Ž . A Steiner minimum tree SMT in the rectilinear plane is the shortest length tree interconnecting a set of points, called the regular points, possibly using Ž . additional vertices. A k-size Steiner minimum tree kSMT is one that can be split into components where all regular points are leaves and all components have at most k leaves. The k-Steiner ratio in the rectilinear plane, r , is the in...

Given a set P of terminals in the plane and a partition of P into k subsets P1, . . . , Pk, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree Ti connecting the terminals in each set Pi (i = 1, . . . , k) and a top-level tree Ttop connecting the trees T1, . . . , Tk. The goal is to minimize the total length of all trees. This problem arises naturally in the design of lo...

Multi-layer context tree (MCT) modeling has been recently applied for lossless compression of multi-layer map images and showed its efficiency. Though it is not applicable directly to compression of gray-scale images, it could be utilized together with bit-plane separation technique. In this work we evaluated the performance of MCT modeling according to three bit-plane separation methods and co...

In the present paper, the minimal proper alternating cycle (MPAC) rotation graph R(G) of perfect matchings of a plane bipartite graph G is defined. We show that an MPAC rotation graph R(G) of G is a directed rooted tree, and thus extend such a result for generalized polyhex graphs to arbitrary plane bipartite graphs. As an immediate result, we describe a one-to-one correspondence between MPAC s...

We propose an algorithm that creates optimized cut-out sheets for paper models from textured polygon meshes. Crafting time and usage of paper and glue are reduced by first computing an initial folding tree to unfold the mesh into a plane. Overlaps in the plane are then eliminated by adding new cuts. Finally, glue tabs are generated along all cuts before fitting all unfolded parts onto paper she...

For every n ∈ N, we present a set Sn of O(n log n) points in the plane such that every planar 3-tree with n vertices has a straight-line embedding in the plane in which the vertices are mapped to a subset of Sn. This is the first subquadratic upper bound on the size of universal point sets for planar 3-trees, as well as for the class of 2-trees and serial parallel graphs.

SYLVIE CORTEEL AND CARLA D. SAVAGE Abstra t. In this note we generalize the plane partition diamonds of Andrews, Paule, and Riese to plane partition polygons and plane tree diamonds and show how to ompute their generating fun tions. 1. Introdu tion In [1℄, Andrews, Paule, and Riese introdu e the family of plane partition diamonds. A plane partition diamond of length n is a sequen e of length 3n...

For every n ∈ N, we present a set Sn of O(n log n) points in the plane such that every planar 3-tree with n vertices has a straight-line embedding in the plane in which the vertices are mapped to a subset of Sn. This is the first subquadratic upper bound on the size of universal point sets for planar 3-trees, as well as for the class of 2-trees and serial parallel graphs.

This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size n is proved to have a limiting theta distribution, both in a central and local sense. Moderate as well as large deviations estimates are also derived. The proofs rely on the analysis (in the complex plane) of generating fun...