Finding maximum degrees in hidden bipartite graphs
Proceedings of the 2010 ACM SIGMOD International Conference on Management of data
Self-improving algorithms for convex hulls
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On finding skylines in external memory
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Orthogonal range searching on the RAM, revisited
Proceedings of the twenty-seventh annual symposium on Computational geometry
Convex hull of imprecise points in o(n log n) time after preprocessing
Proceedings of the twenty-seventh annual symposium on Computational geometry
SIAM Journal on Computing
Exact and approximate algorithms for the most connected vertex problem
ACM Transactions on Database Systems (TODS)
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Self-improving algorithms for coordinate-wise maxima
Proceedings of the twenty-eighth annual symposium on Computational geometry
Worst-Case I/O-Efficient Skyline Algorithms
ACM Transactions on Database Systems (TODS)
Convex hull of points lying on lines in o(nlogn) time after preprocessing
Computational Geometry: Theory and Applications
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We prove the existence of an algorithm $A$ for computing 2-d or 3-dconvex hulls that is optimal for {\em every point set\/} in the following sense: %for every set $S$ of $n$ points and for every algorithm $A'$ in a certain class $\A$, the running time of $A$ on the worst permutation of $S$ for $A$ is at most a constant factor times the running time of $A'$ on the worst permutation of $S$ for $A'$.%In fact, we can establish a stronger property: for every $S$ and $A'$, the running time of $A$ on $S$ is at most a constant factor times the average running time of $A'$ over all permutations of $S$. %We call algorithms satisfying these properties {\em instance-optimal\/} in the {\em order-oblivious\/} and {\em random-order\/} setting.%Such instance-optimal algorithms simultaneously subsume output-sensitive algorithms and distribution-dependent average-case algorithms, and all algorithms that do not take advantage of the order of the input or that assume the input is given in a random order. The class $\A$ under consideration consists of all algorithms in a decision tree model where the tests involve only {\em multilinear\/}functions with a constant number of arguments. %To establish an instance-specific lower bound, we deviate from traditional Ben--Or-style proofs and adopt an interesting adversary argument. %For 2-d convex hulls, we prove that a version of the well known algorithm by Kirkpatrick and Seidel (1986) or Chan, Snoeyink, and Yap(1995) already attains this lower bound. For 3-d convex hulls, we propose a new algorithm. We further obtain instance-optimal results for a few other standard problems in computational geometry, such as maxima in 2-d and 3-d, orthogonal line segment intersection in 2-d, %finding bichromatic $L_\infty$-close pairs in 2-d, off-line orthogonal range searching in 2-d, %off-line dominance reporting in 2-d and 3-d, off-line halfspace range reporting in 2-d and 3-d, and off-line point location in 2-d. The theory we develop also neatly reveals connections to entropy-dependent data structures, and yields as a byproduct new expected-case results, e.g., for on-line orthogonal range counting in 2-d.