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As one of the most important data structures used in algorithm design and programming, balanced search trees are widely used in real-world applications for organizing data. Answering the challenges thrown up by modern large-volume and ever-changing data,...

A novel mth best average biased received power (ABRP) user association (UA) scheme is proposed for K‐tier heterogeneous networks, where a user is associated with the closest base station (BS) of the kth tier having the mth strongest ABRP, k+1,2,…,K. By ...

Schnyder characterized planar graphs in terms of order dimension. The structures used for the proof have found many applications. Researchers also found several extensions of the seminal result. A particularly far-reaching extension is the Brightwell--Trotter ...

The states of a finite automaton are ordered by height. This order is shown to be graduated, and the well-known Cerny problem on the minimal length of reset words can be formulated in terms of global height. The problem is proved for automata with four ...

Ordered sets of documents are encountered more and more in information distribution systems, such as information retrieval systems. Classical similarity measures for ordinary sets of documents hence need to be extended to these ordered sets. This is ...

Let P be a finite ordered set, and let J(P) be the distributive lattice of order ideals of P. The covering relations of J(P) are naturally associated with elements of P; in this way, each element of P defines an involution on the set J(P). Let Γ(P) be ...

A directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction and no two edges cross. An undirected graph is rectilinear planar if it can be drawn in the plane such ...

A generalized p-cycle is a digraph whose set of vertices is partitioned into p parts that can be ordered in such a way that a vertex is adjacent only to vertices in the next part. The families of BGC(p,d,d/sup k/) (de Bruijn Generalized Cycles) and KGC(...

For an ordered set P and for a linear extension L of P let $s ( P,L )$ stand for the number of ordered pairs $ ( x,y )$ of elements of P such that x is an immediate successor of y in L but x is not even above y in P. Put $s ( P ) = \min \{ s ( P,L ) |L\,{\...