On completing latin squares
نویسندگان
چکیده
منابع مشابه
On Completing Latin Squares
We present a ( 2 3 − o(1))-approximation algorithm for the partial latin square extension (PLSE) problem. This improves the current best bound of 1− 1 e due to Gomes, Regis, and Shmoys [5]. We also show that PLSE is APX-hard. We then consider two new and natural variants of PLSE. In the first, there is an added restriction that at most k colors are to be used in the extension; for this problem,...
متن کاملA note on completing latin squares
We give a condition on the spatial distribution of filled cells in a partial Latin square P that is sufficient to ensure completability, regardless of what symbols are used in the filled cells. For example, if P is of the order mr + t, where m, r are positive integers and t ≥ 0, m is odd, and the filled cells of P are contained in the first m+1 2 r × r subsquares along the main diagonal, our co...
متن کاملCompleting partial latin squares: Cropper's question
Hall’s condition is a well-known necessary condition for the existence of a proper coloring of a graph from prescribed lists. Completing a partial latin square is a very special kind of graph list-coloring problem. Cropper’s question was: is Hall’s condition sufficient for the existence of a completion of a partial latin square? The folk belief that the answer must be no is confirmed here, but,...
متن کاملCompleting partial latin squares with prescribed diagonals
This paper deals with completion of partial latin squares L = (lij) of order n with k cyclically generated diagonals (li+t,j+t = lij + t if lij is not empty; with calculations modulo n). There is special emphasis on cyclic completion. Here, we present results for k = 2, . . . , 7 and odd n ≤ 21, and we describe the computational method used (hill-climbing). Noncyclic completion is investigated ...
متن کاملCompleting Partial Latin Squares with Two Prescribed Diagonals
In the present paper we will prove that every partial latin square L = (lij) of odd order n with 2 cyclically generated diagonals (li+t,j+t = lij+t if lij is not empty; with calculations modulo n) can be cyclically completed.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2001
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(00)00282-1