Showing papers on "Static routing published in 1983"

Route first—Cluster second methods for vehicle routing

Abstract: In this paper we consider route first—cluster second methods for the vehicle routing problem. Extensions to the basic method both to improve its effectiveness and to enable it to cope with practical constraints are described. Computational results are given for the method applied to standard vehicle routing problems drawn from the literature.

A Minimal Technology Routing System for Meals on Wheels

Abstract: A novel routing system based on a new travelling salesman heuristic was successfully implemented to handle the efficient daily routing of a varying number of vehicles to more than 200 delivery points whose locations change daily. The system had to be easily mantained by one person and require no resources for example, no computer. Our system achieved these objectives, cost less than $50, and, moreover, shortened average travel times by 13% compared to previous performance.

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.

Optimal Placement for River Routing

Abstract: River routing is the problem of connecting a set of terminals a 1,…,a n on a line to another set b 1,…,b n in order across a rectangular channel. When the terminals are located on modules, the modules must be placed relative to one another before routing. This placement problem arises frequently in design systems like bristle-blocks where stretch lines through a module can effectively break it into several chunks, each of which must be placed separately. This paper gives concise necessary and sufficient conditions for wirability which are applied to reduce the optimal placement problem to the graph-theoretic single-source-longest-paths problem. By exploiting the special structure of graphs that arise from the placement problem for rectilinear wiring, an optimal solution may be determined in linear time.

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.

Issues in routing for large and dynamic networks

Abstract: The routing function is necessary in computer communication networks in order to create the appearance of complete connectivity in an environment of sparse physical links. The purpose of this dissertation is to examine ways of providing the routing function in large networks or networks which are characterized by frequent topological changes or both. The focus is on distributed routing algorithms because of their failsafe property. Two new event driven distributed route table update algorithms, A and B, are introduced and proven correct. Algorithm A requires less buffer space to store route tables than other event driven algorithms. Algorithm B, a variation of algorithm A, allows each node to maintain a source tree, i.e. a tree rooted at the node and containing the shortest path to all possible destinations in the network. The source tree may be used to implement source routing, i.e. the whole path from source to destination is determined at the source. Transient route table looping is also studied for algorithms A, B, as well as other algorithms in the literature. Hierarchical routing has been suggested in the literature as a means to reduce the size of the route tables when networks become very large. Reduction of the table size may also reduce the communication cost incurred during the update of the route tables. A possible effect of the shrinking of the route tables is that the resulting paths are not optimal. A classification of hierarchical routing schemes is introduced. The trade-off between between route table reduction and path length increase is studied in detail for two classes of schemes. Alternate policies for routing in the absence of necessary information are suggested and evaluated. In order to implement hierarchical routing it is necessary to partition the network into clusters. The network partitioning problem is abstracted to a graph partitioning problem which is shown to be NP complete. A new heuristic procedure, V3.2, is developed which is compared to the agglomerative method, a procedure suggested in the literature. V3.2 is shown to perform considerably better computationally as well as in terms of desired properties of the partitions. The comparison is performed by simulation experiments. An algorithm is developed to randomly generate connected networks suitable to be used in the simulations.

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.

An Automatic Routing Scheme for General Cell LSI

Abstract: An automatic routing scheme intended dedicatedly for general cell LSI is described, which is constructed of a number of algorithms such as for net ordering, global routing, and detailed routing. This scheme is distinctive in that channel constraint loops are broken automatically at the stage of global routing, and a grid-free routing scheme is employed at the state of detailed routing. The routing program based on this scheme has been incorporated into a design system for LSI which is at work in practice. A part of implementation results are also shown.

Adaptive transmission strategies and routing in mobile radio networks.

Abstract: Local throughput in a mobile radio network is roughly defined as the rate at which packets are propagated in specified directions in local network regions. A key factor determining local throughput in an ALOHA or spatial TDMA network with randomly spaced stations is the transmission radius used by the stations. We demonstrate that allowing the transmission radius to depend on the desired direction of propagation can significantly increase local throughput. The local throughput capabilities of a radio network can be effectively used only if adequate routing strategies are employed. This is illustrated by an example based on a symmetric demand assumption for stations uniformly distributed over a disc. Suppose that the population of n stations is uniformly distributed within a circle of radius R. If n is large then in small regions the stations are distributed like a Poisson point process with intensity X satisfying n = ~ R ~ x. Assuming that the traffic demand is symmetric (i.e., uniformly distributed over all n(n-1) directed pairs of distinct stations) the mean distance between the source and destination of a packet is (see [ 4 ] , or see [ 2 ] which is a chapter from [ 4 ]) The network throughput in packet-hops for the ALOHA random access protocol can be approximated by n-where A is the area covered by a transmission and A denotes the mean of A. (If the transmission radius is always a constant r then A-is L not random and is euqal to nr2 .) Thus, if denotes the mean forward progress per successful transmission, the network end-to-end throughput in packets per time slot is where Q = L / A. C Since by equation (1.1) the end-to-end throughput is proportional to ?-I we call tl the efficiency of the transmission radius policy. The constant 17 is perhaps more meaningful than y since it does not depend on the network's global geometry and is thus a "local" measure.

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 formulation and its solution of the problem of determining 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 requirement 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 general feature of channel routers not on any particular one. Related subjects such as the simultaneously routable channels, generalization of the safe order, switch box routing, and the placement with nonrectangular blocks are discussed.

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.

Asymptotic optimality of shortest path routing

Abstract: : Many communication networks use adaptive shortest path routing. By this the authors 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. It is shown 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.

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.

Efficient Single-Layer Routing Along a Line of Points

Abstract: In this paper we present several new procedures for carrying out the track assignment phase involved in channel routing. Our procedures are based upon the concept of an access graph which provides information dealing with the availability of routing space between pins in a layout. Paths for signal nets are then found by searching for optimal paths in the access graph. These paths can then be easily mapped back into routed wire segments on a VLSI chip. We consider only the case of single-layer routing within a single channel. We allow for wires to be on both sides of the line of pins to be processed, as well as between the pins. We consider two models, the first where the track availability is infinite, or equivalently, where wires are infinitely thin. We then consider the more realistic case where the track density in the channel is fixed. Our procedure for this case, called floating-track assignment, allows a wire, once assigned to a track, to be reassigned to a different track in order to enhance routability. For this case, we consider three objective functions, namely, minimal wire length, minimal congestion, and minimal perturbation. Both theoretical and experimental results are presented.

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.