General methods for adding range restrictions to decomposable searching problems

Decomposable Searching Problems

In this paper we will investigate transformations that serve as tools in the design of new data structures. Specifically, we study general methods for converting static structures (in which all elements are known before any searches are performed) to dynamic structures (in which insertions of new elements can be mixed with searches). We will exhibit three classes of such transformations, each b...

Dynamization of Decomposable Searching Problems

In the complexity theory of geometric configurations (and other areas of algorithmic endeavor) one encounters a fair number of problems for which a very efficient static solution is known, but no alternative to complete reconstruction seems to come to mind when we wish to insert or delete even a single point. Bentley [1 3 recognized a large class of problems (which he called decomposable search...

Decomposable Searching Problems I: Static-to-Dynamic Transformation

Transformations that serve as tools in the design of new data structures are investigated. Specifically, general methods for converting static structures (m which all elements are known before any searches are performed) to dynamic structures (in which insertions of new elements can be mixed with searches) are studied. Three classes of such transformations are exhibited, each based on a differe...

On the decomposable numerical range of operators

 ‎Let $V$ be an $n$-dimensional complex inner product space‎. ‎Suppose‎ ‎$H$ is a subgroup of the symmetric group of degree $m$‎, ‎and‎ ‎$chi‎ :‎Hrightarrow mathbb{C} $ is an irreducible character (not‎ ‎necessarily linear)‎. ‎Denote by $V_{chi}(H)$ the symmetry class‎ ‎of tensors associated with $H$ and $chi$‎. ‎Let $K(T)in‎ (V_{chi}(H))$ be the operator induced by $Tin‎ ‎text{End}(V)$‎. ‎Th...

Range Searching Range Searching