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A problem set, sometimes shortened as pset, [1] is a teaching tool used by many universities. Most courses in physics, math, engineering, chemistry, and computer science will give problem sets on a regular basis. [2] They can also appear in other subjects, such as economics.
Dominating set, a.k.a. domination number [3]: GT2 NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. [3]: ND2 Feedback vertex set [2] [3]: GT7
In some variants, the aim is to find the configuration that packs a single container with the maximal packing density. More commonly, the aim is to pack all the objects into as few containers as possible. [1] In some variants the overlapping (of objects with each other and/or with the boundary of the container) is allowed but should be minimized.
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.
A subset Q of J is called a rainbow set if it contains at most a single interval of each color. A set of intervals J is called a covering of P if each point in P is contained in at least one interval of Q. The Rainbow covering problem is the problem of finding a rainbow set Q that is a covering of P. The problem is NP-hard (by reduction from ...
The discrete unit disc cover problem is a geometric version of the general set cover problem which is NP-hard. [2] Many approximation algorithms have been devised for these problems. Due to the geometric nature, the approximation ratios for these problems can be much better than the general set cover/hitting set problems.
In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...
Dominating set is the problem of selecting a set of vertices (the dominating set) in a graph such that all other vertices are adjacent to at least one vertex in the dominating set. The Dominating set problem was shown to be NP complete through a reduction from Set cover. Exact cover problem is to choose a set cover with no element included in ...