Related papers: An Evolver program for weighted Steiner trees
We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of $m$ possible diseases, each test having a cost, and the a-priori likelihood of the patient having any…
We perform an experimental evaluation of algorithms for finding geodesic shortest paths between two points inside a simple polygon in the constant-workspace model. In this model, the input resides in a read-only array that can be accessed…
In this paper, we introduce a specific type of Euclidean tree called LED (Leaves of Equal Depth) tree. LED trees can be used in computational phylogeny, since they are a natural representative of the time evolution of a set of species in a…
There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges…
We describe a technique to reorganize topologies of Steiner trees by exchanging neighbors of adjacent Steiner points. We explain how to use the systematic way of building trees, and therefore topologies, to find the correct topology after…
In this note we analyze the performance of a simple root-finding algorithm in uniform attachment trees. The leaf-stripping algorithm recursively removes all leaves of the tree for a carefully chosen number of rounds. We show that, with…
CNOT circuits are a common building block of general quantum circuits. The problem of synthesizing and optimizing such circuits has received a lot of attention in the quantum computing literature. This problem is especially challenging for…
Given a set of terminals in 2D/3D, the network with the shortest total length that connects all terminals is a Steiner tree. On the other hand, with enough budget, every terminal can be connected to every other terminals via a straight…
We consider N-fold 4-block decomposable integer programs, which simultaneously generalize N-fold integer programs and two-stage stochastic integer programs with N scenarios. In previous work [R. Hemmecke, M. Koeppe, R. Weismantel, 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…
Minimizing wire-lengths is one of the most important objectives in circuit design. The process involves initially placing the logical units (cells) of a circuit onto a physical layout, and subsequently routing the wires to connect the…
Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…
Projected gradient descent has been proved efficient in many optimization and machine learning problems. The weighted $\ell_1$ ball has been shown effective in sparse system identification and features selection. In this paper we propose…
Motivated by hierarchical networks, we introduce the Flow-weighted Layered Metric Euclidean Capacitated Steiner Tree (FLaMECaST) problem, a variant of the Euclidean Steiner tree with layered structure and capacity constraints per layer. The…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…
In tree based adaptive mesh refinement, elements are partitioned between processes using a space filling curve. The curve establishes an ordering between all elements that derive from the same root element, the tree. When representing more…
Evolutionary computation methods have been successfully applied to neural networks since two decades ago, while those methods cannot scale well to the modern deep neural networks due to the complicated architectures and large quantities of…
A recent breakthrough by Ambainis, Balodis, Iraids, Kokainis, Pr\=usis and Vihrovs (SODA'19) showed how to construct faster quantum algorithms for the Traveling Salesman Problem and a few other NP-hard problems by combining in a novel way…
Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. To enable…
We are interested in the design of survivable capacitated rooted Steiner networks. Given a graph G = (V, E), capacity and cost functions on E, a root r, a subset T of V of terminals and an integer k, we search for a minimum cost subset E…