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A rectilinear polygon can always be covered with a finite number of vertices of the polygon. [1] The algorithm uses a local optimization approach: it builds the covering by iteratively selecting maximal squares that are essential to the cover (i.e., contain uncovered points not covered by other maximal squares) and then deleting from the polygon the points that become unnecessary (i.e ...
As input you are given several sets and a number . The sets may have some elements in common. You must select at most of these sets such that the maximum number of elements are covered, i.e. the union of the selected sets has maximal size. Formally, (unweighted) Maximum Coverage
The definition proceeds by examining what happens when the space is covered by open sets. In general, a topological space X can be covered by open sets, in that one can find a collection of open sets such that X lies inside of their union. The covering dimension is the smallest number n such that for every cover, there is a refinement in which ...
[0, 1] 2 is a totally bounded space because for every ε > 0, the unit square can be covered by finitely many open discs of radius ε. A metric space (,) is totally bounded if and only if for every real number >, there exists a finite collection of open balls of radius whose centers lie in M and whose union contains M.
In a finite linearly ordered set {1, 2, ..., n}, i + 1 covers i for all i between 1 and n − 1 (and there are no other covering relations).; In the Boolean algebra of the power set of a set S, a subset B of S covers a subset A of S if and only if B is obtained from A by adding one element not in A.
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