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Edge Flows in the Complete RandomLengths Network
, 2007
"... Consider the complete nvertex graph whose edgelengths are independent exponentially distributed random variables. Simultaneously for each pair of vertices, put a constant flow between them along the shortest path. Each edge gets some random total flow. In the n → ∞ limit we find explicitly the emp ..."
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Consider the complete nvertex graph whose edgelengths are independent exponentially distributed random variables. Simultaneously for each pair of vertices, put a constant flow between them along the shortest path. Each edge gets some random total flow. In the n → ∞ limit we find explicitly the empirical distribution of these edgeflows, suitably normalized.
On the Average Case Behavior of the Multidimensional Assignment Problem
, 2004
"... The multidimensional assignment problem (MAP) is a combinatorial problem where elements of a variable number of sets must be matched, in order to find a minimum cost solution. The MAP has applications in a large number of areas, and is known to be NPhard. We survey some of the recent work being ..."
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The multidimensional assignment problem (MAP) is a combinatorial problem where elements of a variable number of sets must be matched, in order to find a minimum cost solution. The MAP has applications in a large number of areas, and is known to be NPhard. We survey some of the recent work being done in the determination of the asymptotic value of optimal solutions to the MAP, when costs are drawn from a known distribution (e.g., exponential, uniform, or normal). Novel results, concerning the average number of local minima for random instances of the MAP for random distributions are discussed. We also present computational experiments with deterministic local and global search algorithms that illustrate the validity of our results.
A sharp threshold for minimum boundeddepth and boundeddiameter spanning trees and Steiner trees in random networks
, 2008
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Notes on random optimization problems
, 2008
"... These notes are under construction. They constitute a combination of what I have said in the lectures, what I will say in future lectures, and what I will not say due to time constraints. Some sections are very brief, and this is generally because they are not yet written. Some of the “problems and ..."
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These notes are under construction. They constitute a combination of what I have said in the lectures, what I will say in future lectures, and what I will not say due to time constraints. Some sections are very brief, and this is generally because they are not yet written. Some of the “problems and exercises” describe things that I am actually going to write down in detail in the text. This is because I have used the problems & exercises section in this way to take short notes of things I should not forget to mention.
K. MEHTA ET AL. 1 Protecting Location Privacy in Sensor Networks Against a Global Eavesdropper
"... Abstract—While many protocols for sensor network security provide confidentiality for the content of messages, contextual information usually remains exposed. Such contextual information can be exploited by an adversary to derive sensitive information such as the locations of monitored objects and d ..."
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Abstract—While many protocols for sensor network security provide confidentiality for the content of messages, contextual information usually remains exposed. Such contextual information can be exploited by an adversary to derive sensitive information such as the locations of monitored objects and data sinks in the field. Attacks on these components can significantly undermine any network application. Existing techniques defend the leakage of location information from a limited adversary who can only observe network traffic in a small region. However, a stronger adversary, the global eavesdropper, is realistic and can defeat these existing techniques. This paper first formalizes the location privacy issues in sensor networks under this strong adversary model and computes a lower bound on the communication overhead needed for achieving a given level of location privacy. The paper then proposes two techniques to provide location privacy to monitored objects (source location privacy) – periodic collection and source simulation – and two techniques to provide location privacy to data sinks (sink location privacy) – sink simulation and backbone flooding. These techniques provide tradeoffs between privacy, communication cost, and latency. Through analysis and simulation, we demonstrate that the proposed techniques are efficient and effective for source and sink location privacy in sensor networks.
AGAINST A GLOBAL EAVESDROPPER
"... To my family and friends who have always been supportive. ..."
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Size and Weight of Shortest Path Trees with Exponential Link Weights
"... We derive the distribution of the number of links and the average weight for the shortest path tree (SPT) rooted at an arbitrary node to m uniformly chosen nodes in the complete graph of size N with i.i.d. exponential link weights. We rely on the fact that the full shortest path tree to all destinat ..."
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We derive the distribution of the number of links and the average weight for the shortest path tree (SPT) rooted at an arbitrary node to m uniformly chosen nodes in the complete graph of size N with i.i.d. exponential link weights. We rely on the fact that the full shortest path tree to all destinations (i.e., m = N − 1) is a uniform recursive tree to derive a recursion for the generating function of the number of links of the SPT, and solve this recursion exactly. The explicit form of the generating function allows us to compute the expectation and variance ofthesizeofthesubtreeforallm. We also obtain exact expressions for the average weight of the subtree. 1
The Gain and Cost of Multicast Routing Trees
"... Abstract — The last several years we witness the proliferation of multimedia applications on Internet. One of the unavoidable techniques to support this type of communication is multicasting. However, even a decade after its initial proposal, multicast is not widely deployed. One reason lies in the ..."
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Abstract — The last several years we witness the proliferation of multimedia applications on Internet. One of the unavoidable techniques to support this type of communication is multicasting. However, even a decade after its initial proposal, multicast is not widely deployed. One reason lies in the lack of a business model. If the gain and the cost of multicast could be predicted, network operators might be encouraged to deploy multicast on a larger scale. In this paper we propose several analytical expressions that could be used to estimate the gain and cost of networklayer multicast. We show that the theoretical model we propose matches simulation and Internet measurement results remarkably well.