Related papers: Streaming Algorithms for Geometric Steiner Forest

The Planar Steiner Tree problem is one of the most fundamental NP-complete problems as it models many network design problems. Recall that an instance of this problem consists of a graph with edge weights, and a subset of vertices (often…

We study the problem of extracting a small subset of representative items from a large data stream. In many data mining and machine learning applications such as social network analysis and recommender systems, this problem can be…

We introduce a new variant of the geometric Steiner arborescence problem, motivated by the layout of flow maps. Flow maps show the movement of objects between places. They reduce visual clutter by bundling lines smoothly and avoiding…

We propose two one-pass streaming algorithms for the $\mathcal{NP}$-hard hypergraph matching problem. The first algorithm stores a small subset of potential matching edges in a stack using dual variables to select edges. It has an…

We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations and flows. The network may contain other unprescribed nodes, known as Steiner points. For concave…

We study the generalized minimum Manhattan network (GMMN) problem: given a set $P$ of pairs of two points in the Euclidean plane $\mathbb{R}^2$, we are required to find a minimum-length geometric network which consists of axis-aligned…

In the Steiner Forest problem, we are given a graph with edge lengths, and a collection of demand pairs; the goal is to find a subgraph of least total length such that each demand pair is connected in this subgraph. For over twenty years,…

We introduce a new computational model for data streams: asymptotically exact streaming algorithms. These algorithms have an approximation ratio that tends to one as the length of the stream goes to infinity while the memory used by the…

In the graph stream model of computation, an algorithm processes the edges of an input graph in one or more sequential passes while using a memory sublinear in the input size. This model poses significant challenges for constructing long…

We consider the problem of embedding the Steiner points of a Steiner tree with given topology into the rectilinear plane. Thereby, the length of the path between a distinguished terminal and each other terminal must not exceed given length…

In streamed graph drawing, a planar graph, G, is given incrementally as a data stream and a straight-line drawing of G must be updated after each new edge is released. To preserve the mental map, changes to the drawing should be minimized…

Graph coloring is a fundamental problem in computer science. In the semi-streaming model, an input graph $G$ on $n$ vertices and maximum degree $\Delta$ is presented as a stream of edges, and the goal is to compute a vertex coloring using a…

Data streaming, in which a large dataset is received as a "stream" of updates, is an important model in the study of space-bounded computation. Starting with the work of Le Gall [SPAA `06], it has been known that quantum streaming…

In the Steiner Tree problem we are given an edge weighted undirected graph $G = (V,E)$ and a set of terminals $R \subseteq V$. The task is to find a connected subgraph of $G$ containing $R$ and minimizing the sum of weights of its edges. We…

The sheer increase in the size of graph data has created a lot of interest into developing efficient distributed graph processing frameworks. Popular existing frameworks such as Graphlab and Pregel rely on balanced graph partitioning in…

We provide the first streaming algorithm for computing a provable approximation to the $k$-means of sparse Big data. Here, sparse Big Data is a set of $n$ vectors in $\mathbb{R}^d$, where each vector has $O(1)$ non-zeroes entries, and…

Decision forests, including random forests and gradient boosting trees, remain the leading machine learning methods for many real-world data problems, especially on tabular data. However, most of the current implementations only operate in…

We consider the problem of estimating the value of MAX-CUT in a graph in the streaming model of computation. At one extreme, there is a trivial $2$-approximation for this problem that uses only $O(\log n)$ space, namely, count the number of…

Graph partitioning is an important preprocessing step to distributed graph processing. In edge partitioning, the edge set of a given graph is split into $k$ equally-sized partitions, such that the replication of vertices across partitions…

In this work we consider the Metric Steiner Forest problem in the sublinear time model. Given a set $V$ of $n$ points in a metric space where distances are provided by means of query access to an $n\times n$ distance matrix, along with a…