Amortized efficiency of list update and paging rules
Communications of the ACM
Information and Computation
Optimal constructions of hybrid algorithms
Journal of Algorithms
On-line choice of on-line algorithms
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Computing the median with uncertainty
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Optimal aggregation algorithms for middleware
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
On computing functions with uncertainty
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Efficient Update Strategies for Geometric Computing with Uncertainty
Theory of Computing Systems
Instance-Optimal Geometric Algorithms
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Competitive query strategies for minimising the ply of the potential locations of moving points
Proceedings of the twenty-ninth annual symposium on Computational geometry
Unions of onions: preprocessing imprecise points for fast onion layer decomposition
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
| Hi-index | 0.00 |
We study the complexity of one-dimensional extrema testing: given one input number, determine if it is properly contained in the interval spanned by the remaining n input numbers. We assume that each number is given as a finite stream of bits, in decreasing order of significance. Our cost measure, referred to as the leading-input-bits-cost (or LIB-cost for short), for an algorithm solving such a problem is the total number of bits that it needs to consume from its input streams. An input-thrifty algorithm is one that performs favorably with respect to this LIB-cost measure. A fundamental goal in the design of such algorithms is to be more efficient on "easier" input instances, ideally approaching the minimum number of input bits needed to certify the solution, on all orderings of all input instances. In this paper we present an input-thrifty algorithm for extrema-testing that is log-competitive in the following sense: if the best possible algorithm for a particular problem instance, including algorithms that are only required to be correct for presentations of this one instance, has worst-case (over all possible input presentations) LIB-cost c, then our algorithm has worst-case LIB-cost $O(c\lg \min\{c, n\})$. In fact, our algorithm achieves something considerably stronger: if any input sequence (i.e. an arbitrary presentation of an arbitrary input set) can be tested by a monotonic algorithm (an algorithm that preferentially explores lower indexed input streams) with LIB-cost c, then our algorithm has LIB-cost $O(c\lg \min\{c, n\})$. Since, as we demonstrate, the cost profile of any algorithm can be matched by that of a monotonic algorithm, it follows that our algorithm is to within a log factor of optimality at the level of input sequences. We also argue that this log factor cannot be reduced, even for algorithms that are only required to be correct on input sequences with some fixed intrinsic monotonic LIB-cost c. The extrema testing problem can be cast as a kind of list-searching problem, and our algorithm employs a variation of a technique called hyperbolic sweep that was introduced in that context. Viewed in this light, our results can be interpreted as another variant of the well-studied cow-path problem, with applications in the design of hybrid algorithms.