presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. the method is easy to u...

Presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. Also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. The method is easy to u...

Asynchronous and parallel implementation of standard reinforcement learning (RL) algorithms is a key enabler the tremendous success modern RL. Among many asynchronous RL algorithms, arguably most popular effective one advantage actor-critic (A3C) algorithm. Although A3C becoming workhorse RL, its theoretical properties are still not well-understood, including non-asymptotic analysis performance...

Many distributed applications repeatedly perform the same sequence of operations creating a cyclic pattern of behavior. This pattern can be used to model the steady–state behavior of the application, and to predict its performance. In particular, the relationship between the execution time, or the speedup, and the number of processors is studied for distributed iterative solution of (large) sys...

We consider a scheduling problem where a set of jobs is apriori distributed over parallel machines. The processing time of any job is dependent on the usage of a scarce renewable resource, e.g. personnel. An amount of k units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The dependence of processi...

The linear speedup theorem states, informally, that constants do not matter: It is essentially always possible to find a program solving any decision problem a factor of 2 faster. This result is a classical theorem in computing, but also one of the most debated. The main ingredient of the typical proof of the linear speedup theorem is tape compression, where a fast machine is constructed with t...

Program speedup is an important measure of the performance of an algorithm on a parallel machine. Of particular importance is the near linear or superlinear speedup exhibited by the most performance-eecient algorithms for a given system. We describe network and program models for heterogeneous networks, deene notions of speedup and superlinear speedup, and observe that speedup consists of both ...

Many academic papers imply that parallel computing is only worthwhile when applications achieve nearly linear speedup (i.e., execute nearly p times faster on p processors). This note shows that parallel computing is cost-eeective whenever speedup exceeds costup| the parallel system cost divided by uniprocessor cost. Furthermore, when applications have large memory requirements (e.g., 512 megaby...