Traffic-Redundancy Aware Network Design

We consider network design problems for information networks where routers can replicate data but cannot alter it. This functionality allows the network to eliminate data-redundancy in traffic, thereby saving on routing costs. We consider two problems within this framework and design approximation algorithms. The first problem we study is the traffic-redundancy aware network design (RAND) problem. We are given a weighted graph over a single server and many clients. The server owns a number of different data packets and each client desires a subset of the packets; the client demand sets form a laminar set system. Our goal is to connect every client to the source via a single path, such that the collective cost of the resulting network is minimized. Here the transportation cost over an edge is its weight times times the number of distinct packets that it carries. The second problem is a facility location problem that we call RAFL. Here the goal is to find an assignment from clients to facilities such that the total cost of routing packets from the facilities to clients (along unshared paths), plus the total cost of "producing" one copy of each desired packet at each facility is minimized. We present a constant factor approximation for the RAFL and an O(log P) approximation for RAND, where P is the total number of distinct packets. We remark that P is always at most the number of different demand sets desired or the number of clients, and is generally much smaller.Comment: 17 pages. To be published in the proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithm

Distinguishing Infections on Different Graph Topologies

The history of infections and epidemics holds famous examples where understanding, containing and ultimately treating an outbreak began with understanding its mode of spread. Influenza, HIV and most computer viruses, spread person to person, device to device, through contact networks; Cholera, Cancer, and seasonal allergies, on the other hand, do not. In this paper we study two fundamental questions of detection: first, given a snapshot view of a (perhaps vanishingly small) fraction of those infected, under what conditions is an epidemic spreading via contact (e.g., Influenza), distinguishable from a "random illness" operating independently of any contact network (e.g., seasonal allergies); second, if we do have an epidemic, under what conditions is it possible to determine which network of interactions is the main cause of the spread -- the causative network -- without any knowledge of the epidemic, other than the identity of a minuscule subsample of infected nodes? The core, therefore, of this paper, is to obtain an understanding of the diagnostic power of network information. We derive sufficient conditions networks must satisfy for these problems to be identifiable, and produce efficient, highly scalable algorithms that solve these problems. We show that the identifiability condition we give is fairly mild, and in particular, is satisfied by two common graph topologies: the grid, and the Erdos-Renyi graphs

Detecting Oriented Text in Natural Images by Linking Segments

Most state-of-the-art text detection methods are specific to horizontal Latin text and are not fast enough for real-time applications. We introduce Segment Linking (SegLink), an oriented text detection method. The main idea is to decompose text into two locally detectable elements, namely segments and links. A segment is an oriented box covering a part of a word or text line; A link connects two adjacent segments, indicating that they belong to the same word or text line. Both elements are detected densely at multiple scales by an end-to-end trained, fully-convolutional neural network. Final detections are produced by combining segments connected by links. Compared with previous methods, SegLink improves along the dimensions of accuracy, speed, and ease of training. It achieves an f-measure of 75.0% on the standard ICDAR 2015 Incidental (Challenge 4) benchmark, outperforming the previous best by a large margin. It runs at over 20 FPS on 512x512 images. Moreover, without modification, SegLink is able to detect long lines of non-Latin text, such as Chinese.Comment: To Appear in CVPR 201

Spanning trees short or small

We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is the $k$MST problem in which we require a tree of minimum weight spanning at least $k$ nodes in an edge-weighted graph. We show that the $k$MST problem is NP-hard even for points in the Euclidean plane. We provide approximation algorithms with performance ratio $2\sqrt{k}$ for the general edge-weighted case and $O(k^{1/4})$ for the case of points in the plane. Polynomial-time exact solutions are also presented for the class of decomposable graphs which includes trees, series-parallel graphs, and bounded bandwidth graphs, and for points on the boundary of a convex region in the Euclidean plane. We also investigate the problem of finding short trees, and more generally, that of finding networks with minimum diameter. A simple technique is used to provide a polynomial-time solution for finding $k$-trees of minimum diameter. We identify easy and hard problems arising in finding short networks using a framework due to T. C. Hu.Comment: 27 page