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A Greedy Approximation Algorithm for MinimumGap Scheduling
"... Abstract. We consider scheduling of unitlength jobs with release times and deadlines to minimize the number of gaps in the schedule. The best algorithm for this problem runs in time O(n4) and requires O(n3) memory. We present a simple greedy algorithm that approximates the optimum solution within a ..."
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a factor of 2 and show that our analysis is tight. Our algorithm runs in time O(n2 logn) and needs only O(n) memory. In fact, the running time is O(ng ∗ logn), where g ∗ is the minimum number of gaps. 1
Resolution lower bounds for perfect matching principles
 Journal of Computer and System Sciences
"... For an arbitrary hypergraph H, letPM(H) be the propositional formula asserting that H contains a perfect matching. We show that every resolution refutation of PM(H) musthavesize exp Ω δ(H) λ(H)r(H)(log n(H))(r(H)+logn(H)) where n(H) is the number of vertices, δ(H) is the minimal degree of a vertex, ..."
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Cited by 36 (5 self)
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For an arbitrary hypergraph H, letPM(H) be the propositional formula asserting that H contains a perfect matching. We show that every resolution refutation of PM(H) musthavesize exp Ω δ(H) λ(H)r(H)(log n(H))(r(H)+logn(H)) where n(H) is the number of vertices, δ(H) is the minimal degree of a vertex
A New Solution Method for the FiniteHorizon DiscreteTime EOQ Problem
, 2007
"... This is the PrePublished Version. We consider the finitehorizon discretetime economic order quantity problem. Kovalev and Ng (2008) have developed a solution approach for solving this problem. Their approach requires a search for the optimal number of orders, which takes O(logn) time. In this not ..."
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This is the PrePublished Version. We consider the finitehorizon discretetime economic order quantity problem. Kovalev and Ng (2008) have developed a solution approach for solving this problem. Their approach requires a search for the optimal number of orders, which takes O(logn) time
FAST, OPTIMAL ENTROPY CODER *
, 2004
"... Quantized Indexing ‡ (QI) is a fast and spaceefficient form of enumerative coding 1, the most “desirable ” 12,30 among asymptotically optimal universal source coding algorithms. The present advance in enumerative coding is similar to that made by arithmetic coding with respect to its unlimited prec ..."
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precision predecessor, Elias coding. The arithmetic precision, execution time, table sizes and coding delay are all reduced by a factor ≈ n/g at a redundancy below log(e)/2 g1 bits/symbol (for n input symbols and precision g ~ log(n)). Due to its tighter enumeration, QI output redundancy is below
RICE UNIVERSITY Regime Change: Sampling Rate vs. BitDepth in Compressive Sensing
, 2011
"... The compressive sensing (CS) framework aims to ease the burden on analogtodigital converters (ADCs) by exploiting inherent structure in natural and manmade signals. It has been demonstrated that structured signals can be acquired with just a small number of linear measurements, on the order of t ..."
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The compressive sensing (CS) framework aims to ease the burden on analogtodigital converters (ADCs) by exploiting inherent structure in natural and manmade signals. It has been demonstrated that structured signals can be acquired with just a small number of linear measurements, on the order of the signal complexity. In practice, this enables lower sampling rates that can be more easily achieved by current hardware designs. The primary bottleneck that limits ADC sampling rates is quantization, i.e., higher bitdepths impose lower sampling rates. Thus, the decreased sampling rates of CS ADCs accommodate the otherwise limiting quantizer of conventional ADCs. In this thesis, we consider a different approach to CS ADC by shifting towards lower quantizer bitdepths rather than lower sampling rates. We explore the extreme case where each measurement is quantized to just one bit, representing its sign. We develop a new theoretical framework to analyze this extreme case and develop new algorithms for signal reconstruction from such coarsely quantized measurements. The 1bit CS framework leads us to scenarios where it may be more appropriate to reduce bitdepth instead of sampling rate. We find that there exist two distinct regimes of operation that correspond to high/low signaltonoise ratio (SNR). In the measurement
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"... Anne SABOURIN Mélanges bayésiens de modèles d'extrêmes multivariés, Application à la prédétermination régionale des crues avec données incomplètes. Sous la direction de: ..."
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Anne SABOURIN Mélanges bayésiens de modèles d'extrêmes multivariés, Application à la prédétermination régionale des crues avec données incomplètes. Sous la direction de: