Related papers: On a Shape Optimization Problem for Tree Branches
We consider the shape and topology optimization problem to design a structure that minimizes a weighted sum of material consumption and (linearly) elastic compliance under a fixed given boundary load. As is well-known, this problem is in…
The problems of maximizing the spectral radius and the number of spanning trees in a class of bipartite graphs with certain degree constraints are considered. In both the problems, the optimal graph is conjectured to be a Ferrers graph.…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
Multi-material structural topology and shape optimization problems are formulated within a phase field approach. First-order conditions are stated and the relation of the necessary conditions to classical shape derivatives are discussed. An…
Tree-based phylogenetic networks, which may be roughly defined as leaf-labeled networks built by adding arcs only between the original tree edges, have elegant properties for modeling evolutionary histories. We answer an open question of…
For a given metric space $(P,\phi)$, a tree cover of stretch $t$ is a collection of trees on $P$ such that edges $(x,y)$ of trees receive length $\phi(x,y)$, and such that for any pair of points $u,v\in P$ there is a tree $T$ in the…
Tree containment problem is a fundamental problem in phylogenetic study, as it is used to verify a network model. It asks whether a given network contain a subtree that resembles a binary tree. The problem is NP-complete in general, even in…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
Shape-constrained optimization arises in a wide range of problems including distributionally robust optimization (DRO) that has surging popularity in recent years. In the DRO literature, these problems are usually solved via reduction into…
We determine the maximum distance between any two of the center, centroid, and subtree core among trees with a given order. Corresponding results are obtained for trees with given maximum degree and also for trees with given diameter. The…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
A measure representation result for a functional modelling optimal design problems for plastic deformations, under linear growth conditions, is obtained. Departing from an energy with a bulk term depending on the deformation gradient and…
We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one…
For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by its removal and present corresponding…
The {\sc Directed Maximum Leaf Out-Branching} problem is to find an out-branching (i.e. a rooted oriented spanning tree) in a given digraph with the maximum number of leaves. In this paper, we obtain two combinatorial results on the number…
Shape matching has been a long-studied problem for the computer graphics and vision community. The objective is to predict a dense correspondence between meshes that have a certain degree of deformation. Existing methods either consider the…
We propose a new arithmetic for non-empty rooted unordered trees simply called trees. After discussing tree representation and enumeration, we define the operations of tree addition, multiplication and stretch, prove their properties, and…