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The partition problem is a special case of two related problems: In the subset sum problem, the goal is to find a subset of S whose sum is a certain target number T given as input (the partition problem is the special case in which T is half the sum of S).
LPT might not find the optimal partition. For example, in the above instance the optimal partition {8,7}, {6,5,4}, where both sums are equal to 15. However, its suboptimality is bounded both in the worst case and in the average case; see Performance guarantees below.
Despite its worst-case hardness, optimal solutions to very large instances of the problem can be produced with sophisticated algorithms. In addition, many approximation algorithms exist. For example, the first fit algorithm provides a fast but often non-optimal solution, involving placing each item into the first bin in which it will fit.
First-fit-decreasing (FFD) is an algorithm for bin packing.Its input is a list of items of different sizes. Its output is a packing - a partition of the items into bins of fixed capacity, such that the sum of sizes of items in each bin is at most the capacity.
When there are at most 4 items, LDM returns the optimal partition. LDM always returns a partition in which the largest sum is at most 7/6 times the optimum. [4] This is tight when there are 5 or more items. [2] On random instances, this approximate algorithm performs much better than greedy number partitioning. However, it is still bad for ...
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Equivalence partitioning or equivalence class partitioning (ECP) [1] is a software testing technique that divides the input data of a software unit into partitions of equivalent data from which test cases can be derived. In principle, test cases are designed to cover each partition at least once.