17321203
On a Simple, Practical, Optimal, Output-Sensitive Randomized Planar Convex Hull Algorithm
In this paper we present a truly practical and provably optimalO(nlogh) time output-sensitive algorithm for the planar convex hull problem. The basic algorithm is similar to the algorithm presented by2, where the median-finding step is replaced by an approximate median. We analyze two such schemes and show that for both methods, the algorithm runs in expectedO(nlogh) time. We further show that the probability of deviation from expected running time approaches 0 rapidly with increasing values ofnandhfor any input. Our experiments suggest that this algorithm is a practical alternative to the worst-caseO(nlogn) algorithms such as Graham's and is especially faster for small output-sizes. Our approach bears some resemblance to a recent algorithm of13, but our analysis is substantially different.
9302549
Planar Graph Blocking for External Searching

AbstractWe present a new scheme for storing a planar graph in external memory so that any online path can be traversed in an I-O efficient way. Our storage scheme significantly improves the previous results for planar graphs with bounded face size. We also prove an upper bound on I-O efficiency of any storage scheme for well-shaped triangulated meshes. For these meshes, our storage scheme achieves optimal performance.

32334601
Finding an Approximate Median with High Probability in Constant Parallel Time
Given n elements from a totally ordered set we outline a method for choosing an element whose rank is γn for some 0 0.
11169442
Linear Time Algorithms for Clustering Problems in Any Dimensions
We generalize the k-means algorithm presented by the authors [14] and show that the resulting algorithm can solve a larger class of clustering problems that satisfy certain properties (existence of a random sampling procedure and tightness). We prove these properties for the k-median and the discrete k-means clustering problems, resulting in O(2(k/e)O(1)dn) time (1+e)-approximation algorithms for these problems. These are the first algorithms for these problems linear in the size of the input (nd for n points in d dimensions), independent of dimensions in the exponent, assuming k and e to be fixed. A key ingredient of the k-median result is a (1+e)-approximation algorithm for the 1-median problem which has running time O(2(1/e)O(1)d). The previous best known algorithm for this problem had linear running time.
10562059
Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths
We present improved algorithms for maintaining transitive closure and all-pairs shortest paths/distances in a digraph under deletion of edges.(MATH) For the problem of transitive closure, the previous best known algorithms, for achieving O(1) query time, require O(\min(m, \frac{n^3}{m}))$ amortized update time, implying an upper bound of O(n^{\frac{3}{2}})$ on update time per edge-deletion. We present an algorithm that achieves $O(1)$ query time and O(n \log^2n + \frac{n^2}{\sqrt{m}}{\sqrt{\log n}})$ update time per edge-deletion, thus improving the upper bound to O(n^{\frac{4}{3}}\sqrt[3]{\log n})$.(MATH) For the problem of maintaining all-pairs shortest distances in unweighted digraph under deletion of edges, we present an algorithm that requires O(\frac{n^3}{m} \log^2 n)$ amortized update time and answers a distance query in O(1) time. This improves the previous best known update bound by a factor of log n. For maintaining all-pairs shortest paths, we present an algorithm that achieves O(\min(n^{\frac{3}{2}} \sqrt{\log n}, \frac{n^3}{m} \log ^2n))$ amortized update time and reports a shortest path in optimal time (proportional to the length of the path). For the latter problem we improve the worst amortized update time bound by a factor of O(\sqrt{\frac{n}{\log n}})$.(MATH) We also present the first decremental algorithm for maintaining all-pairs (1+ε) approximate shortest paths/distances, for any ε > 0, that achieves a sub-quadratic update time of O(n log2n + \frac{n^2}{\sqrt{\epsilon m}}\sqrt{\log n})$ and optimal query time.Our algorithms are randomized and have one-sided error for query (with probability O(1/nc) for any constant c).
1068367
An Efficient Output-Size Sensitive Parallel Algorithm for Hidden-Surface Removal for Terrains
Abstract. We describe an efficient parallel algorithm for hidden-surface removal for terrain maps. The algorithm runs in O(log 4 n) steps on the CREW PRAM model with a work bound of O((n+k) \polylog ( n)) where n and k are the input and output sizes, respectively. In order to achieve the work bound we use a number of techniques, among which our use of persistent data structures is somewhat novel in the context of parallel algorithms.
16584682
You are what you say: privacy risks of public mentions
In today's data-rich networked world, people express many aspects of their lives online. It is common to segregate different aspects in different places: you might write opinionated rants about movies in your blog under a pseudonym while participating in a forum or web site for scholarly discussion of medical ethics under your real name. However, it may be possible to link these separate identities, because the movies, journal articles, or authors you mention are from a sparse relation space whose properties (e.g., many items related to by only a few users) allow re-identification. This re-identification violates people's intentions to separate aspects of their life and can have negative consequences; it also may allow other privacy violations, such as obtaining a stronger identifier like name and address.This paper examines this general problem in a specific setting: re-identification of users from a public web movie forum in a private movie ratings dataset. We present three major results. First, we develop algorithms that can re-identify a large proportion of public users in a sparse relation space. Second, we evaluate whether private dataset owners can protect user privacy by hiding data; we show that this requires extensive and undesirable changes to the dataset, making it impractical. Third, we evaluate two methods for users in a public forum to protect their own privacy, suppression and misdirection. Suppression doesn't work here either. However, we show that a simple misdirection strategy works well: mention a few popular items that you haven't rated.
1456313
Fast Concurrent Reinforcement Learners
When several agents learn concurrently, the payoff received by an agent is dependent on the behavior of the other agents. As the other agents learn, the reward of one agent becomes non-stationary. This makes learning in multiagent systemsmore difficult than single-agent learning. A few methods, how-ever, are known to guarantee convergence to equilibrium in the limit in such systems. In this paper we experimentally study one such technique, the minimax-Q, in a competitive domain and prove its equivalence with another well-known method for competitive domains. We study the rate of convergence of minimax-Q and investigate possible ways for increasing the same. We also present a variant of the algorithm, minimax-SARSA, and prove its convergence to minimax-Q values under appropriate conditions. Finally we show that this new algorithm performs better than simple minimax-Q in a general-sum domain as well.
123541189
Believing others: Pros and cons
Abstract In open environments there is no central control over agent behaviors. On the contrary, agents in such systems can be assumed to be primarily driven by self interests. Under the assumption that agents remain in the system for significant time periods, or that the agent composition changes only slowly, we have previously presented a prescriptive strategy for promoting and sustaining cooperation among self-interested agents. The adaptive, probabilistic policy we have prescribed promotes reciprocative cooperation that improves both individual and group performance in the long run. In the short run, however, selfish agents could still exploit reciprocative agents. In this paper, we evaluate the hypothesis that the exploitative tendencies of selfish agents can be effectively curbed if reciprocative agents share their “opinions” of other agents. Since the true nature of agents is not known a priori and is learned from experience, believing others can also pose its own hazards. We provide a learned trust-based evaluation function that is shown to resist both individual and concerted deception on the part of selfish agents in a package delivery domain.
12702435
Robustness of reputation-based trust: boolean case
We consider the problem of user agents selecting processor agents to processor tasks. We assume that processor agents are drawn from two populations: high and low-performing processors with different averages but similar variance in performance. For selecting a processor, a user agent queries other user agents for their high/low rating of different processors. We assume that a known percentage of "liar" users, who give inverse estimates of processors. We develop a trust mechanism that determines the number of users to query given a target guarantee threshold likelihood of choosing high-performance processors in the face of such "noisy" reputation mechanisms. We evaluate the robustness of this reputation-based trusting mechanism over varying environmental parameters like percentage of liars, performance difference and variances for high and low-performing agents, learning rates, etc.
8938271
Kernel-Based Reinforcement Learning
We present a kernel-based approach to reinforcement learning that overcomes the stability problems of temporal-difference learning in continuous state-spaces. First, our algorithm converges to a unique solution of an approximate Bellman's equation regardless of its initialization values. Second, the method is consistent in the sense that the resulting policy converges asymptotically to the optimal policy. Parametric value function estimates such as neural networks do not possess this property. Our kernel-based approach also allows us to show that the limiting distribution of the value function estimate is a Gaussian process. This information is useful in studying the bias-variance tradeoff in reinforcement learning. We find that all reinforcement learning approaches to estimating the value function, parametric or non-parametric, are subject to a bias. This bias is typically larger in reinforcement learning than in a comparable regression problem.