Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How good is the Warnsdorff's knight's tour heuristic?   Warnsdorffs rule for a knights tour is a heuristic, i.e., it is a rule that
does not produce the desired result all the time. It is a classic example of a
greedy method in that it is based on a series of locally optimal choices. This
note describes an analysis that determines how good the heuristic is on an 8 X
8 chessboard. The order of appearance in a permutation of the eight possible
moves a knight can make determines the path the knight takes. A computer
analysis is done of the 8! permutations of the order of a knights moves in
Warnsdorffs rule on an 8 X 8 chessboard for tours starting on each of the 64
squares. Whenever a tie occurs for moves to vertices that have the lowest
degree, the first of these vertices encountered in the programming loop is
chosen. The number of permutations of the 8! total that yield non-Hamiltonian
paths is tallied. This will be the same value if we consistently choose the
last of these vertices encountered.

31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol