Lee maze routing algorithm pdf

This algorithm represents the routing singlelayer as a grid map, where each grid map point can contain connections to adjacent grid map points and. Weaknesses requires large memory for dense layout slow. Steiner routing ece63 physical design automation of vlsi systems. On the other hand, dijkstra algorithm 2 is the routing algorithm for the later category, and it is applied to route guidance problem such as car navigation system. An ultrafast incremental maze routing algorithm tsungwei huang. The maze routing problem is to find an optimal path between a given pair of cells on a grid plane. An implicit connection graph maze routing algorithm for. Another drawback of special hardware for the lee algorithm is that a uniprocessor implementation can be. Several enhancements to this idea have been shown in 8. Wire routing is a key problem in electronic design automation. Assume, we have to connect cell1 with cell2, as shown in below image. Via design rule consideration in multilayer maze routing.

Understanding how it works the algorithm is a breadthfirst based algorithm that uses queues to store the steps. Fieldprogrammable gate arrays fpgas are a new type of userprogrammable integrated circuits that supply designers with inexpensive, fast access to customized vlsi. The maze is effectively flooded with water, and each point in the maze keeps track of which direction it was flooded from. Given a 2d layout with some obstacles, use lee s algorithm to find the shortest route input file format. Lees algorithm maze routing grid routing if a path exists between two points, it is surely found. Lets have a glimpse of the algorithm using below images. These are evaluated experimentally on an ncube7 hypercube computer with 64 processors. Figure 1 shows the basic operation of the lee algorithm, as. If its a deadend, go back to tha last point of decision and take the next choice. A hexagonal array machine for concurrent multilayer maze routing by r. An application of simulated annealing to maze routing dr.

Pathfinding using the lee algorithm alien pbl platform. This algorithm represents the routing singlelayer as a grid map, where each grid map point can contain connections to adjacent grid map points and finding a way between two terminals. In this paper, we propose timeefficient algorithms to solve the mazerouting problem on a reconfigurable mesh architecture. Their work reduced the search space of lee s algorithm by 3050% but exhibited long convergence time as compared to the recent.

If no way leads to the exit, go to the previous last. It uses a wave propagation style a wave are all cells that can be reached in n steps throughout the routing space. Pdf a 4geometry maze router and its application on multiterminal. A novel slittree plus intervaltreedata structure is developed, combined with a cache structure, to. The lee algorithm is one possible solution for maze. The maze routing algorithm is a low overhead method to find the way between any two locations of the maze. For path planning using maze routing, lee algorithm 6 is an wellknown method which is based on the breadthfirst search bfs technique. It provides minimum path and guarantees to find the path if two nodes start, destination are present.

Lees algorithm and its variants, probably the most widely used maze routing method, fails to work in the 4geometry of the grid plane. Details of the domain negotiation algorithm are shown in figure 4. Lee s 1961 maze routing algorithm has been a popular method for routing wires in vlsi circuits. Remeber every point, where you have multiple choices to continue. Tki jf routing is a key problem in electronic design automation. In this paper, we propose timeefficient algorithms to solve the maze routing problem on a reconfigurable mesh architecture. Mazerouting algorithms are used in vlsi routing and robot path planning. An example of the incremental maze routing problem is given in figure 2. The maze we are going to use in this article is 6 cells by 6 cells. The maze router wavefront6 a search routing the maze routing is a. Maze routing algorithms are used in vlsi routing and robot path planning. Maze routing on a hypercube multicomputer springerlink.

Lee, an algorithm for path connection and its application, ire trans. This paper propose a maze routing algorithm based on cellular automata. Hmaze routing and its variations lee, robin, soukup, ohtsuki hhierarchical wire routing burstein and pelavin channel routing channel switchbox and general area routing. Routing algorithms and architectures for fieldprogrammable. The first known algorithm is lees algorithm 7 which uses an improved version of the breadth first search bfs to find the shortest path between source s and target t.

Timeefficient maze routing algorithms on reconfigurable. It always gives an optimal solution, if one exists, but is slow and requires considerable memory. One disadvantage to sequential routing is that the. The algorithm is initially proposed for chip multiprocessors cmps domain and guarantees to work for any gridbased maze. The idea is inspired from lee algorithm and uses bfs. An application of simulation annealing to maze routing. If a path exists between a pair of points s and t, it is definitely found. Ant colony optimization routing algorithm with tabu search. The implementation of lees maze routing algorithm on an mimd hypercube multiprocessor computer can follow several plausible mappings and synchronization strategies. Research article ship pipe routing design using nsgaii and. It can also be applied to a variety of other problems, such as robot path planning. Lee s algorithm and its variants, probably the most widely used maze routing method, fails to work in the 4geometry of the grid plane. So, back to the saying learn by doing routing, by itself, means an algorithm to connect at least 2 points using shortest available path and using real physical wires, while maintaining recommended wirevia design rules drc. A maze routing algorithm based on two dimensional cellular.

The aim of this algorithm is find the shortest path between the source cell and the target cell, so that the path does not pass from the obstacles. The mazerouting algorithm is a low overhead method to find the way between any two locations of the maze. Discussion mainly on singlelayer routing strengths guarantee to nd connection between 2 terminals if it exists. All nets are considered at the same time complexity. In this paper, we propose to use an implicit representation of a nonuniformgrid graph for gridless maze routing algorithm.

A new look at hardware maze routing lafayette college. As such they lack the flexibility that is required in practical cad soft ware. Pdf the maze routing problem is to find an optimal path between a given pair of cells on a grid plane. Our algorithm solves this problem by using a suitable data structure for uniform wave propagation in the 4geometry, 8geometry, etc. The lee algorithm is one possible solution for maze routing problems. Aug 20, 2016 lee algorithm refers to a shortest path maze solving algorithm, implemented with a breadth first search. As the lee maze algorithm is used for semiconductor design, it is expanded to support 3d pipelines. Also, if anybody can send me the a link to the full artice of the following paper i will be very glad, the paper is. Given a mxn matrix where each element can either be 0 or 1. Lee algorithm searches for the shortest path between two terminals and guarantees to find a route between two points if the connection exists. For an algorithm which finds its way out of all possible mazes, you need to have some sort of backtracking.

In figure b only layer h is used and no vias required. The wave stops when the target is reached, and the path is determined by backtracking through the cells. The starting cell is at the bottom left x0 and y0 colored in green. We need to find the shortest path between a given source cell to a destination cell. It is thus important to understand such tradeoffs when choosing to use a particular algorithm. Lee, an algorithm for path connections and its applications 1961 strategy. Timeefficient maze routing algorithms on reconfigurable mesh. Jan 25, 2019 lecture 9 covers the routing process, including basic approaches to maze routing algorithms and how routing is carried out in practice within eda tools. A stochastic evolution algorithm based 2d vlsi global router. Algorithm 1 leemoore maze router for a single layer. Routing by maze search electrical and computer engineering. Guarantee to find connection between 2 terminals if it exists. Stochastic evolution stoce algorithm maze routing abstract. A hexagonal array machine for concurrent multilayer maze.

Mazerouting algorithms and linesearching algo rithms. The knowledge reduction process speeds up the reasoning process, and the knowledgebase is made of rules. Maze routing, is, perhaps, the most widely used algorithm to find path between 2 points. Lees algorithm the most common maze routing algorithm. Classi cation of global routing algorithm sequential approach. Maze algorithm 1 which was propos ed by lee is the routing algorithm for the former category, and it is applied to vlsi cad problems. Its drawback in the form of large memory consumption for dense layouts leads to the. Lee algorithm is one of the possible solutions for maze routing problem mrp and was firstly defined by the chaster lee in 1961 6. The path can only be created out of a cell if its value is 1. Mazerouting algorithms rely on a gridbased layout repre sen tation. Both lees maze algorithm and the proposed algorithm are implemented on an aap1 twodimensional array.

The maze routing algorithm is an algorithm to find connections between the terminals and the lee algorithm is one possible solution for maze routing problems. In some cases, because of blockages, it is necessary to go around an object. This embodiment of the lees algorithm has high complexity, especially if the grid size is higher than the one shown in the example above. While routing has been studied extensively over the years and many different algorithms have been explored, the classic gridbased lee algorithm for maze routing 1 remains popular as a basic ingredient of many approaches. Maze routers the lee algorithm always finds a shortest path if one exits starting at the source node, explore out in a breadthfirst fashion, keeping a list of the leaf nodes. Perhaps the most widely used algorithm for finding a path between two points is the maze routing algorithm also called lee s algorithm, which is based on the breadthfirstsearch bfs technique. An ultrafast incremental maze routing algorithm tsungwei huang, peici wuy, and martin d.

It is guaranteed to be the shortest available path. Maze routing adopts a twophase approach of filling followed by retracing. A 4geometry maze router and its application on multiterminal. Path planning through maze routing for a mobile robot with. Grid routing indian institute of technology kharagpur. Physical design automation of vlsi circuits and systems 7.

Dijkstras algorithm 9 generates the shortest path for a general graph, which is later modi. Lee algorithm lee, \an algorithm for path connection and its application, ire trans. It always gives an optimal solution, if one exists, but is slow and requires large memory for dense layout. Thanks also for researching the other, routing based algorithm. To solve this specific problem, students will use the lee algorithm also known as the wave algorithm.

A design expert system for autorouting of ship pipes. Single step current driven routing of multiterminal signal net. The implementation of lees maze routing algorithm on an mimd hypercube multiprocessor. Previous work on parallel routing 6, 4, 111, 181, 30, 12, 35 has focused on a fixed hardware mapping for the lee maze routing algorithm 15. Time and space complexities are on2 for a grid of dimension n.

For example, a cellular mesh connected processor array is. A key component in the design of an fpga is its routing architecture, which comprises the wiring segments and routing switches that interconnect the fpgas logic cells. In figure a, when connecting points a to a we place the vertical wires on layer v and the horizontal wires on layer h. A straightforward extension to the maze routing algorithm that disallows viarule incorrect routes may either cause a suboptimal route to be found, or more seriously, cause the failure to find any. The lee algorithm is one possible solution for maze routing problems based on breadthfirst search. The implementation of lee s maze routing algorithm on an mimd hypercube multiprocessor computer can follow several plausible mappings and synchronization strategies. Douglas edwards department of computer science, university of manchester oxford road, manchester, uk, m 9pl abstract the simulated annealingoptimisationtechnique is used to provide a framework for controlling ripup and rerouting. Pdf via design rule consideration in multilayer maze. Via design rule consideration in multilayer maze routing algorithms jason cong, jie fang, and keiyong khoo abstract maze routing algorithms are widely used for finding an optimal path in detailed routing for very large scale integration, printed circuit board and multichip modules in this paper. W e provide both serial and parallel implementation as well as develop. Issues with the lee algorithm lee algorithm is serial. The algorithm ensures that all routing demands are satis. Most modern global routers employ lee s algorithm to output the minimumcost routing.

In this paper, we propose timeefficient algorithms to. As a result, some routers use hightowers algorithm for a quick first try, and if it fails, then the full power of the leemoore maze search algorithm is used. In sequential routing, the nets are ordered based on certain criteria and routed one by one in this sequential order. This post describes how to solve mazes using 2 algorithms implemented in python. Implementing lees algorithm for maze routing c programming. Lee algorithm refers to a shortest path maze solving algorithm, implemented with a breadth first search. In addition to finding paths between two location of the grid maze, the algorithm can.