Related papers: A PTAS for the Steiner Forest Problem in Doubling …
Constrained forest problems form a class of graph problems where specific connectivity requirements for certain cuts within the graph must be satisfied by selecting the minimum-cost set of edges. The prize-collecting version of these…
We give the first deterministic fully polynomial-time approximation scheme (FPTAS) for computing the partition function of a two-state spin system on an arbitrary graph, when the parameters of the system satisfy the uniqueness condition on…
We introduce a new approach to spectral sparsification that approximates the quadratic form of the pseudoinverse of a graph Laplacian restricted to a subspace. We show that sparsifiers with a near-linear number of edges in the dimension of…
The Polyline Bundle Simplification (PBS) problem is a generalization of the classical polyline simplification problem. Given a set of polylines, which may share line segments and points, PBS asks for the smallest consistent simplification…
We consider the $k$-prize-collecting Steiner tree problem. An instance is composed of an integer $k$ and a graph $G$ with costs on edges and penalties on vertices. The objective is to find a tree spanning at least $k$ vertices which…
Prize-Collecting Steiner Tree (PCST) is a generalization of the Steiner Tree problem, a fundamental problem in computer science. In the classic Steiner Tree problem, we aim to connect a set of vertices known as terminals using the…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
Stochastic programming can be applied to consider uncertainties in energy system optimization models for capacity expansion planning. However, these models become increasingly large and time-consuming to solve, even without considering…
We study approximation algorithms for the forest cover and bounded forest cover problems. A probabilistic $2+\epsilon$ approximation algorithm for the forest cover problem is given using the method of dual fitting. A deterministic algorithm…
We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rounding techniques yield novel and powerful ways of rounding.…
Spanning trees are an important primitive in many data analysis tasks, when a data set needs to be summarized in terms of its "skeleton", or when a tree-shaped graph over all observations is required for downstream processing. Popular…
This paper extends the RRT* algorithm, a recently developed but widely-used sampling-based optimal motion planner, in order to effectively handle nonlinear kinodynamic constraints. Nonlinearity in kinodynamic differential constraints often…
We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the Subtree…
Moss and Rabani[12] study constrained node-weighted Steiner tree problems with two independent weight values associated with each node, namely, cost and prize (or penalty). They give an O(log n)-approximation algorithm for the…
In the Directed Steiner Tree (DST) problem the input is a directed edge-weighted graph $G=(V,E)$, a root vertex $r$ and a set $S \subseteq V$ of $k$ terminals. The goal is to find a min-cost subgraph that connects $r$ to each of the…
A {$t$-stretch tree cover} of a metric space $M = (X,\delta)$, for a parameter $t \ge 1$, is a collection of trees such that every pair of points has a $t$-stretch path in one of the trees. Tree covers provide an important sketching tool…
As a hybrid of the Parallel Two-stage Flowshop problem and the Multiple Knapsack problem, we investigate the scheduling of parallel two-stage flowshops under makespan constraint, which was motivated by applications in cloud computing and…
This paper introduces a novel scheduling problem, where jobs occupy a triangular shape on the time line. This problem is motivated by scheduling jobs with different criticality levels. A measure is introduced, namely the binary tree ratio.…
We present a unified framework for designing deterministic monotone polynomial time approximation schemes (PTAS's) for a wide class of scheduling problems on uniformly related machines. This class includes (among others) minimizing the…
A rectilinear Steiner tree for a set $P$ of points in $\mathbb{R}^2$ is a tree that connects the points in $P$ using horizontal and vertical line segments. The goal of Minimal Rectilinear Steiner Tree is to find a rectilinear Steiner tree…