Showing papers on "Destination-Sequenced Distance Vector routing published in 1987"

Deadlock-Free Message Routing in Multiprocessor Interconnection Networks

Abstract: A deadlock-free routing algorithm can be generated for arbitrary interconnection networks using the concept of virtual channels. A necessary and sufficient condition for deadlock-free routing is the absence of cycles in a channel dependency graph. Given an arbitrary network and a routing function, the cycles of the channel dependency graph can be removed by splitting physical channels into groups of virtual channels. This method is used to develop deadlock-free routing algorithms for k-ary n-cubes, for cube-connected cycles, and for shuffle-exchange networks.

A classification scheme for vehicle routing and scheduling problems

Abstract: 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. The classification scheme may serve as a first step towards the development of a model and algorithm management system in this area.

A Detailed Router Based on Incremental Routing Modifications: Mighty

Abstract: For the macrocell design style and for routing problems in which the routing regions are irregular, two-dimensional routers are often necessary. In this paper, a new routing technique that can be applied for general two-layer detailed routing problems, including switchboxes, channels, and partially routed areas, is presented. The routing regions that can be handled are very general: the boundaries can be described by any rectilinear edges, the pins can be on or inside the boundaries of the region, and the obstructions can be of any shape and size. The technique is based on an algorithm that routes the nets in the routing region incrementally and intelligently, and allows modifications and rip-up of nets when an existing shortest path is "far" from optimal or when no path exists. The modification steps (also called weak modification) relocate some segments of nets already routed to find a shorter path or to make room for a blocked net. The rip-up and reroute steps (called strong modifiction) remove segments of nets already routed to make room for a blocked connection; these steps are invoked only if weak modification fails. The algorithm has been rigorously proven to complete in finite time and its complexity has been analyzed. The algorithm has been implemented in the "C" programming language. Many test cases have been run, and on all the examples known in the literature the router has performed as well as or better than existing algorithms. In particular, Burstein's difficult switchbox example has been routed using one less column than the original data. In addition, the router has routed difficult channels such as Deutsch's in density and has performed better than or as well as YACR-II on all the channels available to us.

Routing L-Shaped Channels in Nonslicing-Structure Placement

Abstract: The concept of L-shaped channels was first introduced in RRDO [1] to generate a feasible routing order for nonslicing-structure placement in building-block layout design. This paper presents two approaches for the L-shaped channel-routing problem. In the Manhattan approach, only horizontal and vertical wires are used. The L-shaped channel is divided into two subchannels. The vertical subchannel will be routed first, then the horizontal subchannel will be routed by a special channel router which can handle fixed terminals on 3 sides. Since the routing constraints will change during the boundary movement, several iterations may be needed to complete the routing. In the non-Manhattan approach, 45 ° wires are used to preserve the routing constraints when the boundary is moved in the 45 ° direction. With all the vertical constraints substituted by 45 ° constraints, the L-shaped channel-routing problem can be directly mapped into the straight-type channel-routing problem. Horizontal or vertical extension wires are used to connect terminals on an indented boundary and to separate terminals which are too close to allow the generation of 45 ° wires. Experimental results show that both approaches provide good solutions to the L-shaped channel-routing problem.

A new look at fault-tolerant network routing

Abstract: We model a communication network as a graph in which a processor is a node and a communication link is an edge. A routing for such a network is a fixed path, or route, between each pair of nodes. Given a network with a predefined routing, we study the effects of faulty components on the routing. Of particular interest is the number of routes along which a message must travel between any two non-faulty nodes. This problem is analyzed for specific families of graphs and for classes of routings. We also give some bounds for general versions of the problem. Finally, we conclude with one of the most important contributions of this paper, a list of interesting and apparently difficult open problems.

A Preliminary Investigation into Parallel Routing on a Hypercube Computer

Abstract: This paper describes an experiment in which parallel routing is performed on a medium grained hypercube parallel processor having 64 processing elements. Each node is a complete 32-bit computer with 128 K-bytes of memory and is connected to the other nodes via a direct hypercube interconnection network. A new parallel routing algorithm was developed to exploit this parallel structure. It is a three step algorithm consisting of a global routing step, a boundary crossing placement step, and a detailed routing step. All steps can be performed in parallel. When applied to a standard benchmark it was able to route 95 % of the wires. The algorithm was also executed on a large mainframe computer using the same benchmark. The execution time was compared to that for the hypercube. The hypercube was about three times as fast.

Comparison of Routing Procedures for Circuit-Switched Traffic in Nonhierarchical Networks

Abstract: In this paper, we compare the use of different types of routing procedures for circuit-switched traffic in nonhierarchical networks. The main performance criterion used is the end-to-end blocking probability. The results show that if the network traffic is light, alternate routing performs better than nonalternate routing, but if the network traffic is heavy, the situation is reversed. To improve the performance of networks using alternate routing, different types of strategies varying from fixed control to dynamic control are introduced. A comparison based on numerical examples shows the improvement in performance attained by using a dynamic control strategy compared to fixed control. Good control techniques result in nonalternate routing under heavy traffic loads; nonalternate routing is the most viable alternative in nonhierarchical networks under heavy traffic conditions.

Single-layer wire routing

Abstract: : This dissertation concerns the problem of routing wires on a single layer of an integrated circuit or printed circuit board, starting from a sketch of the layer. A sketch specifies the positions of layout features and the topology of the interconnecting wires. Efficient algorithms are presented that (1) determine whether a sketch is routable, and (2) produce for a routable sketch a proper routing that minimizes both individual and total wire length. Both algorithms run in time O(sq n log n) on input of size n, and both are simple to implement. They can be adapted to a variety of wiring models, and they subsume most of the polynomial-time algorithms in the literature for single-layer routing and routability testing. The algorithms are based on two theorems concerning the routings of a sketch. One states that a sketch is routable if and only if for each cut between fixed features, the total amount of wiring forced to cross the cut is no greater than the length of the cut. The second theorem states that every routable sketch has a routing that simultaneously minimizes the length of every wire, and that it characterizes the wires in this routing. To formalize and prove these theorems, a rich mathematical theory of single-layer wire routing is developed. Its central tool, which is new to the wire-routing literature, is the lifting of wires and cuts to a simply connected topological covering space of the routing region.

An optimal randomized routing algorithm for the mesh and a class of efficient mesh-like routing networks

Abstract: We present an optimal oblivious randomized algorithm for permutation routing on the MIMD version of Mesh. Our routing algorithm routes n2 elements on an n×n Mesh in 2n+O(log n) parallel communication steps with very high probability. Further, the maximum queue length at any node at any time is at the most O(log n) with the same probability. Since 2n is the distance bound for the Mesh, our algorithm is indeed optimal. Generalization of this result to k-dimensional (for any k) Meshes yields an algorithm that runs in time equal to the diameter of the Mesh. A lower bound result of [Schnorr and Shamir 86] states that sorting of n2 elements takes at least 3n steps on an n × n MIMD Mesh (for indexing schemes of practical interest). Thus our algorithm demonstrates that routing is easier than sorting on the MIMD Mesh.

A Framework for Adaptive Routing

Abstract: : Message-passing concurrent computers such as the Caltech Cosmic Cube(1) and its commercial descendents consist of many computing nodes that interact with each other by sending and receiving messages over communication channels between the nodes. For finer grain message-passing concurrent machines, such as the Caltech Mosaic(2), it becomes progressively more difficult to achieve the performance required of the communication network. The bisection capacity of physically realizable communication networks grow more slowly than the expected message traffic, which is the least linear in the number of nodes.

The Multi-Depot Routing Allocation Problem

Abstract: SYNOPTIC ABSTRACTCurrent mathematical models for analyzing distribution systems usually consider the long-term “strategic problem” of Distribution Center (DC) location, and the short-term “tactical problem” of vehicle routing, independently and sequentially. While in the short-term, both the capacities and variable costs at the DC's are given, existing vehicle routing models do not consider either the capacities of the variable costs at the DC's. The proposed Multi-Depot Routing Allocation Problem (MDRAP) is that of designing vehicle routes from multiple capacitated depots with different variable costs. It can be formulated as a zero-one integer programming problem. We present an efficient heuristic for the MDRAP based on a sequential savings approach. The computational analysis suggests that DC capacities and variable costs may have significant effects on vehicle routing.

Reduced distance routing in single-state shuffle-exchange interconnection networks

Abstract: In multiprocessor architectures, it is frequently necessary to provide parallel communication among a potentially large number of processors and memories. Among the many interconnection schemes that have been proposed and analyzed, shuffle-exchange networks have received much attention due to their ability to allow a message to pass from any node to any other node in a number of steps that grows only logarithmically with the number of interconnected nodes (in the absence of contention) while keeping the number of hardware connections per node independent of the number of nodes.Straight-forward use of shuffle-exchange networks to interconnect N nodes involves having every packet pass through log2N stages enroute to its destination. By exploiting common structure in the addresses of the source and destination nodes, however, more sophisticated routing can reduce the average number of steps per message below log2N. In this paper, we describe and evaluate three levels of improvements to basic single-stage shuffle-exchange routing. Each one yields successively more benefit at the cost of more complexity. Using simulation, we show that the use of routing schemes that reduce the average distance can substantially reduce average message delay times and increase interconnection network capacity. We quantify the performance gains only in the case where messages from one node are destined with uniform probability over all nodes. However, it is clear that the advantage of the new schemes we propose would be still greater if there is some “locality” of communication that can be exploited by having the most frequent communication occur between pairs of nodes with shorter distances separating them.

Combined routing and flow control in computer communication networks: A two-level adaptive scheme

Abstract: The problem of designing combined routing and flow control strategies for packet-switched computer communication networks is considered in this paper and a new two-level adaptive scheme is presented. State dependent models for routing and input buffer limit flow control are introduced to facilitate formulating the problem, for which a solution in the framework of system stabilization is developed. The overall decision-making consists of a distributed computation of the routing parameters and the flow control parameters at the lower level of network nodes and a computation on a slower time-scale of a set of combined parameters by a supervisor (network control center) at a higher hierarchical level. The parameters are adaptively updated at both levels to improve the network performance with respect to a set of objectives concerning delay, throughput, and buffer utilization. Some implementational aspects of the algorithm are discussed and simulation results that illustrate the performance are presented. Major strong points of the present scheme are i) adaptivity to changes in load and/or network topology, ii) capability of handling different objectives individually at different hierarchical levels, and iii) consideration of capacity constrained nodal buffers in addition to capacity limited links, unlike in the earlier developed schemes, for a more realistic representation of network environment.

Efficient routing algorithm

Abstract: The line expansion algorithm provided by Heynes was a new kind of routing algorithm that took advantage of both Lee's algorithm and linear expansion algorithms, and hence was more efficient. However, it was less efficient in two layer routing situations. In this paper, this problem is analysed and several ways of solving it are proposed. Three criteria are provided in the paper, and these are used in the development of a modified line expansion algorithm. The modified algorithm is not only fast but also consumes less memory in two layer routing situations. Based on this algorithm, a Fortran printed circuit board routing system is built that can solve two layer routing problems with up to 2600 connection lines on a microcomputer with 64 kbyte RAM.

Hierarchical Loose Routing for Gate Arrays

Abstract: In this paper, we present a new, quasi-parallel approach to the loose routing problem for gate array LSI design. It is based on a new modeling for the decomposition problem of each net using a compact net graph which maps sets of feed-throughs instead of individual ones. The loose routing is done by calculation of a minimum spanning tree in this net graph and by a proper embedding of the tree as a set of single-channel subnets and feed-throughs. Moreover, a hierarchical approach is proposed, leading to a quasi-parallel embedding of all nets. It also allows different routing priorities for single connections within multiterminal nets. The hierarchical loose routing concept presented here is implemented in the fully integrated gate array design system MEGA and has been successfully tested on several industrial design examples.

Packet routing algorithms for integrated switching networks

Abstract: Repeated studies have shown that a single switching technique, either circuit or packet switching, cannot optimally support a heterogeneous traffic mix composed of voice, video and data. Integrated networks support such heterogeneous traffic by combining circuit and packet switching in a single network. To manage the statistical variations of network traffic, we introduce a new, adaptive routing algorithm called hybrid, weighted routing. Simulations show that hybrid, weighted routing is preferable to other adaptive routing techniques for both packet switched networks and integrated networks.

The Effect of Idle Server First Random Routing on the Behavior of a Finite Queue

Abstract: This paper studies the effect of routing on the behavior of a finite queue which accepts batch Poisson inputs and receives service from multiple synchronous servers. Upon the arrival of a group of customers idle or pseudoidle servers will be considered first in routing decisions. Otherwise routing will be determined randomly in accordance with a preset probability distribution. Results obtained include state probability, blocking probability, delay, and throughput. Validity of analysis has been verified by computer simulations. These results can he used in evaluating the performance of a computer communication network.

On routability for channel routing problem

Abstract: The routing requirement in the channel routing problem for automatic wire routing in the interior of LSI is realizable if the constraint graph contains no cycle. Otherwise, the trunks for several appropriate nets must be divided into pieces. In this paper we modify a routing requirement with cyclic conflicts into one without them by dividing trunks into two parts. First we define a directed bipartite graph G to represent the routing requirement. A set of vertices in a strongly connected component in G is called a crowded set. It is shown that a routing requirement is realizable if there exists no crowded set in G. On the other hand, in the presence of a crowded set we define a method of dividing a net n contained in the crowded set into two subnets n' and n'' at some terminal position. If n' and n'' are not contained in any crowded set in the graph modified by division, we say that the division is effective. We then present a necessary and sufficient condition for the existence of effective division. Further, a semi-effective division is defined to deal with the case where there is no effective division and then the routability for the channel routing problem is discussed.

A New Approach to Hierarchical Routing in Large Networks

Abstract: The overhead of an adaptive routing algorithm becomes prohibitive in a network with numerous nodes (in the order of hundreds or more) and a flat organization. In this paper, we present and analyze a new hierarchical routing algorithm for large networks. The algorithm is based on (1) the definition and maintenance of a hierarchical addressing scheme that is in turn based on the names of nodes that are well known in the network or within regions of the network, and (2) an extension of a new distributed routing algorithm first proposed by the author for flat networks.

An adaptive routing method for computer networks by electric‐circuit modeling

Abstract: The computer network and multiprocessor system have been developed and studied. They are based on a network composed of nodes containing processors, aiming at the improvement of performance by distributed processing as well as the improvement of reliability by resource distribution. To realize high system performance, adequate routing and flow controls are required in the communication of information among nodes. This paper proposes a new routing control scheme to be used in the packet communication in the computer network or multiprocessor system. The scheme is called potential routing, which models the computer network by an electric circuit, and the packet routing from the source node to the destination node is performed to the potential difference between the adjacent nodes. The node potential is determined first by Kirchhoff's law and is modified dynamically according to the traffic situation during the routing procedure, providing an adequate criterion for the routing. The proposed scheme has a feature in that ping-pong and loop phenomena, which cause traffic congestion, are not produced in principle. It was verified by simulation that the transmission delay is reduced when the traffic is high or unbalanced.

New channel routing algorithm for bit-slice applications

Abstract: A new algorithm for channel routing is presented which addresses the special problems of bit-slice architectural assembly, namely the broadcasting and cascading of signals through layout slices. This is achieved by end-on abutment of channels. The method, used in the bit-slice assembler Slicesyn, is based on a heuristic approach using graph theory.

Algorithms for Routing around a Rectangle: Extended Abstract

Abstract: Efficient algorithms are given for the routing problems around a rectangle. These algorithms find a routing with two or three layers for two-terminal nets specified on the sides of a rectangle. The minimum area routing problem is also solved.