We develop a simple theory of flows to study the flow of data in real-time computing networks. Flow Theory is based on discrete and nondeterministic mathematics, rather than the customary continuous or probabilistic mathematics. The theory features two types of flows: smooth and uniform, and eight types of flow operators. We prove that, if the input flow to any of these operators is smooth or u...

Introduction The knowledge of the arterial transit time, δa, from the labeling plane into the brain is essential for blood-flow quantification. In previous work, the MATISSE (Mapping of Arterial Transit times by Intravascular Signal Selection) approach for the mapping of δa was introduced (1). It relies on the use of short repetition times, TR, and the application of an amplitude-modulated shap...

Given an instance of the minimum cost flow problem, a version of the corresponding inverse problem, called the capacity inverse problem, is to modify the upper and lower bounds on arc flows as little as possible so that a given feasible flow becomes optimal to the modified minimum cost flow problem. The modifications can be measured by different distances. In this article, we consider the capac...

We consider the classic online scheduling problem of minimizing the total weighted flow time on a single machine with preemptions. Here, each job j has an arbitrary arrival time rj , weight wj and size pj , and given a schedule its flow time is defined as the duration of time since its arrival until it completes its service requirement. The first non-trivial algorithms with poly-logarithmic com...

We give a procedure of solving the weighted minimax flow problem in a polynomial time. The procedure utilizes the capacity modification technique and the binary search method. 1 . I NTRODUCTI ON We have considered variants of the maximum flow problems [5,6]. [5] discusses a minimax flo1N, i.e., the flow which minimizes the maximum arc-flow value among all flows of maximum flow value. [6] treats...

This paper revisits the online problem of flow-time scheduling on a single processor when jobs can be rejected at some penalty [4]. The user cost of a job is defined as the weighted flow time of the job plus the penalty if it is rejected before completion. For jobs with arbitrary weights and arbitrary penalties, Bansal et al. [4] gave an online algorithm that is O((logW + logC)2)competitive for...

We propose a general dual-fitting technique for analyzing online scheduling algorithms in the unrelated machines setting where the objective function involves weighted flow-time, and we allow the machines of the on-line algorithm to have (1 + ε)-extra speed than the offline optimum (the so-called speed augmentation model). Typically, such algorithms are analyzed using non-trivial potential func...

We consider the online scheduling problem of minimizing total weighted flow time plus energy in the dynamic speed scaling model, where a processor can scale its speed dynamically between 0 and some maximum speed T . In the past few years this problem has been studied extensively under the clairvoyant setting, which requires the size of a job to be known at release time [1, 4, 5, 8, 15, 18–20]. ...