13097054
RQL: Global Placement via Relaxed Quadratic Spreading and Linearization
This paper describes a simple and effective quadratic placement algorithm called RQL. We show that a good quadratic placement, followed by local wirelength-driven spreading can produce excellent results on large-scale industrial ASIC designs. As opposed to the current top performing academic placers [4,7,11], RQL does not embed a linearization technique within the solver. Instead, it only requires a simpler, pure quadratic objective function in the spirit of [8,10,23]. Experimental results show that RQL outperforms all available academic placers on the ISPD-2005 placement contest benchmarks. In particular, RQL obtains an average wire- length improvement of 2.8%, 3.2%, 5.4%, 8.5%, and 14.6% versus mPL6 [5], NTUPlaceS [7], Kraflwerk [20], APlace2.0 [11], and Capo10.2 [18], respectively. In addition, RQL is three, seven, and ten times faster than mpL6, Capo10.2, and APlace2.0, respectively. On the ISPD-2006 placement contest benchmarks, on average, RQL obtains the best scaled wirelength among all available academic placers.
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%.
53246587
A revisit to floorplan optimization by Lagrangian relaxation
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
12805154
Efficient rectilinear Steiner tree construction with rectilinear blockages
Given n points on a plane, a rectilinear Steiner minimal tree (RSMT) connects these points through some extra points called Steiner points to achieve a tree with minimal total wire length. Taking blockages into account dramatically increases the problem complexity. It is extremely unlikely that an efficient optimal algorithm exists for rectilinear Steiner minimal tree construction with rectilinear blockages (RSMTRB). Although there exist some heuristic algorithms for this problem, they have either poor quality or expensive running time. In this paper, we propose an efficient and effective approach to solve RSMTRB. The connection graph we used in this approach is called spanning graph which only contains O(n) edges and vertices. An O(n log n) time algorithm is proposed to construct spanning graph for RSMTRB. The experimental results show that this approach can achieve a solution with significantly reduced wire length. The total run time increased is negligible in the whole design flow.
10804649
Information markets vs. opinion pools: an empirical comparison
In this paper, we examine the relative forecast accuracy of information markets versus expert aggregation. We leverage a unique data source of almost 2000 people's subjective probability judgments on 2003 US National Football League games and compare with the "market probabilities" given by two different information markets on exactly the same events. We combine assessments of multiple experts via linear and logarithmic aggregation functions to form pooled predictions. Prices in information markets are used to derive market predictions. Our results show that, at the same time point ahead of the game, information markets provide as accurate predictions as pooled expert assessments. In screening pooled expert predictions, we find that arithmetic average is a robust and efficient pooling function; weighting expert assessments according to their past performance does not improve accuracy of pooled predictions; and logarithmic aggregation functions offer bolder predictions than linear aggregation functions. The results provide insights into the predictive performance of information markets, and the relative merits of selecting among various opinion pooling methods.
17686405
A time-series biclustering algorithm for revealing co-regulated genes
Although existing bicluster algorithms claimed to be able to discover co-regulated genes under a subset of given experiment conditions, they ignore the inherent sequential relationship between crucial time points and thus are not applicable to analyze time-series gene expression data. A simple and effective deletion-based algorithm, using the mean squared residue score as a measure, was developed to bicluster time-series gene expression data. While enforcing a threshold value for the score, the algorithm alternately eliminates genes and time points according to their correlation to the bicluster. To ensure the time locality, only the starting and ending points in the time interval are eligible for deletion. As a result, the number of genes and the length of time interval are simultaneously maximized. Our experimental results shown that the proposed method is capable of identifying co-regulated genes characterized by partial time-course data that previous methods failed to discover.
6546539
The generalized lambda test
We generalize the /spl lambda/ test. The generalized /spl lambda/ test can be applied towards determining whether there exist data dependencies for coupled arrays with both constant and variable limits under any given direction vectors, improving the applicable range of the /spl lambda/ test. Experimental data reflecting the effect of the generalized /spl lambda/ test are also presented.
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.
12245644
Multicast communication in wormhole-routed star graph interconnection networks
Multicast, an important communication mechanism, is frequently applied in parallel computing. The star graph interconnection network, when compared with the hypercube network, being with low degree and small diameter, has been recognized to be an attractive alternative to the popular hypercube network. In this paper, we derive a node labeling formula based on a hamiltonian path and 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 (toward high label nodes and low label nodes). The second one, shortcut-node-based dual-path 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.