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Finding Spread Blockers in Dynamic Networks
"... Social interactions are conduits for various processes spreading through a population, from rumors and opinions to behaviors and diseases. In the context of the spread of a disease or undesirable behavior, it is important to identify blockers: individuals that are most effective in stopping or slow ..."
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Social interactions are conduits for various processes spreading through a population, from rumors and opinions to behaviors and diseases. In the context of the spread of a disease or undesirable behavior, it is important to identify blockers: individuals that are most effective in stopping or slowing down the spread of a process through the population. This problem has so far resisted systematic algorithmic solutions. In an effort to formulate practical solutions, in this paper we ask: Are there structural network measures that are indicative of the best blockers in dynamic social networks? Our contribution is twofold. First, we extend standard structural network measures to dynamic networks. Second, we compare the blocking ability of individuals in the order of ranking by the new dynamic measures. We found that overall, simple ranking according to a node’s static degree, or the dynamic version of a node’s degree, performed consistently well. Surprisingly the dynamic clustering coefficient seems to be a good indicator, while its static version performs worse than the random ranking. This provides simple practical and locally computable algorithms for identifying key blockers in a network.
Joint Monitoring and Routing in Wireless Sensor Networks using Robust Identifying Codes
"... Abstract—Wireless Sensor Networks (WSNs) provide an important means of monitoring the physical world, but their limitations present challenges to fundamental network services such as routing. In this work we utilize an abstraction of WSNs based on the theory of identifying codes. This abstraction ha ..."
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Cited by 12 (5 self)
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Abstract—Wireless Sensor Networks (WSNs) provide an important means of monitoring the physical world, but their limitations present challenges to fundamental network services such as routing. In this work we utilize an abstraction of WSNs based on the theory of identifying codes. This abstraction has been useful in recent literature for a number of important monitoring problems, such as localization and contamination detection. In our case, we use it to provide a joint infrastructure for efficient and robust monitoring and routing in WSNs. Specifically, we make use of efficient and distributed algorithm for generating robust identifying codes, an NPhard problem, with a logarithmic performance guarantee based on a reduction to the set kmulticover problem. We also show how this same identifyingcode infrastructure provides a natural labeling that can be used for nearoptimal routing with very small routing tables. We provide experimental results for various topologies that illustrate the superior performance of our approximation algorithms over previous identifying code heuristics. I.
Identifying Codes and the Set Cover Problem
, 2006
"... We consider the problem of finding a minimum identifying code in a graph, i.e., a designated set of vertices whose neighborhoods uniquely overlap at any vertex on the graph. This identifying code problem was initially introduced in 1998 and has been since fundamentally connected to a wide range of a ..."
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We consider the problem of finding a minimum identifying code in a graph, i.e., a designated set of vertices whose neighborhoods uniquely overlap at any vertex on the graph. This identifying code problem was initially introduced in 1998 and has been since fundamentally connected to a wide range of applications, including fault diagnosis, location detection, environmental monitoring, and connections to information theory, superimposed codes, and tilings. Though this problem is NPcomplete, its known reduction is from 3SAT and does not readily yield an approximation algorithm. In this paper we show that the identifying code problem is computationally equivalent to the set cover problem and present a Θ(log n)approximation algorithm based on the greedy approach for set cover; we further show that, subject to reasonable assumptions, no polynomialtime approximation algorithm can do better. Finally, we show that a generalization of the identifying codes problem, for which no complexity results were known thusfar, is NPhard. 1
Identifying codes and covering problems
 IEEE Transaction on Information Theory
, 2008
"... The identifying code problem for a given graph involves finding a minimum set of vertices whose neighborhoods uniquely overlap at any given graph vertex. Initially introduced in 1998, this problem has demonstrated its fundamental nature through a wide variety of applications, such as fault diagnosis ..."
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Cited by 11 (4 self)
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The identifying code problem for a given graph involves finding a minimum set of vertices whose neighborhoods uniquely overlap at any given graph vertex. Initially introduced in 1998, this problem has demonstrated its fundamental nature through a wide variety of applications, such as fault diagnosis, location detection, and environmental monitoring, in addition to deep connections to information theory, superimposed and covering codes, and tilings. This work establishes efficient reductions between the identifying code problem and the wellknown setcovering problem, resulting in a tight hardness of approximation result and novel, provably tight polynomialtime approximations. The main results are also extended to rrobust identifying codes and analogous set (2r + 1)multicover problems. Finally, empirical support is provided for the effectiveness of the proposed approximations, including good constructions for wellknown topologies such as infinite twodimensional grids.
Graph Theoretic Measures for Identifying Effective Blockers of Spreading Processes in Dynamic Networks
"... Many processes within a society, such as diseases, opinions, information, or behavior, spread through a network of personal interactions. Whether a phenomenon is going to spread widely within a population depends ..."
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Many processes within a society, such as diseases, opinions, information, or behavior, spread through a network of personal interactions. Whether a phenomenon is going to spread widely within a population depends
Localization and identification in networks using robust identifying codes,” Information Theory and Application Workshop
, 2008
"... Abstract — Many practical problems in networks such as fault detection and diagnosis, location detection, environmental monitoring, etc, require to identify specific nodes or links based on a set of observations, which size is a subject of optimization. In this paper we focus on a combinatorial app ..."
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Abstract — Many practical problems in networks such as fault detection and diagnosis, location detection, environmental monitoring, etc, require to identify specific nodes or links based on a set of observations, which size is a subject of optimization. In this paper we focus on a combinatorial approach to these problems, which is closely related to coding techniques, and specifically to identifying codes. The identifying code problem for a given graph involves finding a minimum set of vertices whose neighborhoods uniquely overlap at any given graph vertex. In this paper we show efficient reductions between the identifying code problem and wellknown covering problems, resulting in a tight hardness of approximation result and provable good centralized and distributed approximations. We further provide empirical and theoretical results on identifying codes in random networks and efficient constructions of these codes in infinite grids. I.
Connected Identifying Codes for Sensor Network Monitoring
"... Abstract—Identifying codes have been proposed as an abstraction for implementing monitoring tasks such as indoor localization using wireless sensor networks. In this approach, sensors ’ radio coverage overlaps in unique ways over each identifiable region, according to the codewords of an identifying ..."
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Abstract—Identifying codes have been proposed as an abstraction for implementing monitoring tasks such as indoor localization using wireless sensor networks. In this approach, sensors ’ radio coverage overlaps in unique ways over each identifiable region, according to the codewords of an identifying code. While connectivity of the underlying identifying code is necessary for routing data to a sink, existing algorithms that produce identifying codes do not guarantee such a property. As such, we propose a novel polynomialtime algorithm called ConnectID that transforms any identifying code into a connected version that is also an identifying code and is provably at most twice the size of the original. We evaluate the performance of ConnectID on various random graphs, and our simulations show that the connected codes generated are actually at most 25% larger than their nonconnected counterparts. Index Terms—Localization, graph theory, approximation algorithms. I.
Connected Identifying Codes
, 2011
"... We consider the problem of generating a connected identifying code for an arbitrary graph. After a brief motivation, we show that the decision problem regarding the existence of such a code is NPcomplete, and we propose a novel polynomialtime approximation ConnectID that transforms any identifyin ..."
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We consider the problem of generating a connected identifying code for an arbitrary graph. After a brief motivation, we show that the decision problem regarding the existence of such a code is NPcomplete, and we propose a novel polynomialtime approximation ConnectID that transforms any identifying code into a connected version of at most twice the size, thus leading to an asymptotically optimal approximation bound. When the input identifying code to ConnectID is robust to graph distortions, we show that the size of the resulting connected code is related to the best errorcorrecting code of a given minimum distance, permitting the use of known coding bounds. In addition, we show that the size of the input and output codes converge for increasing robustness, meaning that highly robust identifying codes are almost connected. Finally, we evaluate the performance of ConnectID on various random graphs. Simulations for ErdősRényi random graphs show that the connected codes generated are actually at most 25 % larger than their unconnected counterparts, while simulations with robust input identifying codes confirm that robustness often provides connectivity for free.
IIICXT: Collaborative Research: Computational Methods for Understanding Social Interactions in Animal Populations
"... Which individual will animals follow when moving away from a predator? When one of the animals leaves the population, will it affect the entire social structure? Which females are likely to form a harem? Will a group of animals move together or disperse when their territory is destroyed? For animals ..."
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Which individual will animals follow when moving away from a predator? When one of the animals leaves the population, will it affect the entire social structure? Which females are likely to form a harem? Will a group of animals move together or disperse when their territory is destroyed? For animals that live in groups, social interactions and structure play a key role in their response to
The Paradoxical Nature of Locating Sensors in Paths and Cycles: The Case of 2Identifying Codes
, 2006
"... For a graph G and a set D ⊆ V (G), define Nr[x] = {xi ∈ V (G) : d(x, xi) ≤ r} (where d(x, y) is graph theoretic distance) and Dr(x) = Nr[x] ∩ D. D is known as an ridentifyingcode if for every vertex x, Dr(x) = ∅, and for every pair of vertices x and y, x = y ⇒ Dr(x) = Dr(y). The various appli ..."
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For a graph G and a set D ⊆ V (G), define Nr[x] = {xi ∈ V (G) : d(x, xi) ≤ r} (where d(x, y) is graph theoretic distance) and Dr(x) = Nr[x] ∩ D. D is known as an ridentifyingcode if for every vertex x, Dr(x) = ∅, and for every pair of vertices x and y, x = y ⇒ Dr(x) = Dr(y). The various applications of these codes include attack sensor placement in networks and fault detection/localization in multiprocessor or distributed systems. In [2] and [16], partial results about the minimum size of D for ridentifying codes are given for paths and cycles and complete closed form solutions are presented for the case r = 1, based in part on [14]. We provide complete solutions for the case r = 2 as well as present our own solutions (verifying earlier results) to the r = 1 case. We use these closed form solutions to illustrate some surprisingly counterintuitive behavior that arises when the length of the path or cycle or the value of r varies.