666927
Greedy wire-sizing is linear time
In interconnect optimization by wire-sizing, minimizing weighted sink delay has been shown to be the key problem. Wire-sizing with many important objectives such as minimizing total area subject to delay bounds or minimizing maximum delay can all be reduced to solving a sequence of weighted sink delay problems by Lagrangian relaxation [1, 3]. GWSA, first introduced in [10] for discrete wire-sizing and later extended in [2] to continuous wire-sizing, is a greedy wire-sizing algorithm for the weighted sink delay problem. Although GWSA has been experimentally shown to be very efficient, no mathematical analysis on its convergence rate has ever been reported. In this paper, we consider GWSA for continuous wire sizing. We prove that GWSA converges linearly to the optimal solution, which implies that the run time of GWSA is linear with respect to the number of wire segments for any fixed precision of the solution. Moreover, we also prove that this is true for any starting solution. This is a surprising result because previously it was believed that in order to guarantee convergence, GWSA had to start from a solution in which every wire segment is set to the minimum (or maximum) possible width. Our result implies that GWSA can use a good starting solution to achieve faster convergence. We demonstrate this point by showing that the minimization of maximum delay using Lagrangian relaxation can be speed up by 57.7%.
6347443
IPR: An Integrated Placement and Routing Algorithm
In nanometer-scale VLSI technologies, several interconnect issues like routing congestion and interconnect delay have become the main concerns in placement. However, all previous placement approaches optimize some very primitive interconnect models during placement. These models are far from the actual interconnect implementation in the routing stage. As a result, placement solution considered to be good by primitive interconnect models may turn out to be poor after routing. In addition, the placement may not even be routable and timing closure may not be achievable. In this paper, we propose to address the inconsistency between the placement and routing objectives by fully integrating global routing into placement. As a first attempt to this novel approach, we focus on routability issue. We call the proposed algorithm for routing congestion minimization IPR (integrated placement and routing). To ensure the algorithm to be computationally efficient, efficient placement and routing algorithms FastPlace, FastDP and FastRoute are integrated, and well-designed methods are proposed to integrate them efficiently and effectively. Experimental results show that IPR reduces overflow by 36%, global routing wirelength by 3.6%, and runtime by 36% comparing to ROOSTER, which is the previous best academic routability- driven placer.
24078054
Greedy wire-sizing is linear time
The greedy wire-sizing algorithm (GWSA) has been experimentally shown to be very efficient, but no mathematical analysis on its convergence rate has ever been reported. In this paper, we consider GWSA for continuous wire sizing. We prove that GWSA converges linearly to the optimal solution, which implies that the run time of GWSA is linear with respect to the number of wire segments for any fixed precision of the solution. Moreover, we also prove that this is true for any starting solution. This is a surprising result because previously it was believed that in order to guarantee convergence, GWSA had to start from a solution in which every wire segment is set to the minimum (or maximum) possible width. Our result implies that GWSA can use a good starting solution to achieve faster convergence. We demonstrate this point by showing that the minimization of maximum delay and the minimization of area subject to maximum delay bound using Lagrangian relaxation can be sped up by more than 50%.
52810492
Optimal cell flipping in placement and floorplanning
In a placed circuit, there are a lot of movable cells that can be flipped to further reduce the total wirelength, without affecting the original placement solution. We aim at solving this flipping problem optimally. However, solving such a problem optimally is non-trivial given the gigantic sizes of modern circuits. We are able to identify a large portion of cells (about 75%) of which the orientation (flipped or not flipped) can be determined independent of the orientations of all the other cells. We have derived three non-trivial conditions to identify those so called independent cells, strictly solvable cells and conditionally solvable cells. In this way, we can greatly reduce the number of cells whose orientations are dependent on each other. Finally, the cell flipping problem of the remaining dependent cells can be formulated as a mixed integer linear programming (MILP) problem and solved optimally. However, this may still be too slow for extremely large circuits and we have applied two other methods, linear programming (LP) and linear programming followed by mixed integer linear programming (LP+MILP) to solve the problem. Experimental results show that by identifying those independent and solvable cells first and applying the LP+MILP technique, we can solve this flipping problem effectively and obtain results just 0.01% more than the optimal. In addition, we can improve the wirelength and number of overflow tiles by 5% and 9% respectively on the floorplanning benchmarks
53246587
A revisit to floorplan optimization by Lagrangian relaxation
6722156
An efficient and effective detailed placement algorithm
In the past few years, there has been a lot of research in the area of global placement. In comparison, not much attention has been paid to the detailed placement problem. Existing detailed placers either fail to improve upon the excellent solution quality enabled by good global placers or are very slow. To handle the above problems, we focus on the detailed placement problem. We present an efficient and effective detailed placement algorithm to handle the wirelength minimization problem. The main contributions of our work are: (1) an efficient Global Swap technique to identify a pair of cells that can be swapped to reduce wirelength; (2) a flow that combines the Global Swap technique with other heuristics to produce very good wirelength; (3) an efficient single-segment clustering technique to optimally shift cells within a segment to minimize wirelength. On legalized mPL5 global placements on the IBM standard-cell benchmarks, our detailed placer can achieve 19.0%, 13.2% and 0.5% more wirelength reduction compared to Fengshui5.0, rowironing and Domino respectively. Correspondingly we are 3.6/spl times/ 2.8/spl times/ and 15/spl times/ faster. On the ISPD05 benchmarks (Gi-Joon Nam et al., 2005), we achieve 8.1% and 9.1% more wirelength reduction compared to Fengshui5.0 and rowironing respectively. Correspondingly we are 3.1/spl times/ and 2.3/spl times/ faster.
13064248
Path-based multicast communication in wormhole-routed star graph multicomputers
In this paper, we propose four efficient multicast routing schemes in wormhole-routed star networks with multidestination routing capability. All of the four proposed schemes are path-based and deadlock-free. The first scheme, dual-path routing, sends the message in parallel through two independent paths. The second one, shortcut-node-based datapath routing, is similar to dual-path routing except that the routing tries to find a shortcut node to route the message as soon as possible to reduce the length of transmission path. The third one, multipath routing, is a multiple dual-path routing strategy that includes source-to-relay and relay-to-destination phases. The last scheme, proximity grouping routing, is similar to multipath routing except that in the partitioning step of source and destination nodes the relation of spatial locality of nodes is also taken into account to reduce the length of transmission paths. Finally, the experimental results are given to show that the performance based on unicast-based and traditional Hamiltonian-path routing schemes can be improved significantly by the four proposed routing schemes respectively.
41515379
The I+ Test
The I test is an efficient and precise data dependence method to ascertain whether integer solutions exist for one-dimensional arrays with constant bounds. For one-dimensional arrays with variable limits, the I test assumes that there may exist integer solutions. In this paper, we propose the I+ test|an extended version of the I test. The I+ test can be applied towards determining whether integer solutions exist for onedimensional arrays with either variable or constant limits, improving the applicable range of the I test. Experiments with benchmark cited from EISPACK, LINPACK, Parallel loops, Livermore loops and Vector loops showed that among 1189 pairs of one-dimensional arrays tested, 183 had their data dependence analysis amended by the I+ test. That is, the I+ test increases the success rate of the I test by approximately 15:4 percent. Comparing with the Power test and the Omega test, the I+ test has higher accuracy than the Power test and shares the same accuracy with the Omega test when determining integer solutions for these 1189 pairs of one-dimensional arrays, but has much better efficiency over them.
37782928
A multi-dimensional version of the I test
Abstract Two-dimensional arrays with linear subscripts occur quite frequently in real programs. In general, for multi-dimensional linear arrays under constant bounds the Lambda test is an efficient data dependence method to check whether there exist real solutions. In this paper, we propose a multi-dimensional version of the I test, the multi-dimensional I test, that can be applied to testing whether there are integer solutions for multi-dimensional linear arrays under constant limits. Experiments with benchmark showing the effects of the multi-dimensional I test on testing precision and testing efficiency are also presented.
37789043
On the development paradigm of distributed applications
We propose an ideal development paradigm facilitating the implementation of distributed applications. In this paradigm a developer focuses his mind only on the application itself and does not need to spend time on application-unrelated activities. The programming style is nearly consistent with that of centralized system. The mechanism of the general support environment to this paradigm is described. An example explaining the implementation for an environment using the Sun RPC facility as the underlying communication component is also presented.
41639900
An Evolutionary Fuzzy Multi-objective Approach to Cell Formation
Fuzzy mathematical programming (FMP) has been shown not only providing a better and more flexible way of representing the cell formation (CF) problem of cellular manufacturing, but also improving solution quality and computational efficiency. However, FMP cannot meet the demand of real-world applications because it can only be used to solve small-size problems. In this paper, we propose a heuristic genetic algorithm (HGA) as a viable solution for solving large-scale fuzzy multi-objective CF problems. Heuristic crossover and mutation operators are developed to improve computational efficiency. Our results show that the HGA outperforms the FMP and goal programming (GP) models in terms of clustering results, computational time, and user friendliness.