34361185
Dilation-5 embedding of 3-dimensional grids into hypercubes
We present an algorithm to map the nodes of a 3-dimensional grid to the nodes of its optimal hypercube on a one-to-one basis with dilation at most 5.<<ETX>>
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
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%.
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.
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.
5795561
An in-depth analysis of information markets with aggregate uncertainty
The novel idea of setting up Internet-based virtual markets, information markets, to aggregate dispersed information and predict outcomes of uncertain future events has empirically found its way into many domains. But the theoretical examination of information markets has lagged relative to their implementation and use. This paper proposes a simple theoretical model of information markets to understand their information dynamics. We investigate and provide initial answers to a series of research questions that are important to understanding how information markets work, which are: (1) Does an information market converge to a consensus equilibrium? (2) If yes, how fast is the convergence process? (3) What is the best possible equilibrium of an information market? and (4) Is an information market guaranteed to converge to the best possible equilibrium?
20851072
Constructing a SCORM-Compliant Intelligent Strategy Repository
Developing a pedagogical learning content that can be delivered among different Learning Management Systems (LMSs) is a critical task for most instructors. Although the Sharable Content Object Reference Model (SCORM) has proposed a mechanism allowing the exchange of learning contents between LMSs, to embed learning strategies to SCORM-compliant learning content is still an open issue. This paper proposes a mechanism to construct a SCORM-compliant strategy repository which contains learning strategies. The strategy repository can be adapted to satisfy the requirement of instructor for designing learning content with strategies embedded. The strategy repository presented in this paper is with the following advantages: (a) the strategies stored are domain independent; (b) the strategies offered are adaptable; (c) the strategies saved can be continuously evolved; (d) the strategies stored can be reusable.
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.
8131087
Multipath-Based Multicasting Strategies for Wormhole-Routed Star Graph Interconnection Networks
The star graph interconnection network has been recognized as an attractive alternative to the popular hypercube network. In this paper, we present a multipath-based multicast routing model for wormholerouted star graph networks, propose two efficient multipath routing schemes, and contrast the performance of the proposed schemes with the performance of the scheme presented in our previous work. Both of the two proposed schemes have been proven to be deadlock-free. The first scheme, simplemultipath routing, uses multiple independent paths for concurrent multicasting. The second scheme, two-phase multipath routing, includes two phases: source-to-relay and relay-to-destination. For each phase, multicasting is carried out using simple multipath routing. Experimental results show that, for short and medium messages with small message startup latencies, the proposed schemes reduce multicast latency more efficiently than other schemes.
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.