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Optimal computation of probability functions for pedigree analysis.

¹Department of Statistics and Computational Mathematics, Brownlow Hill, Liverpool.

IMA Journal of Mathematics Applied in Medicine and Biology

|January 1, 1986

Summary

This study explores optimal peeling sequences, linking them to marriage permutations. Search algorithms like random downhill and annealing were compared to analyze sequence topology.

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Area of Science:

Computational mathematics
Combinatorial optimization
Algorithm analysis

Background:

Optimal peeling sequences are crucial in various computational problems.
Understanding the structure of these sequences is an ongoing challenge.

Purpose of the Study:

To establish a novel correspondence between peeling sequences and marriage permutations.
To compare the efficacy of different search methods for identifying optimal sequences.
To investigate the topological properties of the space of peeling sequences.

Main Methods:

Establishing a mathematical correspondence between peeling sequences and permutations of marriages.
Implementing and comparing random downhill search and the annealing algorithm.
Topological analysis of the solution space.

Main Results:

A clear link was found between optimal peeling sequences and specific marriage permutations.
The annealing algorithm demonstrated superior performance over random downhill search in finding optimal sequences.
The topology of the peeling sequence space exhibits complex, multi-dimensional characteristics.

Conclusions:

The marriage permutation model provides a new framework for understanding optimal peeling sequences.
Algorithmic approaches significantly impact the efficiency of finding optimal solutions.
Further topological studies may reveal deeper insights into sequence optimization.

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