Financial institutions and the collapse of real estate markets

Real property ; Mortgages ; Financial institutions

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

Generation of optimal binary split trees

A binary split tree is a search structure combining features of heaps and binary search trees. Building an optimal binary split tree was originally conjectured to be intractable due to difficulties in applying dynamic programming techniques to the problem. However, two algorithms have recently been published which purportedly generate optimal trees in O(n^5) time, for records with distinct access probabilities. An extension allowing non-distinct access probabilities required exponential time. These algorithms consider a range of values when only a single value is possible, and may select an infeasible value which leads to an incorrect result. A dynamic programming method for determining the correct value is given, resulting in an algorithm which builds an optimal binary split tree in O(n^5) time for non-distinct access probabilities and Θ(n^4) time for distinct access probabilities

Optimal Pebbling in Products of Graphs

We prove a generalization of Graham's Conjecture for optimal pebbling with arbitrary sets of target distributions. We provide bounds on optimal pebbling numbers of products of complete graphs and explicitly find optimal $t$-pebbling numbers for specific such products. We obtain bounds on optimal pebbling numbers of powers of the cycle $C_5$. Finally, we present explicit distributions which provide asymptotic bounds on optimal pebbling numbers of hypercubes.Comment: 28 pages, 1 figur

Constitutional Law—Right to Counsel—Alleged Parole Violator Has Right to Counsel at a Parole Revocation Hearing

People ex rel. Combs v. La Vallee, 29 A.D. 2d 128, 286 N.Y.S.2d 600 (4th Dept. 1968), appeal dismissed, 22 N.Y.2d 857, 293 N.Y.S.2d 117 (1968)