New application of failure functions

Several algorithms are presented whose operations are governed by a principle of failure functions: when searching for an extremal value within a sequence, it suffices to consider only the subsequence of items each of which is the first possible improvement of its predecessor. These algorithms are more efficient than their more traditional counterparts

Average case analysis of marking algorithms

The Lindstrom marking algorithm uses bounded workspace. Its time complexity is O(n^2) in all cases, but it has been assumed that the average case time complexity O(n lg n). It is proven that the average case time complexity is H(n^2). Similarly, the average size of the Wegbreit bit stack is shown to be H(n)

The set LCS problem

An efficient algorithm is presented that solves a generalization of the Longest Common Subsequence problem, in which one of the two input strings contains sets of symbols which may be permuted. This problem arises from a music application

Self-organizing search lists using probabilistic back-pointers

A class of algorithms is given for maintaining self-organizing sequential search lists, where the only permutation applied is to move the accessed record of each search some distance towards the front of the list. During searches, these algorithms retain a back-pointer to a previously probed record in order to determine the destination of the accessed record's eventual move. The back-pointer does not traverse the list, but rather it is advanced occationally to point to the record just probed by the search algorithm. This avoids the cost of a second traversal through a significant portion of the list, which may be a significant savings when each record access may require a new page to be brought into primary memory. Probabilistic functions for deciding when to advance the pointer are presented and analyzed. These functions demonstrate average case complexities of measures such as asymptotic cost and convergence similar to some of the more common list update algorithms in the literature. In cases where the accessed record is moved forward a distance proportional to the distance to the front of the list, the use of these functions may save up to 50% of the time required for permuting the list

Subtree weight ratios for optimal binary search trees

For an optimal binary search tree T with a subtree S(d) at a distance d from the root of T, we study the ratio of the weight of S(d) to the weight of T. The maximum possible value, which we call ρ(d), of the ratio of weights, is found to have an upper bound of 2/F_d+3 where F_i is the ith Fibonacci number. For d = 1, 2, 3, and 4, the bound is shown to be tight. For larger d, the Fibonacci bound gives ρ(d) = O(ϕ^d) where ϕ ~ .61803 is the golden ratio. By giving a particular set of optimal trees, we prove ρ(d) = Ω((.58578 ... )^d), and believe a similar proof follows for ρ(d) = Ω((.60179 ... )^d). If we include frequencies for unsuccessful searches in the optimal binary search trees, the Fibonacci bound is found to be tight

Cyclic creep and fatigue of TD-NiCr (thoria-dispersion-strengthened nickel-chromium), TD-Ni, and NiCr sheet at 1200 C

The resistance of thin TD-NiCr sheet to cyclic deformation was compared with that of TD-Ni and a conventional nickel-chromium alloy. Strains were determined by a calibration technique which combines room-temperature strain gage and deflection measurements with high-temperature deflection measurements. Analyses of the cyclic tests using measured tensile and creep-rupture data indicated that the TD-NiCr and NiCr alloy specimens failed by a cyclic creep mechanism. The TD-Ni specimens, on the other hand, failed by a fatigue mechanism

The least weight subsequence problem

The least weight subsequence (LWS) problem is introduced, and is shown to be equivalent to the classic minimum path problem for directed graphs. A special case of the LWS problem is shown to be solvable in O(n log n) time generally and, for certain weight functions, in linear time. A number of applications are given, including an optimum paragraph formation problem and the problem of finding a minimum height B-tree, whose solutions realize improvement in asymptotic time complexity

Motion of condensates in non-Markovian zero-range dynamics

Condensation transition in a non-Markovian zero-range process is studied in one and higher dimensions. In the mean-field approximation, corresponding to infinite range hopping, the model exhibits condensation with a stationary condensate, as in the Markovian case, but with a modified phase diagram. In the case of nearest-neighbor hopping, the condensate is found to drift by a "slinky" motion from one site to the next. The mechanism of the drift is explored numerically in detail. A modified model with nearest-neighbor hopping which allows exact calculation of the steady state is introduced. The steady state of this model is found to be a product measure, and the condensate is stationary.Comment: 31 pages, 9 figure

Improved Algorithms for Approximate String Matching (Extended Abstract)

The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants of the problem, including comparison of two strings, approximate pattern identification in a string or calculation of the longest common subsequence that two strings share. We designed an output sensitive algorithm solving the edit distance problem between two strings of lengths n and m respectively in time O((s-|n-m|)min(m,n,s)+m+n) and linear space, where s is the edit distance between the two strings. This worst-case time bound sets the quadratic factor of the algorithm independent of the longest string length and improves existing theoretical bounds for this problem. The implementation of our algorithm excels also in practice, especially in cases where the two strings compared differ significantly in length. Source code of our algorithm is available at http://www.cs.miami.edu/\~dimitris/edit_distanceComment: 10 page