When a wide polygonal dural window is created, a short dural incision length is preferred by surgeons because suturing a wastefully long incision line during closure is troublesome. A locator to facilitate making the shortest dural incision when creating a polygonal dural window would be helpful. We geometrically analyzed the shortest incision design for a pentagonal dural window and produced a...

We introduce a flow-dependent version of the quadratic Steiner tree problem in the plane. An instance of the problem on a set of embedded sources and a sink asks for a directed tree T spanning these nodes and a bounded number of Steiner points, such that ∑ e∈E(T ) f(e)|e| is a minimum, where f(e) is the flow on edge e. The edges are uncapacitated and the flows are determined additively, i.e., t...

This paper describes a biased random-key genetic algorithm for a real-world wireless backhaul network design problem. This is a novel problem, closely related to variants of the Steiner tree problem and the facility location problem. Given a parameter h, we want to build a forest where each tree has at most h hops from the demand nodes, where traffic originates, to the root nodes where each tre...

Given a graph G and a subset W ⊆ V (G), a Steiner W -tree is a tree of minimum order that contains all of W . Let S(W ) denote the set of all vertices in G that lie on some Steiner W -tree; we call S(W ) the Steiner interval of W . If S(W ) = V (G), then we call W a Steiner set of G. The minimum order of a Steiner set of G is called the Steiner number of G. Given two vertices u, v in G, a short...

We discuss properties and values of maximum matchings and minimum median problems for nite point sets. In particular, we consider \minimum stars", which are deened by a choosing a center, such that the total geometric distance to all the points in the set is minimized. Since the center point is not required to be an element of the set (i. e., the center may be a Steiner point), we get a \minimu...

We consider the problem of constructing Steiner minimum trees for a metric defined by a polygonal unit circle (corresponding to σ ≥ 2 weighted legal orientations in the plane). A linear-time algorithm to enumerate all angle configurations for degree three Steiner points is given. We provide a simple proof that the angle configuration for a Steiner point extends to all Steiner points in a full S...

We consider a new Steiner tree problem, called vertex-cover-weighted Steiner tree problem. This problem defines the weight of a Steiner tree as the minimum weight of vertex covers in the tree, and seeks a minimum-weight Steiner tree in a given vertex-weighted undirected graph. Since it is included by the Steiner tree activation problem, the problem admits an O(logn)-approximation algorithm in g...