We study the following problem: given a set of keys and access probabilities, find a minimum-cost binary search tree that uses only 2-way comparisons (=, <,≤) at each node. We give the first polynomialtime algorithm when both successful and unsuccessful queries are allowed, settling a long-standing open question. Our algorithm relies on a new structural theorem that proves a conjecture of Spule...

Combinatorial testing applies factor covering arrays [6, 7] to test all t-way combinations of input or configuration state space. In some testing situations, it is not practical to use covering arrays, but any set of tests with n parameters covers at least some proportion of t-way combinations up to t ≤ n. This report describes measures of combinatorial coverage that can be used in evaluating t...

Combinatorial testing applies factor covering arrays [6, 7] to test all t-way combinations of input or configuration state space. In some testing situations, it is not practical to use covering arrays, but any set of tests with n parameters covers at least some proportion of t-way combinations up to t ≤ n. This report describes measures of combinatorial coverage that can be used in evaluating t...

This note introduces a new general conjecture correlating the dimensionality dT of an infinite lattice with N nodes to the asymptotic value of its Wiener Index W(N). In the limit of large N the general asymptotic behavior W(N)≈Ns is proposed, where the exponent s and dT are related by the conjectured formula s=2+1/dT allowing a new definition of dimensionality dW=(s-2)-1. Being related to the t...

In [1] it was shown that there are very effective attacks leading to collisions for the hash function MD4 designed by R. Rivest [3]. A summary of the status of hash functions of the MD4-family with respect to collision-resistence can be found in [2] and [4]. However, attacking the one-wayness of a hash function is a much more demanding challenge, and in case of success it has much more devastat...

We study the problem of minimizing non-linear trace quotient trace(V^TG(V)V)/trace(V^TH(V)V) over Stiefel manifold all n x p matrices with orthonormal columns. Hereby we assume G(V) and H(V) to be symmetric positive definite for V. In this way generalize robust Rayleigh optimization introduced by Bai et al. in article "Robust rayleigh minimization nonlinear eigenvalue problems". show a possible...

optimizing the herbicide dose by the addition of adjuvants is an acceptable way to increase performance and to reduce the risk of side effects from herbicides. therefore, to detect a suitable adjuvant for clodinafop-propargyl against little seed canary grass (phalaris minor retz.). greenhouse experiment were conducted as factorial in completely randomized design with four replications for compa...