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УДК 658.512
V.M. Kurcichik, B.K. Lebedev, E.V. Nuzhnov A NEW, APPROACH TO INTELLECTUAL MAZE ROUTING
Abstract
New techniques for routing general multi-layer channels (2-4 layers) in the Intellectual Computer Aided Design (ICAD) Systems are introduced. These techiques can looked a variety of technology constraints (different track width, spacing, different wave speed, pin stacking can be allowed or forbidden). These techniques have been implemented in a new maze router called STAR.
It consists of two stages: quick maze router and maze rerouter with recapitulation and path functions optimization. Experimental results show that this algorithm may find decisions for complex cases when other algorihms give no results.
1. Introduction
The Intellectual Computer-Aided Design Systems (1CADS) are based on the notion of the artificial intelligence. The problems of the artificial intelligence are connected with the organization of the knowledge about the surrounding world in the form of mathematical structures. One of the main problems of ICAD is routing.
The routing process in layout design automation VLSI consists of two steps, i.e. the global routing and the detailed routing. We will analise heuristics for detailed routing. There are two main classes of algorithms for detailed routing: channel and maze [1,2].
Channel routing has been used extensively in the layout of VLSI. The traditional channel routng problem assumes that there are two layers (H - horizontal, V - vertical) of material available for routing, In our work it possible to use three or even four layers for interconnections. In this case the problem appears to make better the channel router results and wave router as usual vertical fragments which can't propogate the channel router.
We purpose general ideology of conception and algorithms of wave routing which may be used as independent or in cooperation with channel router for routing unrouted nets.
This problem is known as NP-complete [1]. So we suggest to create new heuristics and try to decrease look over difficulty by decrease task complexity. Our router STAR is based on two parts. In first part we realize fast route procedure on the base of propogation meeting waves which may have different speed in rectangular of track direction. Procedure allows to route nets with different width and spacing, it generates waves or beams which pass in restricted 3D-area from all points of net in all directions and layers simultaneously.
Time complexity of first part of STAR is in proportion 0(a*n* *2), where 'a' - coefficient, n -quantity of routing connections. If routing of net is unsuccessful then go to second part.
In second part we realize almost-optimal rerouting. It based on analysis of unrouted fragments, breaks of the blocking nets and peripheral algorithm using.
Optimization idea consists of deformation a blockage fragments, compaction and recapitulation. Time complexity of second part of STAR is in proportion 0(b*n**3), where *b' coefficient, n - quantity of routing connections.
2. Problem Description
STAR will be run at the last stage of the channel routing process to complete and/or optimize net routing within given local area of the channel. The routing part of channel is closed multiconnected area, left and right edges of which are vertical segments, and top and bottom sides can be either horizontal segments or zigzags. All the area sizes are given in symbolic grid units.
Notes and proposals:
• main task of STAR is routing of pairs points on Discrete Working Field (DWF) for example: previously unrouted vertical segments;
• three following modes are necessary:
> quick and not optimal routing,
> routing with optimization (routing from another more appropriate point of the net,
and 'tails' should be deleted),
> rerouting nets previously routed by some channel router in order to decrease vias
number and net length;
• wave should go from all points which should be connected with different speed;
• the via size should be equal to net (pin) width;
• via size should be the same in all layers to be connected and equal to the maximum one;
• STAR should place vias in accordance with DWF restrictions;
• two modes of vias organization:
y three layer vias are allowed,
> three layer vias are not allowed;
• spacing: some nets have not to have overlapping nets on other layers, but crossing such nets on other layers is allowed;
• Soukup's test should be solved.
The base execution environment for running the STAR software is Sun SPARCstation running SunOS. The program was written in C++.
STAR includes the following modules: pins blockage identification, netlist sorting, routing, rerouting, optimal rerouting.
3. Routing module
Basic procedure of this module is Perform Wave between Point 1 and Point 2. Two modes are
used:
• mode 1: Point-to-Point connection (another points of net are blockages);
• mode 2: connection between arbitrary point of Segment 1 and arbitrary point of Segment 2.
Routing module contains procedures:
• Mark Segments connected to Points 1 and 2;
• Define borders of the WaveZone;
• Clear Front; Wave Propogation with different speed in each direction;
• Create the Track and Delete the Tail.
After that two follows checks are made:
• if given net is carried out, then next check, else Perform Rerouting;
• if all nets from ListPrior are carried out, then Post-optimization Module, else Choice the next net for routing.
The set of height Functions FI, F2......FI is introduced as criteria of track quality.
To speed up the wave algorithm the wave zone is restricted. At first the wave zone is the minimal rectangle including points to be connected. Step by step the rectangle of wave zone sizes increasing on the certain constant value. Such sizes increasing may be repeated until achieve the maximal zone sizes.
The old zone borders are the front one. The wave propogation is done as described below. On the front border we choose the cells with minimal value of function Fi. As it’s shown on Fig.2,a there is the cell with value equal to 0. Then the wave propogates on one step. Then we choose the cells with minimal value on the front border again. Now this cell have value equal to 1. Such process is repeated. The cells with new values are included in the front borders and the cells from which the wave was propogated are deleted. The waves propogate in the whole of increasing zone. The wave is blocked if the adjacent cell is not in this zone or the adjacent cell is blocked or its value more only on
1. The wave propogation process in the increasing zone is shown on Fig.l.a - g (from left to right and from top to bottom).
0 1 2 3
1 2 3 4
X X X 5
9 8 7 6
10 9 8 7
1 11 10 9 8
2 1 2 3 4
1 0 1 2 3 4
2 1 2 3 4
3 X X X 5
4 9 8 7 6
10 9 8 7
11 10 9 8
2 I 2 3 4 5
1 0 1 2 3 4
2 1 2 3 4 5
3 X X X 5
4 5 8 7 6
5 10 9 8 7
11 10 9 8
a) b) c)
2 1 2 3 4 5
1 0 1 2 3 4
2 1 2 3 4 5
3 X X X 5 6
4 9 6 7 6 7
5 6 7 8 7 8
6 7 8 9 8
7 8
2 1 2 3 4 5
1 0 1 2 3 4
2 1 2 3 4 5
3 X X X 5 6
4 9 6 7 6 7
5 6 7 8 7
6 7 10 9 8
7
2 1 2 3 4 5
1 0 1 2 3 4
2 1 2 3 4 5
3 X X X 5 6
4 9 6 7 6
5 6 9 8 7
6 11 10 9 8
d) e) 0
2 1 2 3 4 5
1 0 1 2 3 4
2 1 2 3 4 5
3 X X X 5 6
4 9 6 7 6 7
5 6 7 8 7 8
6 7 8 9 8 9
7 8 9
g)
Fig. 1, a - g
To consider the circuit width we used the next way. The net width is defined as the cells number (d). Let dl = d - 1. We increase the zone (z) sizes on the dl cells to up and to left (Fig.2,a). The zone zl is obtained. Inside the zone zl for all blocked regions we temporary increase the
The main ideas of rerouting are the peripherial wave propogation heuristics organisation. Rerouting procedure solves some difficult routing problems (Soukup’s type). Soukup had proposed the strategy of global routing, based on the definition of critical cells. If we remove this cells, we obtain nonconnecting regions. The procedure of priority calculating is very difficult. The idea is not define very good and this algorithm can not be used in all general cases.
5. Experimental results
Evaluation testing of STAR consists of two parts: testing technology and its instruments and testing the STAR. The main ideas of testing technology are:
• hierarchical system (tree) of test set;
• improving tests complexity;
• consequent seperate checking of the STAR properties;
• simultaneous checking of the several properties;
• special tests for complex topological situations.
Special tests deal with different complex topological situations.
The goal of performance requirements testing is evaluation of running time for maze rerouting most complex local zones of channels. Running time not more then 2 minutes on SUN Sparc station 10.
Quality testing includes the maze rerouting local zones of special channels. The quality criteria are parameters of maze rerouting such as number of rerouted nets, vias, turn, total length.
The goal of testing of rerouting process is checking of complex using peripherial and wave algorithms to solve some difficult tasks such as Soukup type.
The goal of testing of complex cases is checking of all possibilities of maze routing and rerouting processes using with regard to passing and run-time.
6. Conclusion
The efficient wave routing approach, including wave routing and peripherial rerouting procedures, is realized. It allows to realize net connections in 3 metal and Poly-Si layers, which may have different width. Our heuristic algorithm allows to efficiently realize many difficult benchmarks such as Soukup’s tasks [6]. This approach may be used for VLSI realizing in more then 4 layers. The most efficient STAR using is in conbination with some channel router as improving one.
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