Showing papers on "Multipath 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 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.

Geometrical Compaction in One Dimension for Channel Routing

Abstract: A channel router which is to be effective for general-purpose automatic routing must be able to use different sets of routing criteria priorities, in a controllable manner. We present an approach to channel routing with compaction in which channel compaction is adaptable to several routing criteria priorities. We show how overall channel routing performance can be improved by taking advantage of this versatility in channel compaction. We indicate some routing capabilities which cannot be effectively achieved by simply post-processing the output of a traditional gridded channel router. Our solution to this problem is outlined and some results obtained from our router are compared with those of other published channel routers.

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.

Vehicle routing with time windows: optimization and approximation

Abstract: A survey of solution methods for routing problems with time window constraints. Among the problems considered are the traveling salesman problem, the vehicle routing problem, the pickup and delivery problem, and the dial-a-ride problem. Optimization algorithms that use branch and bound, dynamic programming and set partitioning, and approximation algorithms based on construction, iterative improvement and incomplete optimization are presented.

General Purpose Router

Abstract: Numerous solutions to the problem of detailed routing of wires on a chip have been proposed for two routing layers but few are general enough to also handle switchboxes, more than two layers, variable channel widths, or multiple-layer problems with stacked terminals (3-D routing) without extensive modifications. We propose a different routing approach that not only can solve the two layer problem but the other problems as well. The inherent parallelism of the approach lead to a coarse-grained parallel algorithm.

On an Optimally Fault-Tolerant Multiprocessor Network Architecture

Abstract: This correspondence presents a class of optimally fault tolerant multiprocessor network architecture, based on the networks proposed earlier by Pradhan [71, where the networks are represented by regular digraphs. Because of optimal fault tolerapce, the number of connections per node is precisely related to the degree of fault tolerance the network is designed to provide. The routing of messgges in presence Qf faults is adaptive and unless the number of faults is equal to the degree of fault tolerance the increase in routing delay in presence of faults is minimal.

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.

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.

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.

Packet-Switched Performance with Different Circuit-Switched Routing Procedures in Nonhierarchical Integrated Circuit-Switched and Packet-Switched Networks

Abstract: It is shown in [13] that different types of routing procedures for circuit-switched traffic in a nonhierarchical network exhibit various performance tradeoffs. It is, however, not clear if the network is also allowed to carried packet-switched traffic, how the packet-switched traffic will be affected by using different routing procedures for the circuit-switched traffic. In this paper, we examine the average time delay of the packet-switched traffic assuming that the network uses a movable boundary scheme to allocate bandwidth dynamically

A comment on current source routing techniques

Abstract: The purpose of this note is to air the author's belief that there is a certain deficiency in the way the "source route" option is defined in both the ISO and DoD Internet Protocols. The two protocols handle source routing in essentially the same manner, and do not provide the full capability that one might like to have from this option. It is proposed that a very slight addition would rectify this situation in both ISO and DoD IP.

A New Hierarchical Scheme for Combined Routing and Flow Control in Data Networks by Application of Positive System Theory

Abstract: In this paper we shall present some new results obtained from an application of Positive System Theory [1] to the problem of designing combined routing and flow control strategies for data communication networks. This application permits treating the combined routing and flow control problem in the framework of system stabilization and results in a hierarchical control scheme. The overall control effort consists of a distributed computation of a set of routing 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. Specific algorithms are presented for adaptive updating of these parameters in order to realize improved network performance taking into account multiple objectives of end-to-end delay, throughput and nodal buffer management. The combined routing and flow control problem is attaining a great deal of importance in the recent times. This is due to the fact that the routing schemes and the flow control schemes implemented in existing data networks are designed independent of each other, where-as it has recently been determined [2,3] that a high degree of interplay exists between the two forms of control which has to be taken into account for realizing improved network performance. It has also been determined that a hierarchical control structure provides a very useful mechanism for an integration of routing and flow control [4,5].

Designing Networks with Compact Routing Tables AVAILABLE IN A JOURNAL

Abstract: O. Abstract. Classes of network topologies are identified in which shortest path information can be succinctly stored at the nodes, if they are assigned suitable names. The naming allows each edge at a node to be labeled with zero or more intervals of integers, representing all nodes reachable by a shortest path via that edge. Starting with the class of outerplanar networks, a natural hierarchy of networks is established, based on the number of intervals required. The outerplanar networks are shown to be precisely the networks requiring just one interval per edge. An optimal algorithm is given for determining the labels for edges in outerplanar networks.