associated with the nodes. The messages have control information (a message tag) to which the routing system at each node is responsive. The tag contains data identifying the destination node of the message in the network and prioritization data which, when the message is generated, is initialized to have a value (weight) corresponding to the length (number of links) of the minimal path from the source node where the message originates to the destination node of the message. The routing system utilizes the weights to establish message priority. The routing system receives and sends messages not exceeding the number of links connected thereto on each cycle such that messages flow in and flow out of each routing node on each cycle without being held or stored in queues in the node. Messages of lesser priority are switched by the router to alternate links in accordance with their weights thereby dynamically routing and resolving conflicts among messages.
194 citations
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TL;DR: In this article, a classification scheme is proposed for a class of models that arise in the area of vehicle routing and scheduling and illustrated on a number of problems that have been considered in the literature.
164 citations
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11 Nov 1990TL;DR: A detailed routing algorithm, called the coarse graph expander (CGE), that has been designed specifically for field-programmable gate arrays (FPGAs) is described, which can route relatively large FPGAs in very close to the minimum number of tracks as determined by global routing.
Abstract: A detailed routing algorithm, called the coarse graph expander (CGE), that has been designed specifically for field-programmable gate arrays (FPGAs) is described. The algorithm approaches this problem in a general way, allowing it to be used over a wide range of different FPGA routing architectures. It addresses the issue of scarce routing resources by considering the side effects that the routing of one connection has on another, and also has the ability to optimize the routing delays of time-critical connections. CGE has been used to obtain excellent routing results for several industrial circuits implemented in FPGAs with various routing architectures. The results show that CGE can route relatively large FPGAs in very close to the minimum number of tracks as determined by global routing, and it can successfully optimize the routing delays of time-critical connections. CGE has a linear run time over circuit size. >
154 citations
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TL;DR: Using depth-first search, the authors develop and analyze the performance of a routing scheme for hypercube multicomputers in the presence of an arbitrary number of faulty components and derive an exact expression for the probability of routing messages by way of optimal paths from the source node to an obstructed node.
Abstract: Using depth-first search, the authors develop and analyze the performance of a routing scheme for hypercube multicomputers in the presence of an arbitrary number of faulty components. They derive an exact expression for the probability of routing messages by way of optimal paths (of length equal to the Hamming distance between the corresponding pair of nodes) from the source node to an obstructed node. The obstructed node is defined as the first node encountered by the message that finds no optimal path to the destination node. It is noted that the probability of routing messages over an optimal path between any two nodes is a special case of the present results and can be obtained by replacing the obstructed node with the destination node. Numerical examples are given to illustrate the results, and they show that, in the presence of component failures, depth-first search routing can route a message to its destination by means of an optimal path with a very high probability. >
149 citations
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TL;DR: Several simple families of routing schemes for general networks are presented, featuring some desirable properties, and the new important features of these schemes are applicability to networks with arbitrary edge costs and attractive stretch factors for small values of k.
148 citations
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09 Jul 1990
TL;DR: In this article, the authors proposed a method for providing an efficient and adaptive management of message routing in a multi-platform, communication system having dynamically changing platform populations and dynamically changing connectivities between platforms where each of the platforms are capable of performing the steps of recognizing at least certain ones of the nodes in the system, deriving from at least one of the recognized nodes the quality of interconnectivities of other nodes, and employing the derived quality of connectivity to make connectivity-based routing decisions using a selective one of a point-to-point routing algorithm.
Abstract: The method for providing an efficient and adaptive management of message routing in a multi-platform, communication system having dynamically changing platform populations and dynamically changing connectivities between platforms where each of the platforms are capable of performing the steps of recognizing at least certain ones of the platforms in the system, deriving from at least one of the recognized platforms the quality of interconnectivities of the recognized platforms and certain others of the platforms in the system; and employing the derived quality of interconnectivities to make connectivity-based routing decisions using a selective one of a point-to-point routing algorithm, a point-to-multipoint routing algorithm and a broadcast routing algorithm.
134 citations
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01 May 1990TL;DR: Overall, this paper finds that certain greedy algorithms perform surprisingly well on average, and shows that the maximum size of a queue over a time span of T steps is O(e) with high probability.
Abstract: In this paper, we analyze the average case behavior of greedy routing algorithms on arrays under a variety of assumptions. Overall, we find that certain greedy algorithms perform surprisingly well on average. For example, given an N x N array or torus where every node starts with one packet headed for a random destination, we show that some (but not all) greedy store-andforward algorithms route every packet to its destinrt, tion with only O(log N) delay per packet and maximum queuesize 4 with probability near 1. Moreover, the expected delay per packet is only a small constant, independent of N. We also extend the analysis to a steady state model of routing in which packets enter the network at random times. Provided that the overall arrival rate of packets to the network is less than 100% of the network capacity, we show that any packet encounters at most O(log N) delay with high probability. In addition, we show that the maximum size of a queue over a time span of T steps is O(e) with high probability. The results can also be extended to analyze the average case behavior of cut-through (or, flit-serial) routing under lighter loading.
116 citations
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TL;DR: This paper examines computational complexity issues and develops algorithms for a class of "shoreline" single-vehicle routing and scheduling problems with release time constraints and develops and analyzes heuristic algorithms for this class.
Abstract: In this paper we examine computational complexity issues and develop algorithms for a class of "shoreline" single-vehicle routing and scheduling problems with release time constraints. Problems in this class are interesting for both practical and theoretical reasons. From a practical perspective, these problems arise in several transportation environments. For instance, in the routing and scheduling of cargo ships, the routing structure is "easy" because the ports to be visited are usually located along a shoreline. However, because release times of cargoes at ports generally complicate the routing structure, the combined routing and scheduling problem is nontrivial. For the straight-line case a restriction of the shoreline case, our analysis shows that the problem of minimizing the maximum completion time can be solved exactly in quadratic time by dynamic programming. For the shoreline case we develop and analyze heuristic algorithms. We derive data-dependent worst-case performance ratios for these heuristics that are bounded by constant. We also discuss how these algorithms perform on practical data.
99 citations
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03 Jun 1990TL;DR: The analysis indicates that a hypercube, hot-potato routing offers essentially optimal performance for random traffic, regardless of how large the hypercube grows, and it significantly outperforms traditional shortest-path routing with buffering and flow control.
Abstract: Two implementations of a fiber-optic packet-switched hypercube are proposed. In the first, each directed link is implemented with a fixed wavelength laser and photodetector, and all optical transmissions are wavelength multiplexed onto one or more fibers. In the second, the electronic crosspoint matrices within the nodes are eliminated by allowing each laser to be tunable over a range of log N wavelengths. Assume that a hot potato, or deflection, routing algorithm is used; as soon as a packet is received at a node, a routing decision is made and the packet is sent out. The node attempts to send the packet towards its destination. The analysis indicates that a hypercube, hot-potato routing offers essentially optimal performance for random traffic, regardless of how large the hypercube grows, and it significantly outperforms traditional shortest-path routing with buffering and flow control. A few variations, including an algorithm which gives priority to packets closer to their destinations and one which gives priority to various classes of traffic, are also proposed and analyzed. >
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01 May 1990TL;DR: A unified framework for finding efficient permutation routes on parallel networks in an off-line setting if the underlying graph of a parallel network contains an appropriate “approximate” product structure and the existence of non-blocking near-optimal permutations routes is presented.
Abstract: A unified framework for finding efficient permutation routes on parallel networks in an off-line setting is presented. If the underlying graph of a parallel network contains an appropriate “approximate” product structure then our method guarantees the existence of non-blocking near-optimal permutation routes. The routes in question can be determined in polynomial time. Furthermore, our results are extended to finding permutation routes among the remaining “live” nodes in a faulty network.
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24 Jun 1990TL;DR: This paper presents three physical models to utilize the area over the cells for routing in standard cell designs, and presents efficient algorithms to choose and to route a planar subset of nets over the Cells so that the resulting channel density is reduced as much as possible.
Abstract: When an over-the-cell routing layer is available for standard cell layout, efficient utilization of routing space over the cells can significantly reduce layout area. In this paper, we present three physical models to utilize the area over the cells for routing in standard cell designs. We also present efficient algorithms to choose and to route a planar subset of nets over the cells so that the resulting channel density is reduced as much as possible. For each of the physical models, we show how to arrange inter-cell routing, over-the-cell routing and power/ground busses to achieve valid routing solutions. Each algorithm exploits the particular arrangement in the corresponding physical model and produces provably good results in polynomial time. We tested our algorithms on several industrial standard cell designs. In our tests, this method reduces total channel density as much as 21%.
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26 Jun 1990TL;DR: The authors present a distributed table-filling algorithm for point-to-point routing in a degraded hypercube system that finds the shortest length existing path from each source to each destination in the faulty hypercube and fills the routing tables so that messages are routed along these paths.
Abstract: The authors present a distributed table-filling algorithm for point-to-point routing in a degraded hypercube system. This algorithm finds the shortest length existing path from each source to each destination in the faulty hypercube and fills the routing tables so that messages are routed along these paths. A novel scheme for broadcast routing with tables is proposed, and the algorithm required to fill the broadcast tables, given the point-to-point routing tables, is presented. In addition, the modifications necessary to make these algorithms ensure deadlock-free routing are given. A quantitative and equalitative comparison of previously proposed reroute strategies with table routing, where the tables are filled by the authors' algorithms, are presented. >
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TL;DR: A general-purpose routing algorithm for very-large-scale integrated (VLSI) circuits and printed circuit board (PCB) designs is proposed and implemented and integrated into a global router that can handle large-scale routing, such as that encountered in the sea-of-gates layout.
Abstract: A general-purpose routing algorithm for very-large-scale integrated (VLSI) circuits and printed circuit board (PCB) designs is proposed. Ideas behind the maze-running algorithm and the hierarchical routing algorithm are combined into a powerful algorithm called hybrid routing. The new algorithm demonstrates a speed compatible to a hierarchical router and produces routings with quality equivalent to that obtained by a maze router. Hybrid routing is based on the maze-running method with a third search dimension added. The extra search space is built by recursively constructing a hierarchy of coarser grid meshes. By means of a parameter-controlled expansion into the coarser meshes, the hybrid router is able to find the preferred search region very quickly and will not miss local information as a hierarchical router does. A user-given parameter can turn the algorithm into a pure maze router, a pure hierarchical router, or a wide spectrum of hybrid routers with different speed/quality characteristics between the extremes. The algorithm has been implemented and integrated into a global router that can handle large-scale routing, such as that encountered in the sea-of-gates layout. >
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03 Jun 1990TL;DR: Analytical results show that in conjunction with trunk reservation, this alternate-path routing rule can offer a stable throughput at high traffic conditions and can increase the call carrying capacity by about 20% under a blocking requirement of 10/sup -2/ on a fully connected symmetrical nonhierarchical network.
Abstract: An analysis is made of an alternate-path routing rule called maximum free circuit routing (MFCR). In the use of MFCR, a call is routed to the alternate path that has the maximum number of free circuits when the direct path is blocked. Analytical results show that in conjunction with trunk reservation, this routing rule can offer a stable throughput at high traffic conditions and can increase the call carrying capacity by about 20% (compared to direct path routing) under a blocking requirement of 10/sup -2/ on a fully connected symmetrical nonhierarchical network. >
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TL;DR: A dynamic routing algorithm that has as its goal the control of congestion in a packet switching network is presented, based in part on the ARPANET SPF, but instead of employing a delay metric, the authors make use of a combination of link and buffer utilizations.
Abstract: A dynamic routing algorithm that has as its goal the control of congestion in a packet switching network is presented. The algorithm is based in part on the ARPANET SPF algorithm. However, instead of employing a delay metric, the authors make use of a combination of link and buffer utilizations. A detailed simulation model of the ARPANET was constructed to compare the performance of the congestion-based algorithm to the traditional delay-based (SPF) routing algorithm. The results indicate a substantial improvement in the delay and throughput of the network with the congestion-based routing algorithm. >
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IBM1
TL;DR: This work presents a trade-off between the amount of topology information exchanged among these pieces and the efficiency of routing in the network.
Abstract: Routing a message in a network is efficient (in terms of weight of the path used to carry the message) when nodes know the full topology of the network. This may not be the case in large networks since a network may be composed of smaller autonomous pieces by design or by requirements on performance, with each piece having less than complete information about other pieces. We present a trade-off between the amount of topology information exchanged among these pieces and the efficiency of routing in the network. The large network that we study is a collection of networks connected by boundary nodes. Each boundary node knows the topology of its network and the connectivity of networks to each other. The question addressed here is how much topology information about each network should be distributed to other networks in order to achieve reasonably efficient routing.
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01 Aug 1990TL;DR: It is concluded that an architecture based upon source routing, a link state algorithm, and policy information in the link state advertisements, is best able to address the long-term policy requirements of inter-AD routing.
Abstract: Policy Routing (PR) is a new area of development that attempts to incorporate policy related constraints on inter-Administrative Domain (AD) communication into the route computation and forwarding of inter-AD packets.Proposals for inter-AD routing mechanisms are discussed in the context of a design space defined by three design parameters: location of routing decision (i.e., source or hop-by-hop), algorithm used (i.e., link state or distance vector), and expression of policy in topology or in link status. We conclude that an architecture based upon source routing, a link state algorithm, and policy information in the link state advertisements, is best able to address the long-term policy requirements of inter-AD routing. However, such an architecture raises several new and challenging research issues related to scaling.
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TL;DR: A routing strategy called NELHNET has been developed for networks with multiprecedence traffic and operating under dynamic traffic and topological conditions, which permits the network to function stably under more heavily loaded conditions than do the Arpanet strategies.
Abstract: A routing strategy called NELHNET has been developed for networks with multiprecedence traffic and operating under dynamic traffic and topological conditions. An adaptive distributed algorithm that uses least-hop and least-hop-plus-1 routes in a table of routing vectors, as opposed to the usual table of routing scalars, is described. Current delays are passed backward and forward with the packets to allow development of expected delays to each node via all acceptable routes. The route then selected is the acceptable route with the least expected delay. For speedier recovery, a node returning to service receives the current network status from an adjoining node as soon as the link connecting them is operational. The resultant algorithms show far greater than the marginal improvements originally expected over Arpanet simulations. NELHENET strategies also permit the network to function stably under more heavily loaded conditions than do the Arpanet strategies. >
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NEC1
TL;DR: New placement and global routing algorithms are proposed for standard cell layouts that are effective to avoid being trapped in local optimum solutions and are simple and highly efficient.
Abstract: New placement and global routing algorithms are proposed for standard cell layouts. The placement algorithm, called the hierarchical clustering with min-cut exchange (HCME), is effective to avoid being trapped in local optimum solutions. The global routing algorithm does not route the nets one by one and therefore, the results are independent of the net order and channel order. In this algorithm, channel width is minimized under a cost function, in which the trade-off between the minimization of net lengths and the minimization of the number of tracks is considered. These algorithms are simple and highly efficient. This is confirmed by computational experiments.
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14 Mar 1990TL;DR: In this article, a routing logic (RL) for a communication switching element (ISE) of a self-routing multi-stage switching network is presented, which is able to transfer cells or packets of information from any of its inlets (I1/32) to one of its outlets (O 1/32), and is also able to control the transfer of a cell through the switching element according to the execution of a predetermined routing function selected amongst a plurality of routing functions (RS, DI, MC, BH, IS).
Abstract: Routing logic (RL) for a communication switching element (ISE) of a self-routing multi-stage switching network and able to transfer cells or packets of information from any of its inlets (I1/32) to any of its outlets (O1/32). The outlets of the switching element are arranged in routing groups containing one or more of them and of which the identity is derived by the routing logic from an output-port-address (OPA) identifying an output of the switching network and contained in the self-routing-tag (SRT) associated to the cell. This cell is then transferred to one of the outlets belonging to the selected routing group. The routing logic (RL) is also able to control the transfer of a cell through the switching element according to the execution of a predetermined routing function selected amongst a plurality of routing functions (RS, DI, MC, BH, IS). This routing function to be executed is selected by the routing logic according to a routing-control-code (RCC) also contained in the self-routing-tag (SRT) and each value thereof identifies a specific transfer pattern constituted by a predetermined sequence of routing functions to be executed in the switching elements (ISE) through the switching network (SN).
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TL;DR: It is shown that for arrival rates in some possible interval (0, lambda /sub 0/), ever routing policy which minimizes the long-run expected holding cost is contained in the set of routing policies that minimize the expected flow time for a system with fixed initial population and no new arrivals.
Abstract: Consider a set of k(>or=2) heterogeneous and exponential servers that operate in parallel. Customers arrive into a single infinite capacity buffer according to a Poisson process, and are routed to available servers in accordance with some routing policy. It is shown that for arrival rates in some possible interval (0, lambda /sub 0/), ever routing policy which minimizes the long-run expected holding cost is contained in the set of routing policies that minimize the expected flow time for a system with fixed initial population and no new arrivals. >
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TL;DR: The nature of the traffic-routing problem is described, and early studies of state-dependent routing are noted; how the relative costs can be determined for the case of direct routing is shown.
Abstract: The nature of the traffic-routing problem is described, and early studies of state-dependent routing are noted. A state-dependent scheme seeks to route each call so as to minimize the risk of blocking future calls, and thus responds to the current state of the network on the basis of certain assumptions about future traffic demands. State-dependent routing is considered as a Markov decision process. How the relative costs can be determined for the case of direct routing is shown. >
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08 Oct 1990
TL;DR: A new lower bound is derived for distance-limited permutation routing on a ring of processors, and an algorithm that matches this lower bound if the packets are routed independently is given.
Abstract: The bit-serial routing problem wherein each packet consists of a sequence of k flits and is thus called a snake, is considered. On the basis of the properties of the snake during the routing, a formal definition is given for three different packet routing models, namely, the store-and-forward model, the cut-through model, and the wormhole model. The wormhole model, which is most commonly used in practice, is studied. The first algorithms (deterministic and probabilistic) based on the wormhole model for the permutation routing problem on a chain, on a square mesh, and on a square torus are given. A new lower bound is derived for distance-limited permutation routing on a ring of processors, and an algorithm that matches this lower bound if the packets are routed independently is given. >
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TL;DR: The system was very successful in identifying the optimal algorithm to apply to the new problems not used in training, and it is concluded that neural networks have considerable promise in the vehicle routing problem.
Abstract: In the vehicle routing problem (VRP), there is a collection of stops with known demands for service, and a fleet of vehicles with known capacities available to serve the stops. The problem is to assign the stops to vehicles, and specify routing sequences for each vehicle so that total distance is minimized. Many heuristic algorithms for the VRP have been developed over the last 25 years. Given a particular vehicle routing problem instance, we address here the issue of selecting which heuristic algorithm to apply to the problem. A modular system of neural networks is the knowledge base that is used to make the selection. Three types of multiple-layer neural networks are involved, and all are trained with the back-propagation learning paradigm. After training, the neural network system was applied to a collection of new problems not used in training. The system was very successful in identifying the optimal algorithm to apply to the new problems. We conclude that neural networks have considerable promise fo...
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22 Oct 1990TL;DR: The present networks are the first that are simultaneously deterministic and online, and they use two substantially different routing techniques, including a new type of sorting circuit, an area universal circuit, and an area-time lower bound for routers.
Abstract: Two deterministic routing networks, the pruned butterfly and the sorting fat-tree, are presented. Both networks are area universal, i.e. they can simulate with polylogarithmic slowdown, any other routing network fitting in similar area. Previous area-universal networks were either for the offline problem, where the message set to be routed is known in advance and substantial precomputation is permitted, or involved randomization, yielding results that hold only with high probability. The present networks are the first that are simultaneously deterministic and online, and they use two substantially different routing techniques. The performance of the routing algorithms depends on the difficulty of the problem instance, which is measured by a quantity lambda , known as the load factor. The pruned butterfly algorithm runs in time O( lambda log/sup 2/N), where N is the number of possible sources and destinations for messages and lambda is assumed to be polynomial in N. The sorting fat-free algorithm runs in O( lambda log N + log/sup 2/N) time for a restricted class of message sets, including partial permutations. Other results include a new type of sorting circuit, an area universal circuit, and an area-time lower bound for routers. >
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TL;DR: Experimental results, agreeing with theoretical analysis, show that the OCR algorithm behaves quite well in average cases and an optimal solution is obtained for the Deutsch difficult case in 5.5-min-CPU time.
Abstract: An algorithm known as optimal channel routing (OCR) is proposed which finds an optimal solution for the channel routing problem in VLSI design. The algorithm is an A* algorithm with good heuristics and dominance rules for terminating unnecessary nodes in the searching tree. Experimental results, agreeing with theoretical analysis, show that it behaves quite well in average cases. An optimal solution is obtained for the Deutsch difficult case in 5.5-min-CPU time after the algorithm is implemented in Pascal and run on a VAX 11/750 computer. >
01 Apr 1990
TL;DR: A multipath scheme for providing end-to-end fault-tolerance on large networks, which improves routing performance while keeping network latency low and the novel routing component, RN1, which implements this scheme, showing how it can be the basic building block for fault-Tolerant multistage routing networks.
Abstract: As the size of digital systems increases, the mean time between single component failures diminishes. To avoid component related failures, large computers must be fault-tolerant. In this paper, we focus on methods for achieving a high degree of fault-tolerance in multistage routing networks. We describe a multipath scheme for providing end-to-end fault-tolerance on large networks. The scheme improves routing performance while keeping network latency low. We also describe the novel routing component, RN1, which implements this scheme, showing how it can be the basic building block for fault-tolerant multistage routing networks.