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The canonical application of topological sorting is in scheduling a sequence of jobs or tasks based on their dependencies.The jobs are represented by vertices, and there is an edge from x to y if job x must be completed before job y can be started (for example, when washing clothes, the washing machine must finish before we put the clothes in the dryer).
Animation of Fortune's algorithm, a sweep line technique for constructing Voronoi diagrams.. In computational geometry, a sweep line algorithm or plane sweep algorithm is an algorithmic paradigm that uses a conceptual sweep line or sweep surface to solve various problems in Euclidean space.
Poset topology, a kind of topological space that can be defined from any poset; Scott continuity – continuity of a function between two partial orders. Semilattice – Partial order with joins; Semiorder – Numerical ordering with a margin of error; Szpilrajn extension theorem – every partial order is contained in some total order.
The traditional ld (Unix linker) requires that its library inputs be sorted in topological order, since it processes files in a single pass. This applies both to static libraries ( *.a ) and dynamic libraries ( *.so ), and in the case of static libraries preferably for the individual object files contained within.
A topological space X is called orderable or linearly orderable [1] if there exists a total order on its elements such that the order topology induced by that order and the given topology on X coincide. The order topology makes X into a completely normal Hausdorff space. The standard topologies on R, Q, Z, and N are the order topologies.
In this problem, each variable corresponds to an hour that teacher must spend with cohort , the assignment to the variable specifies whether that hour is the first or the second of the teacher's available hours, and there is a 2-satisfiability clause preventing any conflict of either of two types: two cohorts assigned to a teacher at the same ...
The optimization problem of finding such a set is called the maximum independent set problem. It is a strongly NP-hard problem. [3] As such, it is unlikely that there exists an efficient algorithm for finding a maximum independent set of a graph. Every maximum independent set also is maximal, but the converse implication does not necessarily hold.
Therefore, the order in which the strongly connected components are identified constitutes a reverse topological sort of the DAG formed by the strongly connected components. [7] Donald Knuth described Tarjan's SCC algorithm as one of his favorite implementations in the book The Stanford GraphBase. [8] He also wrote: [9]