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Pinwheel Scheduling
In mathematics and computer science, the pinwheel scheduling problem is a problem in real-time scheduling with repeating tasks of unit length and hard constraints on the time between repetitions. Definition The input to pinwheel scheduling consists of a list of tasks, each of which is assumed to take unit time per instantiation. Each task has an associated positive integer value, its minimum repeat time (the minimum time from the start of one instantiation of the task to the next). Only one task can be performed at any given time. The desired output is an infinite sequence specifying which task to perform in each unit of time. Each input task should appear infinitely often in the sequence, with the largest gap between two consecutive instantiations of a task at most equal to the repeat time of the task. For example, the infinitely repeating sequence ''...'' would be a valid pinwheel schedule for three tasks ''a'', ''b'', and ''c'' with repeat times that are at least 2, 4, and 4 r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scheduling Analysis Real-time Systems
The term scheduling analysis in real-time computing includes the analysis and testing of the scheduler system and the algorithms used in real-time applications. In computer science, real-time scheduling analysis is the evaluation, testing and verification of the scheduling system and the algorithms used in real-time operations. For critical operations, a real-time system must be tested and verified for performance. A real-time scheduling system is composed of the scheduler, clock and the processing hardware elements. In a real-time system, a process or task has schedulability; tasks are accepted by a real-time system and completed as specified by the task deadline depending on the characteristic of the scheduling algorithm. Modeling and evaluation of a real-time scheduling system concern is on the analysis of the algorithm capability to meet a process deadline. A deadline is defined as the time required for a task to be processed. For example, in a real-time scheduling algorithm a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Of Two
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer as the exponent. In a context where only integers are considered, is restricted to non-negative values, so there are 1, 2, and 2 multiplied by itself a certain number of times. The first ten powers of 2 for non-negative values of are: : 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ... Because two is the base of the binary numeral system, powers of two are common in computer science. Written in binary, a power of two always has the form 100...000 or 0.00...001, just like a power of 10 in the decimal system. Computer science Two to the exponent of , written as , is the number of ways the bits in a binary word of length can be arranged. A word, interpreted as an unsigned integer, can represent values from 0 () to () inclusively. Corresponding signed integer values can be positive, negative and zero; see signe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covering System
In mathematics, a covering system (also called a complete residue system) is a collection :\ of finitely many residue classes a_i(\mathrm\ ) = \ whose union contains every integer. Examples and definitions The notion of covering system was introduced by Paul Erdős in the early 1930s. The following are examples of covering systems: # \, # \, # \. A covering system is called ''disjoint'' (or ''exact'') if no two members overlap. A covering system is called ''distinct'' (or ''incongruent'') if all the moduli n_i are different (and bigger than 1). Hough and Nielsen (2019) proved that any distinct covering system has a modulus that is divisible by either 2 or 3. A covering system is called ''irredundant'' (or ''minimal'') if all the residue classes are required to cover the integers. The first two examples are disjoint. The third example is distinct. A system (i.e., an unordered multi-set) :\ of finitely many residue classes is called an m-cover if it covers every integ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-hard
In computational complexity theory, NP-hardness ( non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard problem is the subset sum problem. A more precise specification is: a problem ''H'' is NP-hard when every problem ''L'' in NP can be reduced in polynomial time to ''H''; that is, assuming a solution for ''H'' takes 1 unit time, ''H''s solution can be used to solve ''L'' in polynomial time. As a consequence, finding a polynomial time algorithm to solve any NP-hard problem would give polynomial time algorithms for all the problems in NP. As it is suspected that P≠NP, it is unlikely that such an algorithm exists. It is suspected that there are no polynomial-time algorithms for NP-hard problems, but that has not been proven. Moreover, the class P, in which all problems can be solved in polynomial time, is contained in the NP class. Def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
