Related papers: A Simple and Efficient Method to Compute a Single …
Many load balancing problems that arise in scientific computing applications ask to partition a graph with weights on the vertices and costs on the edges into a given number of almost equally-weighted parts such that the maximum boundary…
The Steiner tree enumeration problem is a well known problem that asks for enumerating Steiner trees. Numerous theoretical works proposed algorithms for the problem and analyzed their complexity, but there are no practical algorithms and…
Rotation distances measure the differences in structure between rooted ordered binary trees. The one-dimensional skeleta of associahedra are rotation graphs, where two vertices representing trees are connected by an edge if they differ by a…
We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skeletonization procedure to remove short-range correlations…
In the classical (min-cost) Steiner tree problem, we are given an edge-weighted undirected graph and a set of terminal nodes. The goal is to compute a min-cost tree S which spans all terminals. In this paper we consider the min-power…
Given a planar graph G on n vertices and an integer parameter r<n, an r-division of G with few holes is a decomposition of G into O(n/r) regions of size at most r such that each region contains at most a constant number of faces that are…
Solving optimization problems leads to elegant and practical solutions in a wide variety of real-world applications. In many of those real-world applications, some of the information required to specify the relevant optimization problem is…
Triangle strips have been widely used for efficient rendering. It is NP-complete to test whether a given triangulated model can be represented as a single triangle strip, so many heuristics have been proposed to partition models into few…
We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover…
We study the local evolution of Prim's algorithm on large finite weighted graphs. When performed for $n$ steps, where $n$ is the size of the graph, Prim's algorithm will construct the minimal spanning tree (MST). We assume that our graphs…
This paper proposes a new evolutionary algorithm, called DSMGA-II, to efficiently solve optimization problems via exploiting problem substructures. The proposed algorithm adopts pairwise linkage detection and stores the information in the…
While normalizing flows for continuous data have been extensively researched, flows for discrete data have only recently been explored. These prior models, however, suffer from limitations that are distinct from those of continuous flows.…
Split learning (SL) is a distributed learning paradigm that can enable computation-intensive artificial intelligence (AI) applications by partitioning AI models between mobile devices and edge servers. %fully utilizing distributed computing…
We study a generalization of the Steiner tree problem, where we are given a weighted network $G$ together with a collection of $k$ subsets of its vertices and a root $r$. We wish to construct a minimum cost network such that the network…
Distance based algorithms are a common technique in the construction of phylogenetic trees from taxonomic sequence data. The first step in the implementation of these algorithms is the calculation of a pairwise distance matrix to give a…
We propose a procedure to build a decision tree which approximates the performance of complex machine learning models. This single approximation tree can be used to interpret and simplify the predicting pattern of random forests (RFs) and…
Suppose we label the vertices of a tree by positive integers. The weight of an edge is defined by a monotonically increasing function of the absolute value of the difference of the labels of its endpoints. We define the total cost of the…
The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such…
Hierarchical clustering and community detection are important problems in machine learning and complex network analysis. A common approach to identify clusters is to simply cut dendrograms at some threshold. However, single-level cuts are…
We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We…