7967901
The effect of machine availability on the worst-case performance of LPT
We consider the makespan minimization parallel machine scheduling problem where each machine may be unavailable for a known time interval. For this problem, we investigate how the worst-case behavior of the longest processing time first algorithm (LPT) is affected by the availability of machines. In particular, for given m machines, we analyze the cases where arbitrary number, λ, ranging from one to m - 1, machines are unavailable simultaneously. Then, we show that the makespan of the schedule generated by LPT is never more than the tight worst-case bound of 1 + ½ ⌊m/(m - λ)⌋ times the optimum makespan.
18088728
Order Consolidation for Batch Processing
We consider the batch processing of orders where either whole or part of a single order or a specific pair of different orders may be grouped in a batch with a fixed capacity. The problem can be modelled by a graph G = (V,E), where each node v$${\in}$$V corresponds to an order, its weight w(v) corresponds to the amount of ordered quantity and a pair of orders, say u and v may be grouped in a batch if there exists the edge (u,v) $${\in}$$E. The objective is to maximize the number of batches filled up to its capacity $$\lambda$$. In this paper, we prove that the problem is NP-hard and, moreover, that no PTAS exists unless P = NP. Then, an optimal algorithm is developed with running time O(|V|log |V|) for the special case when G is a tree.
17634440
An optimal cache algorithm for streaming VBR video over a heterogeneous network
High quality video content for on-demand services is usually stored and streamed in a compressed format with a VBR (variable bit rate) property; however, the streaming traffic is extremely bursty. If there is no client buffer to regulate the video's delivery, the backbone WAN (wide area network) bandwidth needs to allocate the video's peak bit rate to guarantee playback quality. To reduce the bandwidth requirement in the backbone WAN, previous researchers have proposed a Video Staging Mechanism to cache portions of the video in a video proxy close to clients. In this paper, we propose a very effective OC (optimal cache) algorithm to handle the Video Staging Mechanism and prove theoretically that the proxy cache computed by our OC algorithm for each video is minimal when all other resources remain constant. On the basis of experiment results, we cache the least amount of video data in the video proxy by using the OC algorithm, and reduce the WAN bandwidth requirement by an amount equal to that of conventional algorithms. In contrast, given the equal size of the storage in a video proxy, the OC algorithm reduces the bandwidth requirement in the backbone WAN much more than conventional algorithms.
40375618
A Visual Optimization Specification Language
44477744
Efficient selection of scheduling rule combination by combining design of experiment and ordinal optimization-based simulation
In a fab with heterogeneous machine groups, the number of scheduling policies grows in a combinatorial way because each machine group has its specific dispatching rules. In this paper, we design a fast simulation methodology by an innovative combination of the notions of ordinal optimization (OO) and design of experiments (DOE) to efficiently select a good scheduling policy for fab operation, Instead of finding the exact performance among scheduling policies, our approach compares their relative orders of performance to a specified level of confidence. The DOE method is exploited to largely reduce the number of scheduling policies to be evaluated by the OO-based simulation. Simulation results of applications to scheduling wafer fabrications show that most of the OO-based DOE simulations require 2 to 3 orders of magnitude less computation time than those of traditional approach, and the speedup is up to 7,000 times in certain cases.
16926226
Optimal histogram matching by monotone gray level transformation
This paper investigates the problem of optimal histogram matching using monotone gray level transformation, which always assigns all picture points of a given gray level <italic>i</italic> to another gray level <italic>T</italic>(<italic>i</italic>) such that if <italic>i</italic> ≥ <italic>j</italic>, then <italic>T</italic>(<italic>i</italic>) ≥ <italic>T</italic>(<italic>j</italic>). The objective is to find a transformed digital picture of a given picture such that the sum of absolute errors between the gray level histogram of the transformed picture and that of a reference picture is minimized. This is equivalent to placing <italic>k</italic>1 linearly ordered objects of different sizes one by one into <italic>k</italic>2 linearly ordered boxes of assorted sizes, such that the accumulated error of space underpacked or overpacked in the boxes is minimized; the placement function is monotonic, which ensures a polynomial time solution to this problem. A tree search algorithm for optimal histogram matching is presented which has time complexity <italic>O</italic>(<italic>k</italic>1 × <italic>k</italic>2). If the monotone property is dropped, then the problem becomes <italic>NP</italic>-complete, even if it is restricted to <italic>k</italic>2 = 2.
203669352
An Efficient Technique to Remove Transformations
Although the application of code transformations is critical to exploit parallelism in pro- gram code, few guidelines or tools are provided to deter- mine what transformations should be applied and where they should be applied. In this paper, we approach this problem by fist providing a taxonomy of code transfor- mations to assist the user in parallelizing programs. We then present an eficient technique to remove transforma- tionsfrom the code when it is determined that they are ineffective or prevent more beneficial transformations from being applied. The technique to remove transforma- tions employs inverse primitive actions, making it transformation independent. The technique uses the pro- gram dependence graph as the intermediate representa- tion, making it language independent.