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Movements, leaders, victories and the continuing fight for equality.
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Katherine Johnson’s mathematical calculations helped guide some of America’s most important early space missions while she confronted the racial and gender barriers faced by Black women in twentieth-century America.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
Open-shop scheduling or open-shop scheduling problem (OSSP) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job-scheduling problem, we are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on m machines with varying processing power, while trying to minimize the makespan - the total length of the schedule (that is, when all the jobs have finished processing). In the specific variant known as open-shop scheduling, each job consists of a set of operations O1, O2, ..., On which need to be processed in an arbitrary order. The problem was first studied by Teofilo F. Gonzalez and Sartaj Sahni in 1976.[1]
In the standard three-field notation for optimal job-scheduling problems, the open-shop variant is denoted by O in the first field. For example, the problem denoted by "O3||" is a 3-machines job-shop problem with unit processing times, where the goal is to minimize the maximum completion time.
The input to the open-shop scheduling problem consists of a set of n jobs, another set of m workstations, and a two-dimensional table of the amount of time each job should spend at each workstation (possibly zero). Each job may be processed only at one workstation at a time, and each workstation can process only one job at a time. However, unlike the job-shop problem, the order in which the processing steps happen can vary freely. The goal is to assign a time for each job to be processed by each workstation, so that no two jobs are assigned to the same workstation at the same time, no job is assigned to two workstations at the same time, and every job is assigned to each workstation for the desired amount of time. The usual measure of quality of a solution is its makespan, the amount of time from the start of the schedule (the first assignment of a job to a workstation) to its end (the finishing time of the last job at the last workstation).
The open-shop scheduling problem can be solved in polynomial time for instances that have only two workstations or only two jobs. It may also be solved in polynomial time when all nonzero processing times are equal: in this case the problem becomes equivalent to edge coloring a bipartite graph that has the jobs and workstations as its vertices, and that has an edge for every job-workstation pair that has a nonzero processing time. The color of an edge in the coloring corresponds to the segment of time at which a job-workstation pair is scheduled to be processed. Because the line graphs of bipartite graphs are perfect graphs, bipartite graphs may be edge-colored in polynomial time.
For three or more workstations, or three or more jobs, with varying processing times, open-shop scheduling is NP-hard.[2]
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Open-shop scheduling or open-shop scheduling problem (OSSP) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job-scheduling problem, we are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on m machines with varying processing power, while trying to minimize the makespan - the total length of the schedule (that is, when all the jobs have finished processing). In the specific variant known as open-shop scheduling, each job consists of a set of operations O1, O2, ..., On which need to be processed in an arbitrary order. The problem was first studied by Teofilo F. Gonzalez and Sartaj Sahni in 1976. In the standard three-field notation for optimal job-scheduling problems, the open-shop variant is denoted by O in the first field. For example, the problem denoted by "O3| p i j {\displaystyle p_{ij}} | C max {\displaystyle C_{\max }} " is a 3-machines job-shop problem with unit processing times, where the goal is to minimize the maximum completion time.
Teofilo Francisco Gonzalez Arce (born January 26, 1948, in Monterrey, Mexico) is a Mexican-American computer scientist who is professor emeritus of computer science at the University of California, Santa Barbara. In 1972, Gonzalez was one of the first students who earned a bachelor's degree in computer science (Ingeniero en Sistemas Computacionales) in Mexico, at the Monterrey Institute of Technology and Higher Education. He completed his Ph.D. in 1975 from the University of Minnesota under the supervision of Sartaj Sahni. He taught at the University of Oklahoma from 1975 to 1976, at the Pennsylvania State University from 1976 to 1979, at the Monterrey Institute of Technology and Higher Education from 1979 to 1980, and at the University of Texas at Dallas from 1980 to 1984, before joining the UCSB computer science faculty in 1984. He spent Sabbatical Leaves at Utrecht University (1990) in the Netherlands and the Monterrey Institute of Technology and Higher Education. Professor Gonzalez became a Fellow of IASTED in 2009. Gonzalez is known for his highly cited pioneering research in the hardness of approximation;[SG76] for his sub-linear and best possible approximation algorithm (unless P = NP) based on the farthest-first traversal for the metric k-center problem[G85] (k-tMM clustering); and for introducing the open-shop scheduling problem as well as algorithms for its solution that have found numerous applications in several research areas as well as for his research on flow shop scheduling, and job shop scheduling algorithms.[GS76][GS78] He is the editor of the Handbook on Approximation Algorithms and Metaheuristics first edition[G07], second edition[G18] and he is co-editor of Volume 1 (Computer Science and Software Engineering) of the Computing Handbook Set.[CH]
A constructive heuristic is a type of heuristic method which starts with an empty solution and repeatedly extends the current solution until a complete solution is obtained. It differs from local search heuristics which start with a complete solution and then try to improve the current solution further via local moves. Examples of some famous problems that are solved using constructive heuristics are the flow shop scheduling, the vehicle routing problem and the open shop problem.
Job-shop scheduling, the job-shop problem (JSP) or job-shop scheduling problem (JSSP) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job scheduling problem, we are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on m machines with varying processing power, while trying to minimize the makespan – the total length of the schedule (that is, when all the jobs have finished processing). In the specific variant known as job-shop scheduling, each job consists of a set of operations O1, O2, ..., On which need to be processed in a specific order (known as precedence constraints). Each operation has a specific machine that it needs to be processed on and only one operation in a job can be processed at a given time. A common relaxation is the flexible job shop, where each operation can be processed on any machine of a given set (the machines in each set are identical). The name originally came from the scheduling of jobs in a job shop, but the theme has wide applications beyond that type of instance. It is a well-known combinatorial optimization problem and was the first to undergo competitive analysis, introduced by Graham in 1966. The best problem instances for a basic model with a makespan objective are due to Taillard. In the standard three-field notation for optimal job scheduling problems, the job-shop variant is denoted by J in the first field. For example, the problem denoted by " J 3 | p i j | C max {\displaystyle J_{3}|p_{ij}|C_{\max }} " is a 3-machines job-shop problem with unit processing times, where the goal is to minimize the maximum completion time.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Shirley Chisholm, elected in 1968.
