2015 IEEE 12th International Conference on Mobile Ad Hoc and Sensor Systems, 2015
Recent advances in energy transfer technology is boosting the development of renewable sensor net... more Recent advances in energy transfer technology is boosting the development of renewable sensor networks. To sustain such a network, a mobile robot travels from node to node to recharge each sensor before its battery runs out. Consider each node's recharge as a real-time task; the robot needs to serve these tasks by their deadlines. This represents a class of challenging mobility scheduling problems, where the nodes' deadlines and spatial distribution are often at odds with each other. In this paper, we focus on the scenario where nodes have heterogeneous energy consumption rates, and our goal is to maximize the percentage of nodes alive. We formulate this scheduling problem and prove its NP-completeness. To solve this problem, we propose a spatial dependent task scheduling algorithm, which quantifies the impact of scheduling proximate tasks on the other tasks. With extensive simulations, we reveal the trade-offs of existing solutions under a wide range of network scenarios. Our evaluation results show that our algorithms out-perform classical TSP scheduler by up to 10% and 85% in terms of coverage ratio and average tardiness, respectively.
In this paper we study the following problem: given a set of m sensors that collectively cover a ... more In this paper we study the following problem: given a set of m sensors that collectively cover a set of n target points with heterogeneous coverage requirements (target j needs to be covered every fj slots), how to schedule the sensor duty cycles such that all coverage requirements are satisfied and the maximum number of sensors turned on at any time slot is minimized. The problem models varied real-world applications in which sensing tasks exhibit high discrepancy in coverage requirements — critical locations often need to be covered much more frequently. We provide multiple algorithms with best approximation ratio of O (log n + log m) for the maximum number of sensors to turn on, and bi-criteria algorithm with (α, β)-approximation factors with high probability, where the number of sensors turned on is an α = O(δ(log (n) + log(m))/β)-approximation of the optimal (satisfying all requirements) and the coverage requirement is a β-approximation; δ is the approximation ratio achievable ...
IEEE INFOCOM 2017 - IEEE Conference on Computer Communications, 2017
Modern planetary-scale online services have massive data to transfer over the wide area network (... more Modern planetary-scale online services have massive data to transfer over the wide area network (WAN). Due to the tremendous cost of building WANs and the stringent timing requirement of distributed applications, it is critical for network operators to make efficient use of network resources to optimize data transfers. By leveraging software-defined networking (SDN) and reconfigurable optical devices, recent solutions design centralized systems to jointly control the network layer and the optical layer. While these solutions show it is promising to significantly reduce data transfer times by centralized crosslayer control, they do not have any theoretical guarantees on the proposed algorithms. This paper presents approximation algorithms and theoretical analysis for the online transfer scheduling problem over optical WANs. The goal of the scheduling problem is to minimize the makespan (the time to finish all transfers) or the total sum of completion times. We design and analyze various greedy, online scheduling algorithms that can achieve 3competitive ratio for makespan, 2-competitive ratio for minimum sum completion time for jobs of unit size, and 3α-competitive ratio for jobs of arbitrary transfer size and each node having degree constraint d, where α = 1 when d = 1 and α = 1.86 when d ≥ 2. We also evaluated the performance of these algorithms and compared the performance with prior heuristics.
Kleinberg's small world model [20] simulates social networks with both strong and weak ties. In h... more Kleinberg's small world model [20] simulates social networks with both strong and weak ties. In his original paper, Kleinberg showed how the distribution of weak-ties, parameterized by γ, influences the efficacy of myopic routing on the network. Recent work on social influence by k-complex contagion models discovered that the distribution of weakties also impacts the spreading rate in a crucial manner on Kleinberg's small world model [15]. In both cases the parameter of γ = 2 proves special: when γ is anything but 2 the properties no longer hold. In this work, we propose a natural generalization of Kleinberg's small world model to allow node heterogeneity: instead of a single global parameter γ, each node has a personalized parameter γ chosen independently from a distribution D. In contrast to the original model, we show that this model enables myopic routing and k-complex contagions on a large range of the parameter space, improving the robustness of the model. Moreover, we show that our generalization is supported by real-world data. Analysis of four different social networks shows that the nodes do not show homogeneity in terms of the variance of the lengths of edges incident to the same node.
IEEE Transactions on Network Science and Engineering, 2017
In this paper, we study the spreading speed of complex contagions in a social network. A k-comple... more In this paper, we study the spreading speed of complex contagions in a social network. A k-complex contagion starts from a set of initially infected seeds such that any node with at least k infected neighbors gets infected. Simple contagions, i.e., k = 1, quickly spread to the entire network in small world graphs. However, fast spreading of complex contagions appears to be less likely and more delicate; the successful cases depend crucially on the network structure [19, 32]. Our main result shows that complex contagions can spread fast in a general family of time-evolving networks that includes the preferential attachment model [10]. We prove that if the initial seeds are chosen as the oldest nodes in a network of this family, a k-complex contagion covers the entire network of n nodes in O(log n) steps. We show that the choice of the initial seeds is crucial. If the initial seeds are uniformly randomly chosen in the PA model, even if we have a polynomial number of them, a complex contagion would stop prematurely. The oldest nodes in a preferential attachment model are likely to have high degrees. However, we remark that it is actually not the power law degree distribution per se that facilitates fast spreading of complex contagions, but rather the evolutionary graph structure of such models. Some members of the said family do not even have a power-law distribution. The main proof has two pillars. The first one is an analysis of a labeled branching process which might be of independent interest. The second pillar is an intricate coupling argument that links the extinction time of the labeled branching process to the speed of a k-complex contagion in the said family of time-evolving networks. The coupling argument itself relies on a careful revealing process that reveals the randomness of the network in a particular order to alleviate dependency/conditioning problems. Using similar techniques, we also prove that complex contagions are fast in the copy model [41], a variant of the preferential attachment family, if the initial seeds are chosen as the oldest nodes. Finally, we prove that when a complex contagion starts from an arbitrary set of initial seeds on a general graph, determining if the number of infected vertices is above a given threshold is P-complete. Thus, one cannot hope to categorize all the settings in which complex contagions percolate in a graph.
2015 IEEE Conference on Computer Communications (INFOCOM), 2015
Analysis of Internet topologies has shown that the Internet topology has negative curvature, meas... more Analysis of Internet topologies has shown that the Internet topology has negative curvature, measured by Gromov's "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.
Proceedings of the 22nd ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, 2014
We describe an online algorithm to simplify large volumes of location and sensor data on the sour... more We describe an online algorithm to simplify large volumes of location and sensor data on the source mobile device, by eliminating redundant data points and saving important ones. Our approach is to use topological persistence to identify large scale sharp features of a data stream. We show that for one-dimensional data streams such as trajectories, simplification based on topologically persistent features can be maintained online, such that each new data-point is processed in O(1) time. Our method extends to multi-resolution simplifications, where it identifies larger scale features that represent more important elements of data, and naturally eliminates noise and small deviations. The multi-resolution simplification is also maintained online in real time, at cost of O(1) per input point. Therefore it is lightweight and suitable for use in embedded sensors and mobile phones. The method can be applied to more general data streams such as sensor data to produce similar simplifications. Our experiments on real data show that this approach when applied to the curvature function of trajectory or sensor data produces compact simplifications with low approximation errors comparable to existing offline methods.
Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science - ITCS '15, 2015
Complex contagions describe diffusion of behaviors in a social network in settings where spreadin... more Complex contagions describe diffusion of behaviors in a social network in settings where spreading requires the influence by two or more neighbors. In a k-complex contagion, a cluster of nodes are initially infected, and additional nodes become infected in the next round if they have at least k already infected neighbors. It has been argued that complex contagions better model behavioral changes such as adoption of new beliefs, fashion trends or expensive technology innovations. This has motivated rigorous understanding of spreading of complex contagions in social networks. Despite simple contagions (k = 1) that spread fast in all small world graphs, how complex contagions spread is much less understood. Previous work analyzes complex contagions in Kleinberg's small world model where edges are randomly added according to a spatial distribution (with exponent γ) on top of a two dimensional grid structure. It has been shown in that the speed of complex contagions differs exponentially when γ = 0 compared to when γ = 2. In this paper, we fully characterize the entire parameter space of γ except at one point, and provide upper and lower bounds for the speed of k-complex contagions. We study two subtly different variants of Kleinberg's small world model and show that, with respect to complex contagions, they behave differently. For each model and each k ≥ 2, we show that there is an intermediate range of values, such that when γ takes any of these values, a k-complex contagion spreads quickly on the corresponding graph, in a polylogarithmic number of rounds. However, if γ is outside this range, then a k-complex contagion requires a polynomial number of rounds to spread to the entire network.
For a set S of points in R d , an s-spanner is a graph on S such that any pair of points is conne... more For a set S of points in R d , an s-spanner is a graph on S such that any pair of points is connected via some path in the spanner whose total length is at most s times the Euclidean distance between the points. In this paper we propose a new sparse (1+ε)-spanner with O(n/ε d) edges, where ε is a specified parameter. The key property of this spanner is that it can be efficiently maintained under dynamic insertion or deletion of points, as well as under continuous motion of the points in both the kinetic data structures setting and in the more realistic blackbox displacement model we introduce. Our deformable spanner succinctly encodes all proximity information in a deforming point cloud, giving us efficient kinetic algorithms for problems such as the closest pair, the near neighbors of all points, approximate nearest neighbor search (aka approximate Voronoi diagram), well-separated pair decomposition, and approximate k-centers.
Proceedings of the 15th ACM international symposium on Mobile ad hoc networking and computing - MobiHoc '14, 2014
Load balanced routing in a network, i.e., minimizing the maximum traffic load any node carries fo... more 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 d 2 , 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.
Space Filling Curves for 3D Sensor Networks with Complex Topology
Several aspects of managing a sensor network (e.g., motion planning for data mules, serial data f... more Several aspects of managing a sensor network (e.g., motion planning for data mules, serial data fusion and inference) benefit once the network is linearized to a path. The linearization is often achieved by constructing a space filling curve in the domain. However, existing methods cannot handle networks distributed on surfaces of complex topology. This paper presents a novel method for generating space filling curves for 3D sensor networks that are distributed densely on some two-dimensional geometric surface. Our algorithm is completely distributed and constructs a path which gets uniformly, progressively denser as it becomes longer. We analyze the algorithm mathematically and prove that the curve we obtain is dense. Our method is based on the Hodge decomposition theorem and uses holomorphic differentials on Riemann surfaces. The underlying high genus surface is conformally mapped to a union of flat tori and then a proportionally-dense space filling curve on this union is construc...
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