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List Scheduling
List scheduling is a greedy algorithm for Identical-machines scheduling. The input to this algorithm is a list of jobs that should be executed on a set of ''m'' machines. The list is ordered in a fixed order, which can be determined e.g. by the priority of executing the jobs, or by their order of arrival. The algorithm repeatedly executes the following steps until a valid schedule is obtained: * Take the first job in the list (the one with the highest priority). * Find a machine that is available for executing this job. ** If a machine is found, schedule this job on that machine. **Otherwise (no suitable machine is available), select the next job in the list. Example Suppose there are five jobs with processing-times , and ''m''=2 processors. Then, the resulting schedule is , , and the makespan is max(18,12)=18; if ''m''=3, then the resulting schedule is , , , and the makespan is max(11,13,6)=13. Performance guarantee The algorithm runs in time O(n), where ''n'' is the number of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identical-machines Scheduling
Identical-machines scheduling is an optimization problem in computer science and operations research. We are given ''n'' jobs ''J''1, ''J''2, ..., ''Jn'' of varying processing times, which need to be scheduled on ''m'' identical machines, such that a certain objective function is optimized, for example, the makespan is minimized. Identical machine scheduling is a special case of uniform machine scheduling, which is itself a special case of optimal job scheduling. In the general case, the processing time of each job may be different on different machines; in the case of identical machine scheduling, the processing time of each job is the same on each machine. Therefore, identical machine scheduling is equivalent to multiway number partitioning. A special case of identical machine scheduling is single-machine scheduling. In the standard three-field notation for optimal job scheduling problems, the identical-machines variant is denoted by P in the first field. For example, " P, , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Makespan
In operations research, the makespan of a project is the length of time that elapses from the start of work to the end. This type of multi-mode resource constrained project scheduling problem (MRCPSP) seeks to create the shortest logical project schedule, by efficiently using project resources, adding the lowest number of additional resources as possible to achieve the minimum makespan. ', Afshar-Nadjafi, B, ''in Applied Computing and Informatics (2014) The term commonly appears in the context of |
Online Algorithm
In computer science, an online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed to the algorithm, without having the entire input available from the start. In contrast, an offline algorithm is given the whole problem data from the beginning and is required to output an answer which solves the problem at hand. In operations research, the area in which online algorithms are developed is called online optimization. As an example, consider the sorting algorithms selection sort and insertion sort: selection sort repeatedly selects the minimum element from the unsorted remainder and places it at the front, which requires access to the entire input; it is thus an offline algorithm. On the other hand, insertion sort considers one input element per iteration and produces a partial solution without considering future elements. Thus insertion sort is an online algorithm. Note that the final result of an insertion sort ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Highest Level First
High may refer to: Science and technology * Height * High (atmospheric), a high-pressure area * High (computability), a quality of a Turing degree, in computability theory * High (tectonics), in geology an area where relative tectonic uplift took or takes place * Substance intoxication, also known by the slang description "being high" * Sugar high, a misconception about the supposed psychological effects of sucrose Music Performers * High (musical group), a 1974–1990 Indian rock group * The High, an English rock band formed in 1989 Albums * ''High'' (The Blue Nile album) or the title song, 2004 * ''High'' (Flotsam and Jetsam album), 1997 * ''High'' (New Model Army album) or the title song, 2007 * ''High'' (Royal Headache album) or the title song, 2015 * ''High'' (EP), by Jarryd James, or the title song, 2016 Songs * "High" (Alison Wonderland song), 2018 * "High" (The Chainsmokers song), 2022 * "High" (The Cure song), 1992 * "High" (David Hallyday song), 1988 * "Hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Longest Path
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A path is called ''simple'' if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges. In contrast to the shortest path problem, which can be solved in polynomial time in graphs without negative-weight cycles, the longest path problem is NP-hard and the decision version of the problem, which asks whether a path exists of at least some given length, is NP-complete. This means that the decision problem cannot be solved in polynomial time for arbitrary graphs unless P = NP. Stronger hardness results are also known showing that it is difficult to approximate. However, it has a linear time solution for directed acyclic graphs, which has important applications in finding the critical path in scheduling problems. NP-hardne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Longest-processing-time-first Scheduling
Longest-processing-time-first (LPT) is a greedy algorithm for job scheduling. The input to the algorithm is a set of ''jobs'', each of which has a specific processing-time. There is also a number ''m'' specifying the number of ''machines'' that can process the jobs. The LPT algorithm works as follows: # Order the jobs by descending order of their processing-time, such that the job with the longest processing time is first. # Schedule each job in this sequence into a machine in which the current load (= total processing-time of scheduled jobs) is smallest. Step 2 of the algorithm is essentially the list-scheduling (LS) algorithm. The difference is that LS loops over the jobs in an arbitrary order, while LPT pre-orders them by descending processing time. LPT was first analyzed by Ronald Graham in the 1960s in the context of the identical-machines scheduling problem. Later, it was applied to many other variants of the problem. LPT can also be described in a more abstract way, as an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |