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We consider node-weighted network design problems, in particular the survivable network design problem (SNDP) and its prize-collecting version (PC-SNDP). The input consists of a node-weighted undirected graph G = (V, E) and integral connectivity requirements r(st) for each pair of nodes st. The goal is to find a minimum node-weighted subgraph H of G such… (More)

We consider node-weighted network design problems, in particular the survivable network design problem (SNDP) and its prize-collecting version (PC-SNDP). The input consists of a node-weighted undirected graph G = (V, E) and integral connectivity requirements r(st) for each pair of nodes st. The goal is to find a minimum node-weighted subgraph H of G such… (More)

We consider node-weighted network design in planar and minor-closed families of graphs. In particular we focus on the edge-connectivity survivable network design problem (EC-SNDP). The input consists of a node-weighted undi-rected graph G = (V, E) and integral connectivity requirements r(uv) for each pair of nodes uv. The goal is to find a minimum… (More)

We develop the first streaming algorithm and the first two-party communication protocol that uses a constant number of passes/rounds and sublin-ear space/communication for logarithmic approximation to the classic Set Cover problem. Specifically, for n elements and m sets, our algorithm/protocol achieves a space bound of O(m · n δ log 2 n log m) using O(4… (More)

We consider the classic Set Cover problem in the data stream model. For n elements and m sets (m ≥ n) we give a O(1/δ)-pass algorithm with a strongly sub-linear ~O(mn<sup>δ</sup>) space and logarithmic approximation factor. This yields a significant improvement over the earlier algorithm of Demaine et al. [10] that uses exponentially larger… (More)

It is well established that extracting and annotating occurrences of entities in a collection of unstructured text documents with their concepts improve the effectiveness of answering queries over the collection. However, it is very resource intensive to create and maintain large annotated collections. Since the available resources of an enterprise are… (More)

A set of vertices in a graph is a dominating set if every vertex outside the set has a neighbor in the set. A dominating set is connected if the subgraph induced by its vertices is connected. The connected domatic partition problem asks for a partition of the nodes into connected dominating sets. The connected domatic number of a graph is the size of a… (More)

We consider <i>degree bounded</i> network design problems with element and vertex connectivity requirements. In the degree bounded Survivable Network Design (SNDP) problem, the input is an undirected graph <i>G</i> = (<i>V, E</i>) with weights <i>w</i>(<i>e</i>) on the edges and degree bounds <i>b</i>(<i>v</i>) on the vertices, and connectivity requirements… (More)

- Chris Musco, Ali Vakilian, Ankur Moitra, Tom Kolokotrones, Mayuri Sridhar, Vincent Tjeng
- 2016

In this lecture, we consider methods for developing approximation algorithms for NP-hard combi-natorial optimization problems using linear programs (LPs). We will consider two approaches: LP Rounding and the Primal-Dual approach. Last week, we talked about submodular functions and showed a way to relax them to convex functions via the Lovasz Theorem. The… (More)