Showing papers on "Multipath routing published in 1986"

Distributed asynchronous optimal routing in data networks

Abstract: In this paper we study the performance of a class of distributed optimal routing algorithms of the gradient projection type under weaker and more realistic assumptions than those considered thus far. In particular, we show convergence to an optimal routing without assuming synchronization of computation at all nodes and measurement of link lengths at all links, while taking into account the possibility of link flow transients caused by routing updates. This demonstrates the robustness of these algorithms in a realistic distributed operating environment.

Near-Optimal n-Layer Channel Routing

Abstract: In this paper we present two n-layer channel routing algorithms that guarantee successful routing of the channel for n greater than three. The first is linear and optimal given a VHV...HV assignment of layers. The second, using an HVH...VH layer assignment, is quasilinear and performs optimally on examples from the literature. Except in pathological cases, we expect the latter router to perform within one row of optimal. For comparison with published examples we implemented the second router in five and three layers. The five-layer implementation routed all examples optimally while the three-layer implementation routed the examples with the same or fewer rows than the published examples. With its n-layer capability this channel router will allow channel routing to be used when more than three layers are available. This router can also be used to evaluate the utility of additional layers.

State-dependent routing for telephone traffic: Theory and results

Abstract: In the modern telephone network, it has become feasible to consider sophisticated call-routing schemes in order to minimize network blocking --- in particular, routing schemes which select a route for a call on the basis of the network 'state' at the time of call-arrival. In this paper, we construct an analytical model for such state-dependent routing in the framework of Markov decision processes, and derive a simple state-dependent routing scheme called 'separable' routing. The performance of this routing scheme in two network designs for a metropolitan network model is compared over a range of loads, by means of call-by-call simulations of traffic flow, with that of two other schemes: the 'sequential' routing used in the Dynamic Non-Hierarchical Routing (DNHR) network, and the 'Least-Loaded Routing' (LLR) proposed for the Trunk Status Map. In one case, separable routing achieves lower network blocking than the other schemes at normal load and overloads, while, in the other case, the improvement occurs only above a certain level of overload. However, a modified version of separable routing (to be presented in a future paper) achieves better performance than the other schemes in both networks over the entire range of loads.

Near-optimaln-layer channel routing

Abstract: In this paper we present two n-layer channel routing algorithms that guarantee successful routing of the channel for n greater than three. The first is linear and optimal given a VHV...HV assignment of layers. The second, using an HVH...VH layer assignment, is quasilinear and performs optimally on examples from the literature. Except in pathological cases, we expect the latter router to perform within one row of optimal. For comparison with published examples we implemented the second router in five and three layers. The five-layer implementation routed all examples optimally while the three-layer implementation routed the examples with the same or fewer rows than the published examples. With its n-layer capability this channel router will allow channel routing to be used when more than three layers are available. This router can also be used to evaluate the utility of additional layers.

Vehicle Routing with Time-Window Constraints

Abstract: (1986). Vehicle Routing with Time-Window Constraints. American Journal of Mathematical and Management Sciences: Vol. 6, Vehicle Routing with Time-Window Constraints: Algorithmic Solutions, pp. 251-260.

Analysis and control of traffic routing in circuit-switched networks

Abstract: The presented paper is concerned with qualitative and quantitative analysis of advanced traffic control concepts. In the first part a survey of traffic control techniques is made with the final aim of separating the factors influencing the network grade of service. The second part is devoted to the performance evaluation of adaptive routing in two trial networks. The simulation is used to highlight the significance of network structure, signalling techniques, multiple overflows and update cycle length for the efficiency of a flexible routing rule.

Reducing Routing Overhead in a Growing DDN

Abstract: The Defense Data Network (DDN), based on ARPANET technology, is expanding rapidly. One segment of the DDN, the MILNET, will include 250 packet switching nodes by the end of 1987 and as many as 700 by 1991. One obstacle that must be overcome to allow this growth is the overhead associated with the current ARPANET dynamic routing mechanism. Both link utilization due to routing updates and routing computational load are roughly proportional to network size. This paper presents three approaches to reducing routing overhead and includes both modifications to the existing routing scheme and a design for a hierarchical extension.

The Routing Problem in Computer Networks

Abstract: Few problems in the field of computer communication networks have received as early and extensive attention as the routing problem. The reason for this is twofold. First there have been numerous studies of flow problems in network theory that provide a basis for modeling the routing problem in a mathematically tractable way and, second, routing has proved to be a necessary and fundamental design choice for the operation of message- or packet- switched networks. In its simplest form the statement of the routing problem is as follows. Consider, as in Figure 12.1, a node that receives messages from an incoming link and has a choice of forwarding them via one of two outgoing links.

Optimal message routing without complete routing tables

Abstract: 1. I n t r o d u c t i o n A basic activity in a distributed network is the routing of messages between pairs of nodes. Assuming a cost function on the edges of the network, it is desirable that the routing of each message be along a shortest path. A straightforward approach is to maintain a complete routing table at each of the n nodes, which gives for each potential destination the name of the next node on a shortest path to the destination. This approach * This research was supported in part by the National Science Foundation under grant DCR-8320124. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specfic permission. requires that n 1 items of routing information be stored at each node in the network, with each item being a node name. If the network is dense and of irregular topology, then one would not expect to be able to do appreciably better spacewise than using complete routing tables. However, for sparse networks, is it possible to maintain o(n 2) items of routing information in the network and still achieve shortest path routings? We examine this question in the context of being free to assign logn-bit names to the nodes. We present a node naming and routing scheme that can handle broad classes of networks with arbitrary nonnegative costs on the edges. The scheme groups networks, starting with the class of outerplanar networks, into a natural hierarchy based on the amount of space devoted to storing routing information. Shortest path routing schemes for tree and unit-cost ring networks have been presented in [SKI and later in [vLT1]. The nodes are assigned names from 1 to n, and the end of every edge {v, w} incident with any node v is labelled with a subinterval of [1,hi. The interval represents the set R.,~ of nodes such that there is a shortest path from v to each node in Rv,w with the first edge on this path being {v, w}. In [vLW2] interval labelling schemes are also given for certain highly regular networks with edges of unit cost, including complete graphs, complete bipartite graphs, and grids. We first give an interval labelling scheme for outerplanar networks with arbitrary nonnegative costs on the edges. The scheme stores just d + 1 items of routing information at every node v, of degree d. Thus O(n) items of routing information are stored in total. For arbitrary nonnegative © 1986 ACM 0-89791-198-9/86/0800-0088 75¢ as edge costs, we show that the outerplanar graphs are precisely the graphs for which such an interval property holds. Furthermore we establish a very nice 'reflection' property of outerplanar graphs. Using this property we are able to generate an optimal algorithm for determining the labels of all edges. In [vLT2] a k-interval labelling scheme is proposed, in which each edge is labeled with up to k intervals. It is shown in [vLT2] that a grid with rowand column-wraparound and unit costs has an optimal 2-interval labelling. We present an incomparable but still stronger result, in that it is applicable to graphs with arbitrary nonnegative edge costs. We show that k-interval labelling schemes, for k > 1, can handle classes of graphs much richer than the class of outerplanar graphs. In particular, we establish that any graph that can be embedded in the plane such that all but q of the vertices are on p faces has a [(3p + q)/2J-interval property. Alternatively, the number of items of routing information required at a node of degree d is at most 3p+q+d-2. If the p faces form s connected components, we show that the graph has a [(2p + s + q)/2J-interval labelling, with a total of at most 2p+ s + q+ d 2 intervals at any node. Our approach can also be applied to graphs that can be embedded on a surface of positive genus g. We show that such graphs possess a [ (2p+ s + q + 4g)/2J-interval labelling, and use a total of at most 2p + s + q + 4g + d 2 intervals at any node. In addition, our labelling scheme can be adapted naturally to planar graphs in which we wish to route messages to vertices on only a selected subset of the faces. This technique can then be applied in a scheme for near-shortest path routings in general planar graphs IF J]. 2. R o u t i n g in o u t e r p l a n a r n e t w o r k s We first summarize the interval routing method presented in [SKI for trees and rings. Assume that the nodes are named in an appropriate manner with the integers from 1 to n. Let v be any node, and let the degree of v be d. Each edge incident with v is labelled by an interval, with the intervals from all edges incident with v forming a partition of [1, hi v. Wraparound is allowed in the intervals. For instance, the interval [ i , j ) , i > j , contains { i , i+ 1, . . . ,n, 1 , . . . , j 1}. Denote the intervals by [li, l~+x), for i = 1, 2 , . . . , d, where ld+l = v. Without loss of generality, assume that interval [/,,/,+1) labels edge {v,w,}. The values li, i = 1 ,2 , . . . ,d, are stored in a table at node v, each with a pointer to associated edge {v, wi). When a message arrives at node v, if its destination u is not equal to v, then the table is searched for the entry li such that li _< u < li+l. The message is then sent out on edge {v, wi). Since the values li, i = 1, 2 , . . . , d + 1 form a rota ted list [MS, F2], the table can be searched in O(log d) time using a modified binary search. The interval labelling method also works for outerplanar networks if the nodes are named appropriately. An outerplanar network is a network that can be embedded in the plane such that all nodes lie on one face [H]. Throughout the paper, we consider outerplanar networks in the context of such an embedding, called an outerplane embedding. We assign as names to the nodes the integers from 1 to n in consecutive order starting at an arbi trary node and proceeding clockwise around the exterior face. If any node v is visited more than once in this traversal, i.e., v is an articulation point of the network, then v may be named on any one of the visits. We call such a naming of the nodes a suitable node naming. An outerplanar network with a suitable node naming is shown in Figure 1. We first show that for any assignment of costs to edges, each end of every edge can be labelled with an interval such that routing is along shortest paths. Such a labelling of the edges of the network of Figure 1 is shown

An optimal adaptive routing algorithm

Abstract: An adaptive routing algorithm for packet-switched networks is proposed. This algorithm updates both the estimate of external traffic input and the routing assignments at each iteration. The routing assignments determine the proportions of the traffic destined for node j to be sent from node i through the outgoing links of i . The algorithm maintains the loop freedom of the routing assignment at each iteration. It also achieves the minimum delay of the network as the limit of its successive updating procedure. The additional features of the algorithm are that it allows at any iteration some routing assignments which theoretically induce infinite delay and that it may utilize variable scaling factors to speed up the convergence.

Continuous routing and batch routing on the hypercube

Abstract: In this paper we study two related routing problems on the n-dimensional hypercube: continuous routing, referring to the infinite routing process in which one new permutation is generated every constant r time steps, and batch routing, in which n permutations axe to be routed at the same time. We show that continuous routing with suitable value of r is feasible by giving a probabilistic routing algorithm that guarantees an 0 (n) completion time for any given permutation with overwhelming probability. The proof relies heavily on a probabilistic batch routing algorithm that has an 0 (n) completion time - an improvement over Valiant's classical 2-phase probabilistic routing algorithm when routing n permutations at the same time.

Optimal Rotation Problems in Channel Routing

Abstract: In the channel routing problem, a problem arising in the design of layout systems, two rows of terminals which are opposite each other, have to be connected. We study what effect the rotation of one row of terminals has on the cost measures of the routing phase. The cost measures we consider are the density, which is proportional to the width of the channel, the crossing number, which is closely related to the number of crossings between two wires in the channel, and the length of nets, which is related to the wire length needed in the routing. We present algorithms for determining the rotations which minimize each of these cost measures. The algorithms can also be used for solving optimal offset problems.

A New Routing Algorithm and Its Hardware Implementation

Abstract: Presented is a new parallel processing wire routing algorithm that can control path quality in two point connections and find a quasi-minimum Steiner tree for multi-point connections. A parallel rip-up technique for finding a candidate path which blocks an unconnected net is also presented. These routing algorithms are implemented on a two-dimensional array processor, the AAP-1. It is experimentally shown that the average AAP-1 execution time per net using the routing algorithm is 100 msec in a 256X256 grid.

Algorithms for Global Routing

Abstract: This paper presents several algorithms for global routing, including a very fast shortest path connection algorithm based on wave propagation and diffraction, a heuristic minimum tree algorithm using 'Common Edge' analysis, an overflow control method, and global rerouting treatment. These algorithms have been implemented in C and very good experimental results have been obtained.

Hierarchical Dynamic Router

Abstract: In this paper we will discuss a new automatic routing method for printed circuit boards(PCBs). In the field of automatic PCB routing, several "rip-up and reroute" techniques ("dynamic routing") have recently been proposed. Dynamic routing works by changing one or more previously routed features, and identifying unrouted connections in a new configuration. Dynamic routing is an important idea, because it has the possibility of 100% completion by automating the wire embedding that was formerly done manually. The method we propose here is based on dynamic routing. Its distinctive feature lies in the organization of three levels of hierarchy; grid routing, local dynamic routing, and global dynamic routing. In recent experiments with this method, improvement in both routing completion rate and processing time has been obtained.

A New Approach to Multi-Layer PCB Routing with Short Vias

Abstract: The routing problem for Printed-Circuit Boards (PCB's) is crucial in the fabrication of today's digital systems. Traditionally, this problem has been divided into two main sub-problems: layer assignment and routing. Considering these two problems apart from each other may cause uneven wire distribution both among the wiring layers and within each layer. Uneven wire distribution among the wiring layers could increase the number of wiring surfaces required for the routing. Uneven wire distribution within a layer could result in an unfeasible routing. We propose a new approach to deal with the routing of PCB's in technologies which allow short vias. The proposed methodology considers the layer assignment and routing problems in a unified fashion. Based on some global information, our algorithm first estimates the initial number of layers required for the routing. It then determines an ordering in which nets should be considered during the layer assignment process. The results of our experiments show that our algorithm is of practical use.

The impact of wire topology on channel routing

Abstract: Channel routing is a method that has been widely used to overcome the inherent difficulties in the routing stage of automated VLSI chip and printed circuit board design. Almost all previous work on channel routing has restricted the wires to paths that are strictly monotonic (i.e. paths that do not backtrack in either the horizontal or vertical direction). The impact on single layer channel routing of wire topologies that provide considerably more wire routing flexibility than has previously been allowed is addressed here. A hierarchy of routing classes stemming from these generalized wire topologies is defined. It is shown that each of the routing classes is applicable to both the two row routing scenario (river routing) and the single row routing scenario. For river routing, it is shown that for all but one of the classes, optimal routings can be produced in time that is no worse than the time that is necessary to produce optimal river routings using the previously considered wire topologies. In addition, tight bounds on the performance improvements achievable among the various classes are derived. In so doing, river routings using wires with the newly defined topologies are shown to result in significantly more compact routings than have previously been possible. The routing classes are examined to see if the flexibility provided by the new wire types is useful for single row routing. The usefulness of these wire types is established in two ways. First, it is shown that the flexibility of the wire topologies that are utilized in the routing classes facilitates a larger group of single row routable instances. (Unlike river routings, there are instances of single row routing that cannot be routed using the traditional type of wire restrictions). Second, these results are supplemented by results showing that single row routings in each richer class of routings can improve by a small constant factor over single row routings in the more restricted classes. The question of finding polynomial time algorithms to produce optimal single row routings is also addressed. Global routing under the channel routing scenario is briefly examined. In particular, a simplistic two layer global channel routing problem is shown to be NP-complete using two separate optimization criteria. These global routing results are used to show that two generalizations of 0-1 network flow are NP-complete. In so doing, the line between the classes P and NP is delineated for these generalized versions of 0-1 network flow.

Routing as a flow control strategy in an integrated circuit/packet switched communications network

Abstract: This research addresses the analysis of an event-driven FORTRAN Simulation Model that simulates a special kind of Computer-Communication network. The network modeled has a circuit-switched communication subnet whose trunk lines carry both voice and data traffic simultaneously. This effort considers the viability of routing strategies as a mechanism for reducing congestion. The performance of seven alternative routing strategies are measured in terms of user-visible metrics.Based on the experimental results obtained, this research concludes that fixed routing, the technique assumed by most models, is not as effective a tool for reducing congestions as would be a strategy based on link utilization. Minimization of congestion can be realized only if the routing strategy is adjusted as workload varies. Experimental data supporting these conclusions is presented.

Distributed control of routing in circuit-switched networks

Abstract: How should calls be routed in a circuit-switched communication network so as to minimize some overall measure of blocking? Here we show that under a simplified analytical model of a circuit-switched network there exist implicit shadow prices associated with each route and with each link of the network. These prices are defined in an essentially local manner, and can be used as a basis for distributed control of routing through the network.

A Heuristic for Manhattan Routing

Abstract: [ U N C L A S S IF IE O /U N L IM IT E D £3 SAME AS RPT. 22a. N A M E OF RESPONSIBLE I N D IV ID U A L [D FORM 1473, 83 APR O TIC USERS □ 21. A B S T R A C T S E C U R IT Y C L A S S IF IC A T IO N Unclassified 22b. T E L E P H O N E N U M B E R (Include Area Codei E D IT IO N OF 1 jA N “3 IS OBSOLETE. 22c. O FFIC E S Y M B O L S E C U R I T Y C L A S S I F I C A T I O N OF T H I S = S E C U R IT Y C L A S S IF IC A T IO N O F T H IS PAGE I accordingly to certain priorities assigned to the vertices of A and B. The algorithm is coded in Pascal and implemented on a VAX 11/780 computer and its running time is 0 (n2), vhere n denotes the number of nets. Experimental results are particularly satisfactory when runs of quite different lengths can be reduced to the same length.