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In computer science, a stable sorting algorithm preserves the order of records with equal keys. In numerical analysis, a numerically stable algorithm avoids magnifying small errors. An algorithm is stable if the result produced is relatively insensitive to perturbations during computation.
In computer science, a sorting algorithm is an algorithm that puts elements of a list ... A sorting algorithm is stable if whenever there are two records R and S with ...
This algorithm is guaranteed to produce a stable marriage for all participants in time where is the number of men or women. [11] Among all possible different stable matchings, it always yields the one that is best for all men among all stable matchings, and worst for all women. [12]
A stable learning algorithm would produce a similar classifier with both the 1000-element and 999-element training sets. Stability can be studied for many types of learning problems, from language learning to inverse problems in physics and engineering, as it is a property of the learning process rather than the type of information being learned.
An algorithm for solving a linear evolutionary partial differential equation is stable if the total variation of the numerical solution at a fixed time remains bounded as the step size goes to zero. The Lax equivalence theorem states that an algorithm converges if it is consistent and stable (in this sense).
Stable sorting algorithms maintain the relative order of records with equal keys (i.e. values). That is, a sorting algorithm is stable if whenever there are two records R and S with the same key and with R appearing before S in the original list, R will appear before S in the sorted list.
Timsort is a stable sorting algorithm (order of elements with same key is kept) and strives to perform balanced merges (a merge thus merges runs of similar sizes). In order to achieve sorting stability, only consecutive runs are merged. Between two non-consecutive runs, there can be an element with the same key inside the runs.
In computer science, merge sort (also commonly spelled as mergesort and as merge-sort [2]) is an efficient, general-purpose, and comparison-based sorting algorithm.Most implementations produce a stable sort, which means that the relative order of equal elements is the same in the input and output.