Detailed Routing Problem Research Articles

Optimal service zones and frequencies for flexible-route freight deliveries

Freight delivery planning is a critical area in transportation and logistics. This paper presents a planning-level model for jointly optimizing headways and zone sizes for flexible-route freight deliveries. The model analyzes deliveries for a one-to-many demand pattern from one terminal to random destinations in a zone, which are reached through approximated travelling salesman problem (TSP) tours. Then, the problem is reformulated as a Lagrangian relaxation problem to constrain the fleet size to an integer value. The proposed model and closed-form solutions provide direct insights into the relations affecting those decision variables. Results from the base case study and sensitivity analyses indicate how various factors affect optimal service frequencies, delivery zone sizes, and costs of freight deliveries. Before detailed vehicle routing problems (i.e., actual delivery scheduling and operations) are solved, the proposed model should be useful for planning freight delivery systems, regarding critical decisions about geographic coverage of services, delivery frequencies, vehicle capacities, and other system characteristics. The developed model can also be used for pickups with a many-to-one demand pattern and extended to serve many-to-many demand patterns in multiple delivery zones through transfers at a central terminal.

A Multicommodity Flow-Based Detailed Router With Efficient Acceleration Techniques

Detailed routing is an important stage in very large scale integrated physical design. Due to the extreme scaling of transistor feature size and the complicated design rules, ensuring routing completion without design rule checking (DRC) violations becomes more and more difficult. Studies have shown that the low routing quality partly results from nonoptimal net-ordering nature of traditional sequential methods. The concurrent routing strategy is always based on an NP-hard model, thus is at a disadvantage in runtime. In this paper, we present a novel concurrent detailed routing algorithm that routes all nets simultaneously. Based on the multicommodity flow model, detailed routing problem with complex design rule constraints is formulated as an integer linear programming. Some model simplification heuristics and efficient model solving algorithms are proposed to improve the runtime. Experimental results show that, the proposed algorithms can reduce the DRC violations by 80%, meanwhile can reduce wirelength and via count by 5% and 8% compared with an industry tool. In addition, the proposed algorithm is general that it can be adopted as an incremental detailed router to refine a routing solution, so the number of DRC violations that industry tool cannot fix are further reduced by 27%.

Some polynomially solvable subcases of the detailed routing problem in VLSI design

There are plenty of NP-complete problems in very large scale integrated design, like channel routing or switchbox routing in the two-layer Manhattan model (2Mm, for short). However, there are quite a few polynomially solvable problems as well. Some of them (like the single row routing in 2Mm) are “classical” results; in a past survey [36] we presented some more recent ones, including: 1. a linear time channel routing algorithm in the unconstrained two-layer model; 2. a linear time switchbox routing algorithm in the unconstrained multilayer model; and 3. a linear time solution of the so called gamma routing problem in 2Mm. (This latter means that all the terminals to be interconnected are situated at two adjacent sides of a rectangular routing area, thus forming a Γ shape. Just like channel routing, it is a special case of switchbox routing, and contains single row routing as a special case.) In the present survey talk we also mention some results from the last three years, including 4. some negative results (NP-completeness) in the multilayer Manhattan model and a channel routing algorithm if the number of layers is even; 5. an interesting relation between channel routing and multiprocessor scheduling; and 6. some improvements of 1–3 above. We present the (positive and negative) results in a systematic way, taking into account two hierarchies, namely that of geometry (what to route) and technology (how to route) at the same time.

A branch-and-price algorithm for the Steiner tree packing problem

This paper deals with the Steiner tree packing problem. For a given undirected graph G=(V, E) with positive integer capacities and non-negative weights on its edges, and a list of node sets (nets), the problem is to find a connection of nets which satisfies the edge capacity limits and minimizes the total weights. We focus on the switchbox routing problem in knock-knee model and formulate this problem as an integer programming using Steiner tree variables. We develop a branch-and-price algorithm. The algorithm is applied on some standard test instances and we compare the performances with the results using cutting-plane approach. Computational results show that our algorithm is competitive to the cutting plane algorithm presented by Grötschel et al. and can be used to solve practically sized problems. Scope and purpose VLSI circuits becomes more complex with the need of miniaturization and sophisticated functions of electronic device. That makes designing a VLSI more difficult. Due to these difficulties, it is common way to decompose it into several sub-problems. One of the sub-problems is the detailed routing problem, where exact path of wires is determined while minimizing some objective (for examples, total wire length) under some design rules. Among many kinds of detailed routing problem, we focus on the switchbox routing problem in knock-knee routing model. For this problem, we developed an integer programming model and solved it successfully for some test problems.

Greedy Segmented Channel Router

An efficient solution to the generalized detailed routing problem in segmented channels for row-based FPGAs is presented. A generalized detailed routing allows routing of each connection using an arbitrary number of tracks, i.e., doglegs are allowed. This approach is different from the normally followed method where each connection is routed on a single straight track. We present a router that performs generalized segmented channel routing using a greedy approach to route channels. The router also renders itself to limited tolerance against faults in the routing architecture.

Recent advances in VLSI layout

The current status of VLSI layout and directions for future research are addressed, with emphasis on the authors' own work. Necessary terminology and definitions and, whenever possible, a precise formulation of the problems are provided. Placement and floorplanning for both the sea-of-gates and building-block designs are examined. The former emphasizes the connectivity specification, whereas the latter must also consider module shape and size. Global routing based on a method of successive cuts on a chip is discussed. This is a hierarchical top-down approach that is useful for both of the above designs. A two-dimensional detailed routing problem and the rip-up and rerouting problem are also discussed. The field of computational geometry and its application to layout-in particular, to gridless routing and compaction-are reviewed, and layout engines are considered.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

SILK: a simulated evolution router

The authors present a rip-up-and-rerouter based on a matrix representation scheme and simulated evolution technique for solving detailed routing problems in VLSI layout. The status of the routing region is represented as a matrix. Rip-up and reroute operations are emulated as matrix subtractions and additions, respectively. The quality of a routing result can be measured by a few simple matrix operations on the matrix. A rip-up and reroute switch-box/channel router, called SILK, using a simulated evolution technique has been implemented based on this representation alone. Experimental results showed that SILK, when solving all the benchmarks from the literature, outperformed WEAVER, the most successful switch-box router to date, in both quality and speed aspects.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Detailed Router Based on Incremental Routing Modifications: Mighty

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.