We show that O(n) exchanging flips suffice to transform any edge-labelled pointed pseudo-triangulation into any other with the same set of labels. By using insertion, deletion and exchanging flips, we can transform any edge-labelled pseudo-triangulation into any other with O(n log c+h log h) flips, where c is the number of convex layers and h is the number of points on the convex hull.

The logarithmic-exponential (log-exp) function has been widely used in convex analysis and mathematical programming. This paper studies a natural generalization of the log-exp function. Certain necessary and sufficient conditions are obtained for establishing such a generalization. The derived sufficient conditions are explicitly expressed in terms of the first and second derivatives of the fun...

In contemporary convex geometry, the rapidly developing Lp-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the Lp-affine surface area for convex bodies. Here, we introduce a functional form of this concept, for log concave and s-concave functions. We show that the new functional form is a generalization of the original Lp-affi...

Abstract In this paper, our aim is to consider the new class of log-convex fuzzy-interval-valued function known as log- s -convex functions (log- fuzzy-IVFs). By concept, we have introduced Hermite–Hadamard inequalities (HH-inequalities) by means fuzzy order relation. This relation defined level-wise through Kulisch–Miranker on interval space. Moreover, some Hermite–Hadamard–Fejér (HH–Fejér-ine...

Let D be a set of n pairwise disjoint unit disks in the plane. We describe how to build a data structure for D so that for any point set P containing exactly one point from each disk, we can quickly find the onion decomposition (convex layers) of P . Our data structure can be built in O(n log n) expected time and has linear size. Given P , we can find its onion decomposition in O(n log k) time,...

Given n points in the plane, we study three optimization problems of computing an empty pseudo-triangle: we consider minimizing the perimeter, maximizing the area, and minimizing the longest maximal concave chain. We consider two versions of the problem: First, we assume that the three convex vertices of the pseudotriangle are given. Let n denote the number of points that lie inside the convex ...

We consider the problem of dynamically maintaining convex hull a set S points in plane under following special sequence insertions and deletions (called window-sliding updates): insert point to right all delete leftmost S. propose an O(|S|)-space data structure that can handle each update O(1) amortized time, such standard binary-search-based queries on be answered $$O(\log |S|)$$ itself output...

Basing on recently developed convex programming framework in the paper [arXiv:2204.10626], we provide a proof for long-standing conjecture optimality of Gaussian encondings ultimate communication rate generalized heterodyne receivers under oscillator energy constraint. Our results generalize previous ones (obtained assumption validity threshold condition) and show drastic difference structure o...

Ravindra K. Ahuja and Dorit S. Hochbaum Abstract In this paper, we study capacitated dynamic lot sizing problems with or without backorders, under the assumption that production costs are linear, that is, there are no set up costs. These two dynamic lot sizing problems (with or without backorders) are minimum cost flow problems on an underlying network that possess a special structure. We show ...

We present e cient algorithms for shortest path and minimum link path queries between two convex polygons inside a simple polygon P which acts as an obstacle to be avoided Let n be the number of vertices of P and h the total number of vertices of the query polygons We show that shortest path queries can be performed optimally in time O logh logn plus O k time for reporting the k edges of the pa...