Showing papers on "Equal-cost multi-path 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 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.

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.

Asymptotic optimality of shortest path routing algorithms

Abstract: Many communication networks use adaptive shortest path routing. By this we mean that each network link is periodically assigned a length that depends on its congestion level during the preceding period, and all traffic generated between length updates is routed along a shortest path corresponding to the latest link lengths. We show that in certain situations, typical of networks involving a large number of small users and utilizing virtual circuits, this routing method performs optimally in an asymptotic sense. In other cases, shortest path routing can be far from optimal.

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.

Abstract Routing of Logic Networks for Custom Module Generation

Abstract: This paper describes a switchbox-type router for custom VLSI module generation as performed by a module planner. A module is decomposed into abstract cells consisting of global routes and boolean functional specifications. Each abstract cell is given to a cell synthesizer which generates the circuit layout and through-the-cell routing. Abstract routing for a module planner is in some sense similar to switchbox routing to the degree that all of the routes are generated internally within a rectangular boundary (routes are coming from four sides). The principle difference with respect to standard switchbox routing is at the geometric level, where a cell synthesizer generates the routing conduction layers along with circuit devices for each abstract cell within this rectangular region. The aspects of this paper which are thought to be novel contributions are 1) a relative pin assignment algorithm for the abstract cells; 2) a global routing penalty function which not only considers previous routes, but also considers gate complexity within the cells; 3) an efficient optimization algorithm for minimizing the number of tracks running through the module.

Routing with a scanning window-8Ma unified approach

Abstract: A general approach to routing by a scanning window is presented, and an experimental switch-box router based on this approach is described. This router first grades conductor segments that are candidates to enter the window according to their estimated contributions to routing success, and then uses a quasi-maximal set of segments. A grade function that imitates human intuition is also described.

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.

Evaluation of Point-to-Point Network Routing Algorithms

Abstract: A sampling of routing algorithms is evaluated through simulation. The algorithms selected are random walk, fixed directory, split traffic, isolated shortest queue (hot potato) and backward learning. Backward learning exhibited the most desirable characteristics, approaching fixed directory routing in delay and path length, while adapting to link failures.

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.

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.