A probabilistic lower bound for checking disjointness of sets
Information Processing Letters
The effect of number of Hamiltonian paths on the complexity of a vertex-coloring problem
SIAM Journal on Computing
On the Optimality of Some Set Algorithms
Journal of the ACM (JACM)
On Finding the Maxima of a Set of Vectors
Journal of the ACM (JACM)
Journal of the ACM (JACM)
A Lower Bound to Finding Convex Hulls
Journal of the ACM (JACM)
On the complexity of computing the measure of ∪[ai,bi]
Communications of the ACM
Probabilistic, nondeterministic, and alternating decision trees (Preliminary Version)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
The impact of synchronous communication on the problem of electing a leader in a ring
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Electing a leader in a synchronous ring
Journal of the ACM (JACM)
A lower bound for integer greatest common divisor computations
Journal of the ACM (JACM)
On the complexity of functions for random access machines
Journal of the ACM (JACM)
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Decision trees: old and new results
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Comparison-based time-space lower bounds for selection
ACM Transactions on Algorithms (TALG)
ALGOSENSORS'10 Proceedings of the 6th international conference on Algorithms for sensor systems, wireless adhoc networks, and autonomous mobile entities
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Combinatorial techniques for extending lower bound results for decision trees to general types of queries are presented. Problems that are defined by simple inequalities between inputs, called order invariant problems, are considered. A decision tree is called k-bounded if each query depends on at most k variables. No further assumptions on the type of queries are made. It is proved that one can replace the queries of any k-bounded decision tree that solves an order-invariant problem over a large enough input domain with k-bounded queries whose outcome depends only on the relative order of the inputs. As a consequence, all existing lower bounds for comparison-based algorithms are valid for general k-bounded decision trees, where k is a constant.An &OHgr;(n log n) lower bound for the element uniqueness problem and several other problems for any k-bounded decision tree, such that k = O(nc) and c n1/2-bounded decision trees of complexity O(n) that solve the element-uniqueness problem. All the lower bounds mentioned above are shown to hold for nondeterministic and probabilistic decision trees as well.