Related papers: Universal Loop-Free Super-Stabilization
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
In this paper, we set forth a new algorithm for generating approximately uniformly random spanning trees in undirected graphs. We show how to sample from a distribution that is within a multiplicative $(1+\delta)$ of uniform in expected…
In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We…
In this paper we study the stability of a tree-shaped network of elastic strings and beams with some feedbacks at the ends. The whole system is asymptotically stable. Moreover, the energy of the solution decay exponentially to zero if there…
Random forests are among the most popular classification and regression methods used in industrial applications. To be effective, the parameters of random forests must be carefully tuned. This is usually done by choosing values that…
Conventional power system optimization framework is becoming less reliable and efficient due to the stability issues brought by the ever-increasing inverter-interfaced renewable penetration. To ensure system stability during system…
This paper addresses problems on the structural design of control systems taking explicitly into consideration the possible application to large-scale systems. We provide an efficient and unified framework to solve the following major…
A \emph{tree cut-sparsifier} $T$ of quality $\alpha$ of a graph $G$ is a single tree that preserves the capacities of all cuts in the graph up to a factor of $\alpha$. A \emph{tree flow-sparsifier} $T$ of quality $\alpha$ guarantees that…
Managing power grids with the increasing presence of variable renewable energy-based (distributed) generation involves solving high-dimensional optimization tasks at short intervals. Linearizing the AC power flow (PF) constraints is a…
An optimal binary search tree for an access sequence on elements is a static tree that minimizes the total search cost. Constructing perfectly optimal binary search trees is expensive so the most efficient algorithms construct almost…
It has been proved that the spanning tree from a given network has the optimal synchronizability, which means the index $R=\lambda_{N}/\lambda_{2}$ reaches the minimum 1. Although the optimal synchronizability is corresponding to the…
The network reconfiguration problem seeks to find a rooted tree $T$ such that the energy of the (unique) feasible electrical flow over $T$ is minimized. The tree requirement on the support of the flow is motivated by operational constraints…
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…
For many nonlinear control systems, the chosen equilibrium determines both the steady-state efficiency and the dynamic performance. This paper addresses the issue of obtaining an optimal equilibrium in terms of some steady-state operation…
Control-flow graphs (CFGs) of structured programs are well known to exhibit strong sparsity properties. Traditionally, this sparsity has been modeled using graph parameters such as treewidth and pathwidth, enabling the development of faster…
The $Aldous\text{-}Broder$ and $Wilson$ are two well-known algorithms to generate uniform spanning trees (USTs) based on random walks. This work studies their relationship while they construct random trees with the goal of reducing the…
Extending some properties from the Euclidean plane to any normed plane, we show the validity of the Monma-Paterson-Suri-Yao algorithm for finding the maximum-weighted spanning tree of a set of $n$ points, where the weight of an edge is the…
We present a new universal source code for distributions of unlabeled binary and ordinal trees that achieves optimal compression to within lower order terms for all tree sources covered by existing universal codes. At the same time, it…
The field of network synchronization has seen tremendous growth following the introduction of the master stability function (MSF) formalism, which enables the efficient stability analysis of synchronization in large oscillator networks.…
In this article, we study the Euclidean minimum spanning tree problem in an imprecise setup. The problem is known as the \emph{Minimum Spanning Tree Problem with Neighborhoods} in the literature. We study the problem where the neighborhoods…