Showing papers on "Equal-cost multi-path routing published in 1988"

Survey Paper—Time Window Constrained Routing and Scheduling Problems

Abstract: We have witnessed recently the development of a fast growing body of research focused on vehicle routing and scheduling problem structures with time window constraints. It is the aim of this paper to survey the significant advances made for the following classes of routing problems with time windows: the single and multiple traveling salesman problem, the shortest path problem, the minimum spanning tree problem, the generic vehicle routing problem, the pickup and delivery problem including the dial-a-ride problem, the multiperiod vehicle routing problem and the shoreline problem. Having surveyed the state-of-the-art in this area, we then offer some perspectives on future research.

Method and apparatus for routing communications among computer networks

Abstract: An improved method and apparatus for routing data transmissions among computer networks. The computer networks are interconnected with a series of gateway circuits. Each gateway identifies all destination computers to which it is connected and identifies the path or paths to each destination computer. For each identified path, the gateway stores the topological delay time for a transmission, the path bandwidth for the narrowest bandwidth segment of a path and a number corresponding to the reliability of the path. When a transmission is received, the gateway examines the various paths in accordance with a predetermined algorithm which also considers the channel occupancy of each path to determine a best path for transmision. The data transmission is then directed over the best path. If more than one path exists, the data may be directed in multiplex fashion over two or more paths with the amount of data on each path being related to the quality of the path. The routing information to destination networks is broadcast periodically by each gateway circuit to its neighboring gateway circuits.

Inter-computer message routing system with each computer having separate routinng automata for each dimension of the network

Abstract: In a multicomputer, concurrent computing system having a plurality of computing nodes, this is a method and apparatus for routing message packets between the nodes. The method comprises providing a routing circuit at each node and interconnecting the routing circuits to define communications paths interconnecting the nodes along which message packets can be routed; at each routing circuit, forming routes to other nodes as a sequence of direction changing and relative address indicators for each node between the starting node and each destination node; receiving a message packet to be transmitted to another node and an associated destination node designator therefor; retrieving the route to the destination node from a memory map; adding the route to the destination node to the beginning of the message packet as part of a header; transmitting the message packet to the routing circuit of the next adjacent node on the route to the destination node; and at each intermediate node, receiving the message packet; reading the header; directing the message packet to one of two outputs thereof as a function of routing directions in the header, updating the header to reflect passage through the routing circuit; and at the destination node, stripping remaining portions of the header from the message packet; storing the message packet; and, informing the node that the message packet has arrived.

A tradeoff between space and efficiency for routing tables

Abstract: Two conflicting goals play a crucial role in the design of routing schemes for communication networks. A routing scheme should use as short as possible paths for routing messages in the network, 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 length of a route computed by the scheme and that of a shortest path connecting the same pair of vertices.Most previous work has concentrated on finding good routing schemes (with a small fixed stretch factor) for special classes of network topologies. In this work we study the problem for general networks, and look at the entire range of possible stretch factors. The results exhibit a tradeoff between the efficiency of a routing scheme and its space requirements. We present almost tight upper and lower bounds for this tradeoff. Specifically, we prove that any routing scheme for general n-vertex networks that achieves a stretch factor k ≥ 1 must use a total of O(n1+1/2k+4) bits of routing information in the networks. This lower bound is complemented by a family H(k) of hierarchical routing schemes (for every fixed k ≥ 1), which guarantee a stretch factor of O(k), require storing a total of O(n1+1/k) bits of routing information in the network and name the vertices with O(log2n)-bit names.

Hypercube message routing in the presence of faults

Abstract: We discuss the problem of routing messages on hypercubes which have faulty processors and/or communication links. We are motivated by the belief that simple algorithms, operating under simple assumptions, can ensure high probabilities of successful message routing. In this paper, we consider the basic problem of routing a single message from an arbitrary source to an arbitrary destination. In our study, a fault is assumed to render the processor or link non-functional for purposes of communicating messages. As such, we may also consider communications hot spots as node faults, and our results also apply to routing in congested hypercubes.A framework for the analysis of fault tolerant routing schemes on a hypercube is presented. This framework includes differing routing schemes, routing information models and fault distribution models. The a priori probabilities of successful routing of a single, indivisible message under each of our possible sets of assumptions are calculated. Using random routing, under the one-step local information routing model, we show that the a priori probability of successful message routing is high even for an exceedingly large number of faults. We also analyze the behavior of sidetracking, a routing method which combines the concepts of local information and randomization. Using sidetracking, and in the one-step local information routing model, a message will be routed forward using random routing. If the message reaches a blocked processor (no non-faulty neighbors along a minimal path to the destination) it will be sent to a non-faulty neighbor, chosen uniformly at random from the set of non-faulty neighbors. We use simulation experiments to determine the performance of this routing scheme, analyzing the probability of successful routing and the expected path length of a routed message. The empirical performance of the sidetracking algorithms indicates strongly that, in the limit as the cube dimension grows larger and for a fixed probability of node failure, the probability of successful message routing is 100%.

Over-the-cell channel routing

Abstract: A common approach to the over-the-cell channel routing problem is to divide the problem into three steps: (1) routing over the cells; (2) choosing net segments; and (3) routing within the channel. It is shown that the first step can be reduced to the problem and finding a maximum independent set of a circle graph, and thus can be solved optimally in quadratic time. Also, it is shown that to determine an optimal choice of net segments in the second step is NP-hard in general, and an efficient heuristic algorithm for this step is presented. The third step can be carried out using a conventional channel router. On the basis of these theoretical results, an over-the-cell channel router that produces solutions which are better than the optimal two-layer channel routing solutions for all test examples is designed. The over-the-cell channel router also outperforms the over-the-cell channel router described by Y. Shiraishi and Y. Sakemi (ibid., vol.CAD-6, no.3, p.462-71, 1987). In particular, for Deutsch's difficult example, the solution yields a saving of 10.5% in channel routing area when compared with the optimal two-layer channel routing solution, and a saving of 15% in channel routing area when compared with the routing solution produced by the over-the-cell channel router. >

A new approach to three- or four-layer channel routing

Abstract: An approach to the three-layer or four-layer channel-routing problem is presented. A general technique that transforms a two-layer routing solution systematically into a three-layer routing solution is developed. The proposed router performs well in comparison with other three-layer channel routers proposed thus far. In particular, it provides a ten-track optimal solution for the famous Deutsch's difficult example, whereas other well-known three-layer channel routers required 11 or more tracks. The approach is extended to four-layer channel routing. Given any two-layer channel-routing solution without an unrestricted dogleg that uses w tracks, the router can obtain a four-layer routing solution using no more than w/2 tracks. A theoretical upper bound d/2+2 for arbitrary four-layer channel routing problems is also given. >

Codar: a congestion-directed general area router

Abstract: A general area router that integrates the phases of global routing and detailed routing has been developed. The global phase coarsely places the nets based on the congestion of the routing region, and the detailed phase modifies the course wiring to find legal positions for all wire segments. Both phases use the same grid space of routing tracks with two or more levels of interconnect. With this integrated data structure, the router can alternate between global and detailed routing operations, both of which use rip-up and reroute techniques. This integration has resulted in a router that can solve difficult problems not solvable by other programs while exhibiting runtimes that grow only moderately with the size of the routing problem. >

Optimal routing algorithms for mesh-connected processor arrays (extended abstract)

Abstract: We show that there is a randomized oblivious algorithm for routing any (partial) permutation on an n × n grid in 2n+O (log n) parallel communication steps. The queues will not grow larger than Θ(log n) with high probability. We then modify this to obtain a (non-oblivious) algorithm with the same running time such that the size of the queues is bounded by a constant with high probability. For permutations with locality, where each packet has to travel distance at most L in either the horizontal or the vertical direction, a generalization of the algorithm routes in time 3L+o(L), while the queue size remains bounded by Θ(log n) with high probability. Finally, we show that for a general class of oblivious deterministic routing strategies, Ω(n 2) time is required if we want to have constant size queues.

Source routing bridge implementation (LANs)

Abstract: Source routing is a bridging technique where the bridge makes a routing decision based on the contents of the media access control (MAC) frame header of the frame. This header consists of a routing information field, which immediately follows the source address field in the frame. The routing information field describes the path across one or more bridges to the ring containing the destination station. With source routing bridges, the source and destination addresses of the frame on the media are the MAC addresses of the originating and target stations, respectively. The operation of a source routing bridge is examined. An implementation example using the TMS380 token-ring-adapter chipset is presented. >

Adaptive packet routing in a hypercube

Abstract: All commercial hypercubes use fixed-path routing for packet switching. However, it has long been known that adaptive routing reduces packet delay by sending packets via less congested areas. Moreover, the hypercube topology contains many alternative, equal-length paths, suggesting the desirability of adaptive routing. Noting the importance of a communication system and the efficiency of adaptive routing, we investigate the effect of packet routing on communication latency and message throughput in a hypercube. As a feasibility study of adaptive routing, we selected four representative adaptive routing methods for testing on the Intel IPSC: NRCC routing, shortest queue, delta, and hybrid weighted routing. In NRCC routing, a single node, the network routing control center (NRCC), collects network status information and distributes routing tables to all other nodes. In contrast, shortest queue routing is fully distributed; each node selects the link with the shortest queue of outgoing messages that is the part of a shortest path to the destination node. Delta and hybrid weighted routing are hybrid schemes, combining centralized NRCC routing and distributed shortest queue routing. Extensive simulation studies and implementation confirm the superiority of adaptive routing to the fixed-path routing in commercial hypercubes. This result holds for a variety of traffic models, including high temporal locality and traffic surges.

Multi-pads, single layer power net routing in VLSI circuits

Abstract: An algorithm is presented for obtaining a planar routing of two power nets in building-block layout. In contrast to other works, more than one pad for each of the power nets is allowed. First, conditions are established to guarantee a planar routing. The algorithm consists of three parts, a top-down terminal clustering, a bottom-up topological path routing, and a wire-width calculation procedure. Because of the hierarchical nature of the algorithm, it is inherently fast. >

Decentralized adaptive routing for virtual circuit networks using stochastic learning automata

Abstract: The problem of routing virtual circuits according to dynamical probabilities in virtual-circuit packet-switched networks is considered. Queueing network models are introduced and performance measures are defined. A decentralized asynchronous adaptive routing methodology based on learning automata theory is presented. Every node in the network has a stochastic learning automaton as a router for every destination node. The routing probabilities that are assigned to the network paths are updated asynchronously on the basis of current network conditions. A learning algorithm suitable for routing is used. Some initial simulation experiments, for a simple network, show convergence to optimal routing. >

Packet forwarding

Abstract: A packet network is viewed as consisting of two major interacting layers: a lower layer responsible for the determination of a set of paths that can be used to carry packet flows, and an upper layer responsible for actually sending the flows over these paths, on a per-packet basis. A systematic review is provided of the various techniques that can be used to perform the actual packet-by-packet routing operation at the upper layer, called the packet forwarding function. The function components of a routing system and its characteristics (responsiveness to changes in network state and degree of centralization) are discussed. Five routing techniques are then examined, namely source, directory, destination, global-path, and channel-link-path routing. >

Permutation Channel Routing

Abstract: Most of the channel routing algorithms in the literature [Deut76, YoKu82, RiFi82, BuPe83, ReSS85] including the simulated annealing channel routers studied in Chapter 4 assume a model in which the pins on the two sides of the channel are fixed (both physically and logically.) Other models that reflect less stringent physical constraints have also been studied. In [GoCW83], it was assumed that only the relative ordering of the pins is fixed. The pins are allowed to “shift” horizontally. This model captures the possibility of expanding or contracting the dimensions of a cell. In [LeLi83] and [Leon86a], the discretionary channel routing problem in which only some of the pins in a given net need to be interconnected was studied. This model captures the possibility of having physically equivalent pins or duplicated pins in a cell. As expected, such flexibilities lead to better routing results, namely, fewer tracks are required for interconnection.

A new self-routing switch driven with input-to-output address difference

Abstract: A self-routing switch for fast packet switching is proposed. The routing method uses the difference between the input and output addresses as a routing header value. Every information block with a routing header is easily routed to its destination line with no congestion in the switch. It is suitable for VLSI technology: a throughput of 1.6 Gb/s for a 16*16 switch is possible in a chip using CMOS technology. The switch consists of multistage circulated shift registers and output buffers. Multipoint connection can also be provided without additional complex hardware. The routing algorithm, mechanism, and applications of the switch are presented. >

Optimal routing in a network with unreliable links

Abstract: An investigation is conducted of the routing of packets in a network in which the link error rates vary A queuing network model that incorporates the effect of the link error rates is developed and is used to find optimal routing assignments for fixed error rates Single-path and multiple-path dynamic routing algorithms that minimize the average packet delay or the failure probability of packet transmission are proposed In case the network state is not exactly known, stochastic learning automata are proposed to drive the routing process >

Connectivity biased channel construction and ordering for building-block layout

Abstract: A number of techniques are presented for the construction and ordering of routing channels for building-block layout. First, before the routing channels are defined the placement is modified such that proper routing space is assigned between the circuit blocks. Second, a channel graph is constructed on which the global routing will be performed. Finally, after the global routing a feasible routing order is assigned to the channels. In contrast to other works, the algorithms use both the geometrical data (the placement) and the topological data (the connectivity) to decide which channel structure should be chosen from the feasible set.

Performance evaluation of a hierarchical hybrid adaptive routing algorithm for large scale computer communication networks

Abstract: A hierarchical hybrid adaptive routing algorithm (HHARA) is presented for dynamic large-scale computer communication networks (LSCCN). The performance of the proposed algorithm is evaluated and compared to that of nonhierarchical routing algorithms by simulation experiments on a 50-node network model. The major evaluation criteria are reliability, communication overhead, computation overhead, and average packet delay. A fixed routing algorithm, the most recent ARPANET routing algorithm, and HHARA are compared using simulation experiments. The simulation study indicates that HHARA makes a good balance between the reduction of routing database maintenance overhead, and the global routing capability as well as the local adaptivity to the network changes. >

Simple three-layer channel routing algorithms

Abstract: In this paper we present a simple three-layer assignment algorithm for planar layouts generated by a class of layout algorithms. This class of algorithms includes simple variations of the currently best algorithms for the three layer channel routing problem (CRP). More specifically, this class includes algorithms "equivalent" to the following algorithms (i–iii) developed by Mehlhorn, Preparata and Sarrafzadeh [7].

Distributed load balancing

Abstract: Summary form only given. The authors solve a load balancing problem for parallel processors, given limited state information. The novelty of the problem is that the routing units at the parallel arrival streams of tasks have different and limited state information. This makes the problem a team problem of a distributed control problem. The engineering model for this problem consists of arrival streams of tasks, routing units and processors. The control problem is to synthesize an algorithm for the routing units. Both open-loop and closed-loop routing algorithms are considered. A performance analysis has been carried out for the case of two processors. >

Discretionary channel routing

Abstract: In the paper, the channel routing model is generalised to incorporate some design flexibilities into the channel routing process. The channel router then makes use of the additional flexibilities to obtain better overall routing solution (and hence more compact layouts). Specifically, the channel routing problem is generalised so that a given net is only required to connect some (not necessarily all) of the pins in that net. The generalised problem is called the discretionary channel routing problem (DCRP). Various applications of the DCRP are presented. Solution of the DCRP involves two phases: the selection phase in which the pins are selected, and the connection phase in which the selected pins are routed. Two classes of algorithms for solving the DCRP are studied. In the first class, a target router is selected and the pins are selected to enhance the performance of that router. In the second class, pins are selected according to some absolute criterion that is independent of the target router. The algorithms have been implemented and tested on various (benchmarks and randomly-generated) problems. For all the test problems, the algorithms produce results that are either nearoptimal or optimal. In particular, excellent results were obtained for all the benchmark problems. Comparisons of these methods are also given, together with recommendations for choice of method for a given situation. Finally, the results show that the additional flexibility in the DCRP model leads to substantial savings in the wiring area, thus leading to more compact layout.

On routing and performance comparison of techniques for packet-switched networks using learning automata

Abstract: Distributed adaptive routing algorithms with the ability to adaptively proportion traffic over several paths is proposed for packet-switched data networks. A learning automaton is situated at each node of the network where a routing decision must be made and directs traffic entering the node onto one of the outgoing links. Using network feedback, and automaton modifies its routing strategy to improve its link selections. This approach has the advantage over existing routing schemes of offering a simple and extremely practical feedback and updating policy. >

Message routing schemes in a hypercube machine

Abstract: The aim of this study is to determine efficient routing schemes for message passing in a hypercube machine. Two different algorithms are considered, namely static routing in which the path of a message is predetermined by the addresses of the source and destination nodes, and dynamic routing where the decision as to the next node in the path is made by the current node on the basis of local information regarding queue lengths. In addition, various different prioritization schemes are compared for both static and dynamic routing. The results show that dynamic routing can be up to twice as efficient as static routing, provided priority is given to messages which have only a few hops to traverse or were transmitted early in the computation sequence.

On routing and performance comparison of techniques for

Abstract: Distributed adaptive routing algorithms with the ability to adaotively proportion traffic over several paths is proposed for packet-switched data networks. A learning automaton is situated at each node of the network where a routing decision must be made and directs traffic entering the node onto one of the outgoing links. Using network feedback, an automaton modifies its routing strategy to improve its link selections. r'his awproach has the advantage over existing routing schemes of offering a simple and extremely practical feedback and Updating policy.

A survey of hierarchical routing algorithms and a new hierarchical hybrid adaptive routing algorithm for large scale computer communication networks

Abstract: A survey is presented of present algorithms, with emphasis of a proposed scheme, the hierarchical hybrid adaptive routing algorithm (HHARA). HHARA reduces the size of routing database by dynamically organizing nodes into hierarchically structured clusters so that only partial information is stored and maintained in each site. The responsibility for routing is shared by the routing hierarchy so that the algorithm can maintain the global routing optimality and the local adaptivity at the same time. In this way, the storage, maintenance, communication, and computation overheads can be reduced while the response time to local status changes is kept small. HHARA can be used with either diagram routing or virtual circuit routing. Due to its ability to adapt to the network changes, it is specially useful for dynamic networks such as large military computer communication networks. >

NOM-a tool for optimal design and performance evaluation of routing strategies and its application to the Telenet network

Abstract: A network optimization model (NOM) that provides a tool for performance analysis and optimal design of a broad class of routing strategies is presented. It can evaluate and optimize both static and dynamic, local and global routing strategies. The tool is applicable to both packet-switched and circuit-switched networks. NOM software is based on original modeling methods and optimization algorithms. It is user-friendly and menu-driven, and has extensive 'what if' capabilities. NOM can be used for performance evaluation of existing routing strategy and for optimal routing design for a given performance criterion. As a performance evaluation tool, for a given network topology, link and node capacities, point-to-point demand matrix, and routing strategy, NOM models the routing and computes important characteristics of network performance. As a routing optimization tool, for a given network topology, link and node capacities, point-to-point demand matrix, and performance criterion, NOM generates the optimal routing, and computes important characteristics of network performance. The current Telenet local dynamic routing strategy is compared with a set of optimal routing strategies designed for various performance criteria. >