Volume 18, 1999, No. 2


Execution  models for a massively parallel prolog implementation. Part II

P. Kacsuk

Abstract. The Generalized Dataflow Model is introduced for OR- and pipeline AND-parallel execution of logic programs. A higher level abstraction of the dataflow model called the Logicflow Model is applied  to  implement Prolog on massively parallel distributed memory computers. Properties of the Logicflow Model concerning the logic programming execution scheme are proved in detail. Based on the two execution models the Distributed DataDriven Prolog Abstract Machine (3DPAM) can be defined. It is shown how the instructions of the 3DPAM are derived from the dataflow and logicflow nodes in the case of alternative clauses.

 

bk-complete problems and greediness

R. Szelepcsényi

Abstract. Kintala and Fischer [7] defined the limited nondeterminism hierarchy within NP, the so called b  hierarchy. bk is the class of languages recognized by polynomial time bounded Turing machines that make at most O(logk n) nondeterministic moves, where n is the length of the input.

It has been conjectured that "by restricting the amount of nondeterminism in NP-complete problems, we do not seem to obtain complete problems for bk [4]". We demonstrate that this statement is incorrect under what seems to us to be  the natural interpretation of the term "restricting the amount of nondeterminism". We develop the concept of limited nondeterminism-preserving reductions, and obtain complete problems for bk by restricting the amount of nondeterminism in NP-complete problems. We also discuss the connections between b hierarchy completeness and greedy algorithms; we show that using greediness we can define many complete problems for b.

 

table rounding problem

J. Šíma

Abstract. From time to time, people dealing with accounting are faced with the following table rounding problem. Consider a m x n table with numerical values (e.g., amount of money) in which the last column contains check sums of numbers in particular rows. Similarly, the last row consists of column check sums. A new table is to be produced in which the original numbers, and check sums, are rounded off (e.g. to integers). However, the classical rounding procedure (e.g., rounding fractions smaller than 0.,5 down, otherwise up) can generally violate the validity of sums. Therefore, the possibility to round off the non-integer numbers in the table to adjacent integers (i.e., either up or down independently on their fractions) is explored in order to preserve the check sums. We formulate a necessary and sufficient condition stating when rounding, which is consistent with prescribed (integer) check sums, exists. We also prove that when rounding of check sums is not given as a part of the input and, at the same time, the sums are allowed to be rounded to adjacent integers such rounding always exists. Using maximum flow algorithm the required rounding can be found in both cases in polynomial time O((m + n)3) (provided that it exists). Moreover, rounding with the minimal sum of absolute round-errors is computed within O(mn(m + n)2) time.

 

Describing candidate keys by hypergraphs

J. Demetrovics, Vu Duc Thi

Abstract. In the paper algorithms are given that find a minimal transversal and all minimal transversals, respectively, of a hypergraph. Some other computational problems related to the hypergraphs are also studied. As applications, new characterizations of candidate keys of a relational datamodel are given, and new algorithms that find all candidate keys of a relation and a relation scheme, respectively, are presented.

 

Random walks and Brownian notion

T. Castell

Abstract. Papadimitriou proved in [7] that the random walk algorithm is a  polynomial Monte-Carlo algorithm for the satisfiable instances of 2SAT. We present a convergence criterion that generalizes it. We used it to demonstrate that the random walk algorithm is also a polynomial Monte-Carlo algorithm for the satisfiable Horn-renamable instances of SAT without unitary clauses.


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