Showing papers on "Destination-Sequenced Distance Vector routing published in 1983"

Minimum-Via Topological Routing

Abstract: A new approach to the two-dimensional routing utilizing two layers is proposed. It consists of two major steps, topological routing and geometrical mapping. This paper describes the topological routing algorithm in detail. Based on a circle graph representation of the net intersection information of the routing problem, a maximal set of nets that can be routed without vias are selected. The layer assignments for the selected nets are determined by a global analysis so that the total number of vias needed is minimum. The layer assignment problem turns out to be a maximum-cut problem on an edge-weighted graph and we developed a greedy algorithm for it. According to the layer assignments, the detailed topological routes are then generated.

A tree convolution algorithm for the solution of queueing networks

Abstract: A new algorithm called the tree convolution algorithm, for the computation of normalization constants and performance measures of product-form queueing networks, is presented. Compared to existing algorithms, the algorithm is very efficient in the solution of networks with many service centers and many sparse routing chains. (A network is said to have sparse routing chains if the chains visit, on the average, only a small fraction of all centers in the network.) In such a network, substantial time and space savings can be achieved by exploiting the network's routing information. The time and space reductions are made possible by two features of the algorithm: (1) the sequence of array convolutions to compute a normalization constant is determined according to the traversal of a tree; (2) the convolutions are performed between arrays that are smaller than arrays used by existing algorithms. The routing information of a given network is used to configure the tree to reduce the algorithm's time and space requirements; some effective heuristics for optimization are described. An exact solution of a communication network model with 64 queues and 32 routing chains is illustrated.

River Routing: Methodology and Analysis

Abstract: The problem of river routing across a channel is only a special case of more general routing configurations Both its methodological and combinatorial characteristics can be extended in useful ways which will be explored in this paper The two characteristics that we generalize here are planarity and grouping Planarity means that the connections are realizable in one layer; ie the interconnection pattern of the nets is planar Grouping means that the connections are made in order, that is to say that the routing of net i+l is adjacent, conceptually and preferably physically, to the routing of net I

Single Row Routing

Abstract: The automated design of multilayer printed circuit boards is of great importance in the physical design of complex electronic systems. Wire routing is a crucial step in the design process. In this paper, the single row routing problem is considered. First, we discuss the relevance of single row routing in the context of the general routing problem. Then, we show that relaxing the restriction that backward moves are not allowed can result in smaller street congestions when there are at least four tracks in each street. Next, we obtain an O((2k)!kn log k) algorithm to determine whether or not an instance involving n nodes can be laid out (without backward moves) when only k tracks per street are available. With the additional restriction that wires are not permitted to cross streets, an efficient (O(n2)) algorithm is obtained. This restricted problem is shown to be related to a furnace assignment problem.

General River Routing Algorithm

Abstract: A general and practical river routing algorithm is described. It is assumed that there is one layer for routing and terminals are on the boundaries of an arbitrarily shaped rectilinear routing region. All nets are two-terminal nets with pre-assigned (may be different) widths and no crossover between nets is allowed. The minimum separation between the edges of two adjacent wires is input as the design rule. This algorithm assumes no grid on the plane and will always generate a solution if a solution exists. The number of corners is reduced by flipping of corners. An analysis to determine the minimum space required for a strait-type river routing problem is included. Let B be the number of boundary segments and T be the total number of terminals. The time complexity is of O(T(B+T) /sup 2/) and the storage required is O((B+T) /sup 2/). This algorithm is implemented as part of the design station under development at the University of California, Berkeley.

Optimal routing in closed queuing networks

Abstract: In this paper, we establish criteria and propose algorithms for the optimal routing of traffic in closed queuing networks. The objective is to maximize total throughput or (equivalently) to minimize overall average delay. We show that delay is convex over the set of routing patterns in networks with a single class of customers. This enables us to develop a downhill technique for finding the global minimum. The efficiency of our algorithm rests on the fact that the steepest descent direction is readily obtained at each iteration from the MVA algorithm. For multiple-class networks a counterexample is presented to show that convexity does not hold. The technique, however, can still be used to obtain local minima. The algorithm is applied to the optimization of routing in flow-controlled packet-switched networks. Several numerical examples are presented.

Dynamic Routing and Call Repacking in Circuit-Switched Networks

Abstract: The performance of three dynamic routing techniques for small circuit-switched networks is compared by simulation with three static routing techniques and with a repacking technique for calls in progress. It is found that dynamic routing algorithms improve network performance by increasing the number of paths available for call connection over what would otherwise be available to a corresponding static routing. It is also shown that call repacking increases the amount of carried traffic significantly, and that this improvement is obtained by a different mechanism than for dynamic routing. The possibility of combining the two techniques is also investigated, and general characteristics of good dynamic routing techniques are presented.

Combinatorial analysis for route first-cluster second vehicle routing

Abstract: Two Route first-cluster second vehicle routing algorithms are contrasted in the first section of the paper. Next, the ‘large’ number of feasible solutions to a multiple travelling salesman problem is established given that each salesman can visit any number of customers in a stated range. An approximate expression is given for the ‘small’ fraction of this solution space searched by a route first-cluster second vehicle routing heuristic. Nevertheless, this heuristic is seen to be a very efficient means of searching its solution space.

Optimal routing in closed queueing networks

Abstract: In this paper, we establish criteria for the optimality of routing and flow control solutions. More precisely, we investigate the convexity of the network delay function in closed queueing networks and show it exists in single chain networks. Then we derive the derivative of the network delay function with respect to relative throughput and show it can be easily obtained from the MVA algorithm. Finally, we propose a closed-network version of the FD algorithm to find the exact optimal routing solution in single chain closed queueing networks. Numerical results are presented to demonstrate the correctness and efficiency of the optimization algorithm.

An algorithm for the optimal placement and routing of a circuit within a ring of pads

Abstract: As the final stage in laying out a chip, the logic of the integrated circuit is assembled into one (not necessarily rectangular) module which must then be connected to pads lying along a rectangular frame. A placement for the module must be determined to assure the feasibility of the (river) routing from the logic inside to the pads on the periphery. We first show how to solve the routing problem in a stationary context: given the placement, can the signals be wired in the given doughnut-shaped area? Then we use the routability analysis developed in the first part to find a placement of the circuit that yields a feasible routing (if one exists). Both algorithms run in time that is quadratic in the size of the input, and there exist cases for which this bound cannot be improved upon.

A New Channel Routing Algorithm

Abstract: This paper presents a new algorithm for solving the two-layer channel routing problem with doglegging. Based on a set of intuitive and reasonable heuristics, the algorithm tries to obtain a channel routing configuration with a minimum number of tracks. For every benchmark problem tested, the algorithm gives a routing configuration with the smallest number of tracks reported in the literature.

Reducing Channel Density in Standard Cell Layout

Abstract: The problem of global routing in standard cell layouts so as to minimize total channel density is considered. A sub-problem of this, called the linear net routing problem (LNRP), is defined and is argued to be the key to a successful solution to the general problem. A polynomial-time heuristic for LNRP is presented and its behavior analyzed. In particular, it is proven that the heuristic can produce results as bad as, but no worse than, 50% over the optimal.

A hierarchical scheme for multiobjective adaptive routing in large communication networks

Abstract: A novel two-level scheme for designing protocols for optimal traffic routing in large communication networks is presented. Major strong points of the scheme are: i) it is adaptive to changes in load and network topology, ii) it permits consideration of multiple objective functions in performance optimization, and iii) it combines elements of flow control and routing for an effective control of traffic congestion.

Order of Channels for Safe Routing and Optimal Compaction of Routing Area

Abstract: For a given placement of blocks and global routing of nets, a new fonnulation and its solution of the problem of detennining the order of channels for the complete channel routing are presented. If the order of channels satisfying the condition exists, it is called the safe order since following it, each channel can be routed the wiring require­ ment without any prediction of necessary width. Thus the compaction of the routing area can be made utmost each time. The idea is based on the gene ral feature of channel routers not on any particular one. Re­ lated subjects such as the simultaneously rout able channels, generaliza­ tion of the safe order, switch box routing, and the placement with non­ rectangular blocks are discussed. ment and its global routing. Following the safe order if it exists, the routing of each channel can be completed without any prediction of necessary width. The formulation is made in an axiomatic way based on the definition of element channels and the common features of channel routers. The discussion is made graph theoretically. It is a direct conse­ quence of the definition that following a safe order, compaction of redundant space (width) of each channel after routing can be made utmost each time. Some further considerations are given to the omission of a certain constraint with respect to the channel width, simultaneously safe channels, routing of the so-called switch boxes (1), and placement including non­ rectangular blocks. It should be remarked that part of essentials of the conclu­ sion in this paper is found in (2) though the formulation and reasoning are pretty different, particularly in that they imposed the idea as the design rule and hence their model always has a safe order while this paper is to present an analysis tool for a given placement and global routing.

On the structure of decentralized dynamic routing strategies

Abstract: The problem of dynamic routing in data communication networks is considered. A model is introduced which takes into proper account the decentralization of the information about the network status. The problem is thus considered in a team-theory framework and the structure of the optimal strategies is derived.

Adaptive Routing for Damaged Networks

Abstract: This paper proposes and examines adaptive routing algorithms for communication networks that are subject to damage. These algorithms route calls through the network when the network configuration is not fully known, and adaptively reorder the routing tables as they gather more information about the network configuration. (The path that a call follows in the network is determined by routing tables. When a call reaches a node, a routing table is consulted to find the next node to attempt.) We concentrate on learning mechanisms that reorder the routing tables in real-time. For example, the success-to-top mechanism moves the table entry that led to a successful connection of a call to the top of the routing table. Success-to-top leaves the relative order of the other entries in the routing table unchanged. Other possible schemes include failure-to-bottom (entries that lead to unsuccessful connection attempts are placed on the bottom of the list), and success-up-one (in which the successful entry is moved up by one in the routing table). Markov chain models are described for success-to-top and failure-to-bottom schemes. Analytical expressions for the steady-state probabilities are used to form measures for these two strategies. We compare these measures for a wide selection of blocking probabilities. Further, a simulation model is used to evaluate the merits of all three (and more) schemes. The simulation provides network measurements not available from the analytical model. The simulation also examines information sharing mechanisms in which a single call is used to change the routing tables at many nodes.

Solving large vehicle routing and scheduling problems in small core

Abstract: In this paper, an efficient implementation of the Clarke and Wright algorithm for solving the single depot vehicle routing and scheduling problem is presented. With this implementation, a 900 customer problem can be solved approximately in less than 9 seconds of CPU time and less than 128K bytes of storage on an IBM 3033 computer.

A new probabilistic routing algorithm for packet-switched computer networks

Abstract: A probabilistic method is proposed for message routing in packet-switched computer networks with distributed control. The routing table associated with each node consists of path entries, instead of branch entries as found in most routing schemes. Packets are assigned with different paths on a probabilistic basis. The path selection is entirely processed at the source node. The routing table is updated dynamically with change of packet-generating rates at all nodes. We introduce a new quantitative measure, path capacity, to model each path as an M/M/1 queue. With the path capacities, routing tables are updated frequently to achieve balanced minimum delays among all paths. The update overhead is a constant, independent of the size of the network. Both analytical and simulation results are presented and compared with the new ARPANET routing method under various traffic conditions. This probabilistic, path-directed routing algorithm performs significantly better than the new ARPANET routing method under moderate and heavy traffic conditions. Under very light traffic conditions, the two methods have almost equal performance. This method can be applied to improve packet routing in any computer communications networks with distributed control.

Theory and algorithms for signal routing in integrated circuit layout

Abstract: Integrated circuit layout deals with the problem of realizing a specified circuit description by a geometrical layout on a silicon chip. With the very high complexity of integrated circuits, hierarchical decomposition is generally used to reduce the size of the layout problem to a level where computation and design is feasible. At each level of the hierarchy, the circuit layout problem becomes the problem of placing a set of circuit blocks (placement) and routing a set of interconnections between circuit blocks (routing). This problem is usually divided into a sequence of subproblems, namely: initial placement, placement improvement, global routing, and detailed routing. This dissertation deals with the development of efficient computer algorithms and basic theoretical understanding for the detailed routing problem. A rectilinear routing region with fixed terminals on all sides is usually referred to as a two dimensional routing problem. For a two-dimensional routing problem with two layers available for routing, we developed a general and practical two-dimensional routing algorithm. For the case when there is only one layer for routing, a general river routing algorithm is devised. Traditional via minimization algorithms try to minimize the number of vias used for a particular routing solution. Here we investigate a new technique which tries to find a topological solution with globally minimal number of vias. This investigation depends on a special graph representation of the routing problem and the use of related graph theoretical algorithms. A geometrical mapping algorithm which maps a topological solution onto a rectilinear plane is also included. Through this investigation, much insight into the global characterization of the routing problem has been achieved. An intelligent automatic hierarchical building block layout (BBL) system has been set up. Different placement and routing algorithms can be implemented and tested by using this system.

Address-independent routing for local networks

Abstract: A routing methodology is introduced which permits messages to be propagated throughout a network without recourse to destination or origin addresses. Two classes of networks, bidirectional trees and augmented rings, are analyzed from this point of view. An optimality property is proved for the bidirectional tree, and three types of address-independent routing strategies are derived. It is shown that augmented loops, a class of structures incorporating redundant links, may be rerouted to compensate for the failure of any single node or link.