Results 1  10
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19
Connected Sensor Cover: SelfOrganization of Sensor Networks for Efficient Query Execution
 MOBIHOC'03
, 2003
"... Spatial query execution is an essential functionality of a sensor network, where a query gathers sensor data within a specific geographic region. Redundancy within a sensor network can be exploited to rv uce the communication cost incurv1 in execution of such quer ies. Anyr eduction in communicatio ..."
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Cited by 107 (6 self)
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Spatial query execution is an essential functionality of a sensor network, where a query gathers sensor data within a specific geographic region. Redundancy within a sensor network can be exploited to rv uce the communication cost incurv1 in execution of such quer ies. Anyr eduction in communication cost wouldr esult in an e#cient use of the batter y ener gy, which is ver y limited in sensor s. One appr oach to r educe the communication cost of a quer y is to selfor ganize the networ# inr esponse to a quer , into a topology that involves only a small subset of the sensor s su#cient to pr ocess the quer y. The quer y is then executed using only the sensor in the constr ucted topology. In thisar icle, we design and analyze algor thms for such selfor"/0 zation of asensor networ tor educe enerP consumption. In par icular we develop the notion of a connected sensor cover and design a centr alized appr oximation algor thm that constr ucts a topology in ol ing anear optimal connected sensor co er . We pr o e that the size of the const rst ed topology is within an O(log n)factor ofthe optimal size, wher n is the networ size. We also de elop a distr ibuted selfor$1" zationer" on ofour algor thm, and prv ose seer/ optimizations tor educe the communication oer"E1 of the algorithm. Finally, we evaluate the distributed algorithm using simulations and show that our approach results in significant communication cost reduction.
Hardness of Set Cover with Intersection 1
, 2000
"... We consider a restricted version of the general Set Covering problem in which each set in the given set system intersects with any other set in at most 1 element. We show that the Set Covering problem with intersection 1 cannot be approximated within a o(log n) factor in random polynomial time u ..."
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Cited by 14 (0 self)
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We consider a restricted version of the general Set Covering problem in which each set in the given set system intersects with any other set in at most 1 element. We show that the Set Covering problem with intersection 1 cannot be approximated within a o(log n) factor in random polynomial time unless NP ` ZT IME(n ). We also observe that the main challenge in derandomizing this reduction lies in find a hitting set for large volume combinatorial rectangles satisfying certain intersection properties. These properties are not satisfied by current methods of hitting set construction. An example
Concise descriptions of subsets of structured sets
 In PODS
, 2003
"... We study the problem of economical representation of subsets of structured sets, that is, sets equipped with a set cover. Given a structured set U, and a language L whose expressions define subsets of U, the problem of Minimum Description Length in L (LMDL) is: “given a subset V of U, find a shorte ..."
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Cited by 10 (0 self)
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We study the problem of economical representation of subsets of structured sets, that is, sets equipped with a set cover. Given a structured set U, and a language L whose expressions define subsets of U, the problem of Minimum Description Length in L (LMDL) is: “given a subset V of U, find a shortest string in L that defines V ”. We show that the simple set cover is enough to model a number of realistic database structures. We focus on two important families: hierarchical and multidimensional organizations. The former is found in the context of semistructured data such as XML, the latter in the context of statistical and OLAP databases. In the case of general OLAP databases, data organization is a mixture of multidimensionality and hierarchy, which can also be viewed naturally as a structured set. We study the complexity of the LMDL problem in several settings, and provide an efficient algorithm for the hierarchical case. Finally, we illustrate the application of the theory to summarization of large result sets, (multi) query optimization for ROLAP queries, and XML queries. 1.
Epsilon nets and union complexity
 Proc. 25th Annu. Sympos. Comput. Geom
, 2009
"... We consider the following combinatorial problem: given a set of n objects (for example, disks in the plane, triangles), and an integer L ≥ 1, what is the size of the smallest subset of these n objects that covers all points that are in at least L of the objects? This is the classic question about th ..."
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Cited by 8 (1 self)
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We consider the following combinatorial problem: given a set of n objects (for example, disks in the plane, triangles), and an integer L ≥ 1, what is the size of the smallest subset of these n objects that covers all points that are in at least L of the objects? This is the classic question about the size of an L nnet for these objects. It is well known that for fairly general classes of geometric objects the size of an Lnet is n O ( n n log). There are some instances where this general L L bound can be improved, and this improvement is usually due to bounds on the combinatorial complexity (size) of the boundary of the union of these objects. Thus, the boundary of the union of m disks has size O(m), and this translates to an O ( n L) bound on the size of annet for disks. For m fat L n triangles, the size of the union boundary is O(m log log m), and this yields L n nnets of size O ( log log n L L). Improved nets directly translate into an upper bound on the ratio between the optimal integral solution and the optimal fractional solution for the corresponding geometric set cover problem. Thus, for covering k points by disks, this ratio is O(1); and for covering k points by fat triangles, this ratio is O(log log k). This connection to approximation algorithms for geometric set cover is a major motivation for attempting to improve bounds on nets. Our main result is an argument that in some cases yields nets that are smaller than those previously obtained from the size of the union boundary. Thus for fat triangles, for instance, we obtain nets of size O ( n log log log n). We use L this to obtain a randomized polynomial time algorithm that gives an O(log log log k)approximation for the problem of covering k points by the smallest subset of a given set of triangles.
Turning clusters into patterns: Rectanglebased discriminative data description
 IEEE International Conference on Data Mining
, 2006
"... The ultimate goal of data mining is to extract knowledge from massive data. Knowledge is ideally represented as humancomprehensible patterns from which endusers can gain intuitions and insights. Yet not all data mining methods produce such readily understandable knowledge, e.g., most clustering al ..."
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Cited by 7 (3 self)
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The ultimate goal of data mining is to extract knowledge from massive data. Knowledge is ideally represented as humancomprehensible patterns from which endusers can gain intuitions and insights. Yet not all data mining methods produce such readily understandable knowledge, e.g., most clustering algorithms output sets of points as clusters. In this paper, we perform a systematic study of cluster description that generates interpretable patterns from clusters. We introduce and analyze novel description formats leading to more expressive power, motivate and define novel description problems specifying different tradeoffs between interpretability and accuracy. We also present effective heuristic algorithms together with their empirical evaluations. 1.
Hyperrectanglebased discriminative data generalization and applications in data mining
, 2007
"... The ultimate goal of data mining is to extract knowledge from massive data. Knowledge is ideally represented as humancomprehensible patterns from which endusers can gain intuitions and insights. Axisparallel hyperrectangles provide interpretable generalizations for multidimensional data points ..."
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Cited by 5 (2 self)
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The ultimate goal of data mining is to extract knowledge from massive data. Knowledge is ideally represented as humancomprehensible patterns from which endusers can gain intuitions and insights. Axisparallel hyperrectangles provide interpretable generalizations for multidimensional data points with numerical attributes. In this dissertation, we study the fundamental problem of rectanglebased discriminative data generalization in the context of several useful data mining applications: cluster description, rule learning, and Nearest Rectangle classification. Clustering is one of the most important data mining tasks. However, most clustering methods output sets of points as clusters and do not generalize them into interpretable patterns. We perform a systematic study of cluster description, where we propose novel description formats leading to enhanced expressive power and introduce novel description problems specifying different tradeoffs between interpretability and accuracy. We also present efficient heuristic algorithms for the introduced problems in the proposed formats. Ifthen rules are
Rectangle covers revisited computationally
, 2005
"... We consider the problem of covering an orthogonal polygon with a minimum number of axisparallel rectangles from a computational point of view. We propose an integer program which is the first general approach to obtain provably optimal solutions to this wellstudied NPhard problem. It applies to c ..."
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Cited by 3 (0 self)
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We consider the problem of covering an orthogonal polygon with a minimum number of axisparallel rectangles from a computational point of view. We propose an integer program which is the first general approach to obtain provably optimal solutions to this wellstudied NPhard problem. It applies to common variants like covering only the corners or the boundary of the polygon, and also to the weighted case. In experiments it turns out that the linear programming relaxation is extremely tight, and rounding a fractional solution is an immediate high quality heuristic. We obtain excellent experimental results for polygons originating from VLSI design, fax data sheets, black and white images, and for random instances. Making use of the dual linear program, we propose a stronger lower bound on the optimum, namely the cardinality of a fractional stable set. We outline ideas how to make use of this bound in primaldual based algorithms. We give partial results which make us believe that our proposals have a strong potential to settle the main open problem in the area: To find a constant factor approximation algorithm for the rectangle cover problem.
An Approximation Algorithm for Minimum Convex Cover with Logarithmic Performance Guarantee
, 2001
"... The problem Minimum Convex Cover of covering a given polygon with a minimum number of (possibly overlapping) convex polygons is known to be NPhard, even for polygons without holes [3]. We propose a polynomialtime approximation algorithm for this problem for polygons with or without holes that ..."
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Cited by 2 (1 self)
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The problem Minimum Convex Cover of covering a given polygon with a minimum number of (possibly overlapping) convex polygons is known to be NPhard, even for polygons without holes [3]. We propose a polynomialtime approximation algorithm for this problem for polygons with or without holes that achieves an approximation ratio of O(log n), where n is the number of vertices in the input polygon. To obtain this result, we first show that an optimum solution of a restricted version of this problem, where the vertices of the convex polygons may only lie on a certain grid, contains at most three times as many convex polygons as the optimum solution of the unrestricted problem. As a second step, we use dynamic programming to obtain a convex polygon which is maximum with respect to the number of "basic triangles" that are not yet covered by another convex polygon. We obtain a solution that is at most a logarithmic factor o# the optimum by iteratively applying our dynamic programming algorithm. Furthermore, we show that Minimum Convex Cover is APXhard, i.e., there exists a constant #>0 such that no polynomialtime algorithm can achieve an approximation ratio of 1 + #. We obtain this result by analyzing and slightly modifying an already existing reduction [3].
The Summarization of Hierarchical Data with Exceptions
 Master Thesis, UBC, 2004. http://www.cs.ubc.ca/grads/resources/thesis/Nov04/Shaofeng Bu.pdf
, 2004
"... In many applications of OLAP or data warehouse, users need to query data of interest, such as a set of data that satisfies specific properties. A normal answer to such query just enumerates all the interesting cells. This is the most accurate but not the most informative method. Summarizations need ..."
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Cited by 2 (1 self)
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In many applications of OLAP or data warehouse, users need to query data of interest, such as a set of data that satisfies specific properties. A normal answer to such query just enumerates all the interesting cells. This is the most accurate but not the most informative method. Summarizations need to be done in order to return more concise descriptions of these interesting cells to the users. MDL approach has been applied on the hierarchical data to get concise descriptions. However in many cases the descriptions are not concise enough to the users. Another method, GMDL, can generate much shorter descriptions, but the GMDL descriptions are not truly pure. The motivation of our research is to overcome the disadvantages in the above methods. In this thesis, we bring up a methodology that focuses on generating the summarization with exceptions of the hierarchical data. We extend the MDL approach to include some exceptions in the description. The exceptios are some uninteresting cells. The result shows that the description with exceptions is pure, which means that the description only covers “interesting cells”. We call this new approach MDLE, i.e. MDL with exceptions. Our new approach aims to find the shortest description with exceptions to cover all “interesting cells”. Firstly, we study two simple cases that can be solved in polynomial time and we give the algorithms. Secondly, we prove that MDL with exceptions is an NPHard problem in general cases and we propose three heuristics. Finally, we show some experiments that we have done to compare MDLE with MDL and GMDL. The experiment results show that MDLE generates more concise descriptions than MDL and meantime MDLE gets shorter descriptions than GMDL when the whiteratio is low or there are some red cells. ii Contents ii
Energy Efficient and SelfHealing 3Dimensional Sensor Cover”, International Journal of Ad Hoc and Ubiquitous Computing (IJAHUC), 2006 (to appear). Mohamed K. Watfa is an Assistant Professor in the department of Computer Science at the American University
 of the ACM and IEEE. Sesh Commuri is an Associate Professor in the School of Electrical and Computer Engineering at the University of Oklahoma in Norman. He received his Masters degree in Electrical Engineering from the Indian Institute of Technology, Kan
, 1996
"... Wireless sensor networks (WSNs) are a significant technology attracting considerable research attention in recent years. They are being developed for a wide range of civil and military applications, such as object tracking, infrastructure monitoring, habitat sensing, and battlefield surveillance. Th ..."
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Cited by 1 (1 self)
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Wireless sensor networks (WSNs) are a significant technology attracting considerable research attention in recent years. They are being developed for a wide range of civil and military applications, such as object tracking, infrastructure monitoring, habitat sensing, and battlefield surveillance. These networks promise a maintenance free, faulttolerant platform for gathering different kinds of data. One of the key prerequisites for effective and efficient embedded sensor systems is development of low cost, low overhead and energy efficient techniques. Cost sensitivity implies that traditional double and triple redundancies are not adequate solutions for embedded sensor systems due to their high cost and high energyconsumption. For widespread adoption of sensor technology, robustness in the event of abnormal behavior such as a network intrusion, or failures of nodes is critical. In this paper, contrary to existing techniques, the coverage problem in a three dimensional space is rigorously analyzed. In the first case, the problem of determining the minimum number of sensors that guarantee complete coverage is studied. In the second case, given a distribution of sensors, an algorithm to choose a subset of working nodes for full coverage is derived. Due to node deaths or leaves, some uncovered holes are created. We address the problem of the selfhealing sensor network by proposing a backup scheme, where each sensor node has a designated substitute set from the sleeping set of nodes.