Chien-Chun Ni

Ricci curvature of the Internet topology

Analysis of Internet topologies has shown that the Internet topology has negative curvature, measured by Gromovs “thin triangle condition”, which is tightly related to core congestion and route reliability. In this work we analyze the discrete Ricci curvature of the Internet, defined by Ollivier [1], Lin et al. [2], etc. Ricci curvature measures whether local distances diverge or converge. It is a more local measure which allows us to understand the distribution of curvatures in the network. We show by various Internet data sets that the distribution of Ricci cuvature is spread out, suggesting the network topology to be non-homogenous. We also show that the Ricci curvature has interesting connections to both local measures such as node degree and clustering coefficient, global measures such as betweenness centrality and network connectivity, as well as auxilary attributes such as geographical distances. These observations add to the richness of geometric structures in complex network theory.

Connected wireless camera network deployment with visibility coverage

We consider the problem of deployment of cameras inside a complex indoor setting for surveillance applications. We formulate the problem of the minimum guarding network that places a minimum number of cameras satisfying both visual coverage of the domain and wireless network connectivity. We prove that finding the minimum guarding network in both the geometric setting and discrete setting is NP-hard. We also give a 2-approximation algorithm to the geometric minimum guarding network. Motivated by the connection of this problem with the watchman tour problem and the art gallery problem, we develop two algorithms that generate satisfactory results in a prototype testbed and in our simulations. Index Terms—Visibility Coverage, Wireless Connectivity, Cam- era Networks

Bounded Stretch Geographic Homotopic Routing in Sensor Networks

Homotopic routing asks for a path going around holes according to a given “threading”. Paths of different homo-topy types can be used to improve load balancing and routing resilience. We propose the first lightweight homotopic routing scheme that generates constant bounded stretch compared to the shortest path of the same homotopy type. Our main insight is that in a sequence of triangles to traverse, a message always routed to the nearest point on the next triangle in the sequence travels at most a constant times the length of any shortest path going through the same sequence of triangles. Our routing scheme operates on two levels enabled by a coarse triangulation. The top level is used to specify and represent the requested homotopy type, while the bottom level executes the local greedy routing on a triangle sequence. After a preprocessing step that triangulates the given region and creates a minimum-size auxiliary structure, routing operates greedily at two different resolutions. We also present simulation analysis in a variety of settings and show that the paths indeed have small stretch in practice, considerably shorter than the bounds guaranteed by the theory.

Load balanced short path routing in large-scale wireless networks using area-preserving maps

Load balanced routing in a network, i.e., minimizing the maximum traffic load any node carries for unsplittable flows, is a well known NP-hard problem. Finding practical algorithms remains a long standing challenge. In this paper we propose greedy routing using virtual coordinates that achieves both small path stretch ratio (compared to shortest path) and small load balancing ratio (compared to optimal load balanced routing), in a large scale wireless sensor network deployed densely inside a geometric domain with complex shape. We first provide a greedy routing scheme on a disk with a stretch ratio of at most 2, and under which the maximum load is a factor 4√2 smaller than the maximum load under shortest path routing. This is the first simple routing scheme with a small stretch that has been proven to outperform shortest path routing in terms of load balancing. Then we transform a network of arbitrary shape to a disk by an area preserving map φ. We show that both the path length and the maximum traffic load in the original network only increases by an additional factor of d2, where d is the maximum length stretch of φ. Combined with the result on a disk we again achieve both bounded stretch and bounded load balancing ratio. Our simulation results evaluated the practical performance on both quality measures.

Robot Coverage Path planning for general surfaces using quadratic differentials

Robot Coverage Path planning (i.e., the process of providing full coverage of a given domain by one or multiple robots) is a classical problem in the field of robotics and motion planning. The goal of such planning is to provide nearly full coverage while also minimize duplicately visited area. In this paper, we focus on the scenario of path planning on general surface, including planar domains with complex topology, complex terrain, and general surface in 3D space. Our approach described in this paper adopts a natural, intrinsic and global parametrization of the surface for robot path planning, namely the holomorphic quadratic differentials. We give each point on the surface a uv-coordinates naturally represented by a complex number, except for a small number of zero points (singularities). We show that natural, efficient robot paths can be obtained by using such coordinate systems. The method is based on intrinsic geometry and thus can be adapted to general surface exploration in 3D.

MinHash hierarchy for privacy preserving trajectory sensing and query

In this work, we study privacy preserving trajectory sensing and query when

Fighting Statistical Re-Identification in Human Trajectory Publication

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Capacitated kinetic clustering in mobile networks by optimal transportation theory

mobile entities (e.g., mobile devices or vehicles) move in an environment of

Decentralized human trajectories tracking using hodge decomposition in sensor networks

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Poster abstract: connected wireless camera network deployment with visibility coverage

checkpoints (e.g, WiFi or cellular towers). The checkpoints detect the appearances of mobile entities in the proximity, meanwhile, employ the MinHash signatures to record the set of mobile entities passing by. We build on the checkpoints a distributed data structure named the MinHash hierarchy, with which one can efficiently answer queries regarding popular paths and other traffic patterns. The MinHash hierarchy has a total of near linear storage, linear construction cost, and logarithmic update cost. The cost of a popular path query is logarithmic in the number of checkpoints. Further, the MinHash signature provides privacy protection using a model inspired by the differential privacy model.We evaluated our algorithm using a large mobility data set and compared with previous works to demonstrate its utilities and performances.