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Adaptive Content Search Through Comparisons
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2011
"... We study the problem of navigating through a database of similar objects using comparisons. This problem is known to be strongly related to the smallworld network design problem. However, contrary to prior work, which focuses on cases where objects in the database are equally popular, we consider h ..."
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Cited by 7 (4 self)
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We study the problem of navigating through a database of similar objects using comparisons. This problem is known to be strongly related to the smallworld network design problem. However, contrary to prior work, which focuses on cases where objects in the database are equally popular, we consider here the case where the demand for objects may be heterogeneous. We show that, under heterogeneous demand, the smallworld network design problem is NPhard. Given the above negative result, we propose a novel mechanism for smallworld design and provide an upper bound on its performance under heterogeneous demand. The above mechanism has a natural equivalent in the context of content search through comparisons, and we establish both an upper bound and a lower bound for the performance of this mechanism. These bounds are intuitively appealing, as they depend on the entropy of the demand as well as its doubling constant, a quantity capturing the topology of the set of target objects. Finally, based on these results, we propose an adaptive learning algorithm for content search that meets the performance guarantees achieved by the above mechanisms.
SamplingBased Temporal Logic Path Planning,”
, 2013
"... AbstractIn this paper, we propose a samplingbased motion planning algorithm that finds an infinite path satisfying a Linear Temporal Logic (LTL) formula over a set of properties satisfied by some regions in a given environment. The algorithm has three main features. First, it is incremental, in t ..."
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Cited by 5 (2 self)
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AbstractIn this paper, we propose a samplingbased motion planning algorithm that finds an infinite path satisfying a Linear Temporal Logic (LTL) formula over a set of properties satisfied by some regions in a given environment. The algorithm has three main features. First, it is incremental, in the sense that the procedure for finding a satisfying path at each iteration scales only with the number of new samples generated at that iteration. Second, the underlying graph is sparse, which guarantees the low complexity of the overall method. Third, it is probabilistically complete. Examples illustrating the usefulness and the performance of the method are included.
Matching triangles and basing hardness on an extremely popular conjecture
 STOC'15
, 2015
"... ..."
Algorithms for Offline Tracking of Connected Components in Large Evolving Networks
 PROC OF DNASDM
, 2012
"... Given a large evolving network with time information on its edges, we are interested in how and when its connected components are formed through time. Such information is useful while analyzing the characteristics of the network’s snapshots taken at different time points. This analysis can be used t ..."
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Given a large evolving network with time information on its edges, we are interested in how and when its connected components are formed through time. Such information is useful while analyzing the characteristics of the network’s snapshots taken at different time points. This analysis can be used to answer various queries such as what is the time point where two people are first connected in a professional network, how the scientific communities merged over time in a citation graph, or how conversations are formed and attracted new users in a forum discussion. The sensitivity of such an analysis increases with the number of time points and the cost of the analysis increase along with. We propose efficient algorithms and a compact representation of component structures evolving through time for both directed and undirected networks. For an undirected network with m edges, the time complexity of the algorithm is almost linear with m. For the directed case, the time complexity is O(mlog τ) where τ is the number of snapshots.
1From SmallWorld Networks to ComparisonBased Search
"... Abstract—The problem of content search through comparisons has recently received considerable attention. In short, a user searching for a target object navigates through a database in the following manner: the user is asked to select the object most similar to her target from a small list of objects ..."
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Abstract—The problem of content search through comparisons has recently received considerable attention. In short, a user searching for a target object navigates through a database in the following manner: the user is asked to select the object most similar to her target from a small list of objects. A new object list is then presented to the user based on her earlier selection. This process is repeated until the target is included in the list presented, at which point the search terminates. This problem is known to be strongly related to the smallworld network design problem. However, contrary to prior work, which focuses on cases where objects in the database are equally popular, we consider here the case where the demand for objects may be heterogeneous. We show that, under heterogeneous demand, the smallworld network design problem is NPhard. Given the above negative result, we propose a novel mechanism for smallworld design and provide an upper bound on its performance under heterogeneous demand. The above mechanism has a natural equivalent in the context of content search through comparisons, and we establish both an upper bound and a lower bound for the performance of this mechanism. These bounds are intuitively appealing, as they depend on the entropy of the demand as well as its doubling constant, a quantity capturing the topology of the set of target objects. They also illustrate interesting connections between comparisonbased search to classic results from information theory. Finally, we propose an adaptive learning algorithm for content search that meets the performance guarantees achieved by the above mechanisms. I.
CRPRL2010070002 First Publication Date: Apr. 28th, 2011
"... Abstract. We study the problem of navigating through a database of similar objects using comparisons under heterogeneous demand, a problem closely related to smallworld network design. We show that, under heterogeneous demand, the smallworld network design problem is NPhard. Given the above nega ..."
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Abstract. We study the problem of navigating through a database of similar objects using comparisons under heterogeneous demand, a problem closely related to smallworld network design. We show that, under heterogeneous demand, the smallworld network design problem is NPhard. Given the above negative result, we propose a novel mechanism for smallworld network design and provide an upper bound on its performance under heterogeneous demand. The above mechanism has a natural equivalent in the context of content search through comparisons, again under heterogeneous demand; we use this to establish both upper and lower bounds on content search through comparisons. These bounds are intuitively appealing, as they depend on the entropy of the demand as well as its doubling constant, a quantity capturing the topology of the set of target objects. Finally, we propose an adaptive learning algorithm for content search that meets the performance guarantees achieved by the above mechanisms. 11
A Labeling Approach to Incremental Cycle Detection
"... In the incremental cycle detection problem arcs are added to a directed acyclic graph and the algorithm has to report if the new arc closes a cycle. One seeks to minimize the total time to process the entire sequence of arc insertions, or until a cycle appears. In a recent breakthrough, Bender, Fine ..."
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In the incremental cycle detection problem arcs are added to a directed acyclic graph and the algorithm has to report if the new arc closes a cycle. One seeks to minimize the total time to process the entire sequence of arc insertions, or until a cycle appears. In a recent breakthrough, Bender, Fineman, Gilbert and Tarjan [6] presented two different algorithms, with time complexity O(n2 log n) and O(m ·min{m1/2, n2/3}), respectively. In this paper we introduce a new technique for incremental cycle detection that allows us to obtain both bounds (up to a logarithmic factor). Furthermore, our approach seems more amiable for distributed implementation.