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Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, people are given: A container, usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers ...
The problem does have a variant which is more tractable. Given any positive integer k≥3, the k-set packing problem is a variant of set packing in which each set contains at most k elements. When k=1, the problem is trivial. When k=2, the problem is equivalent to finding a maximum cardinality matching, which can be solved in polynomial time.
The bin packing problem can also be seen as a special case of the cutting stock problem. When the number of bins is restricted to 1 and each item is characterized by both a volume and a value, the problem of maximizing the value of items that can fit in the bin is known as the knapsack problem .
Parsing, syntax analysis, or syntactic analysis is a process of analyzing a string of symbols, either in natural language, computer languages or data structures, conforming to the rules of a formal grammar by breaking it into parts. The term parsing comes from Latin pars (orationis), meaning part (of speech). [1]
The strip packing problem contains the bin packing problem as a special case when all the items have the same height 1. For this reason, it is strongly NP-hard, and there can be no polynomial time approximation algorithm that has an approximation ratio smaller than 3 / 2 {\displaystyle 3/2} unless P = N P {\displaystyle P=NP} .
The first parser of this family to outperform a chart-based parser was the one by Muhua Zhu et al. in 2013, which took on the problem of length differences of different transition sequences due to unary constituency rules (a non-existent problem for dependency parsing) by adding a padding operation. [15]
While useful, pure parser generators only address the parsing part of the problem of building a compiler. Tools with broader scope, such as PQCC, Coco/R and DMS Software Reengineering Toolkit provide considerable support for more difficult post-parsing activities such as semantic analysis, code optimization and generation.
The package-merge algorithm is an O(nL)-time algorithm for finding an optimal length-limited Huffman code for a given distribution on a given alphabet of size n, where no code word is longer than L. It is a greedy algorithm , and a generalization of Huffman's original algorithm .