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The sparse difference resultant introduced in \citep{gao-2015} is a basicconcept in difference elimination theory.  In this paper, we show that the sparse difference resultant of a genericLaurent transformally essential system can be computed via the sparse resultantof a simple algebraic system arising from the difference system. Moreover, neworder bounds of sparse difference resultant are found. Then we propose anefficient algorithm to compute sparse difference resultant which is thequotient of two determinants whose elements are the coefficients of thepolynomials in the algebraic system.  The complexity of the algorithm is analyzed and experimental results show theefficiency of the algorithm.

New bounds and efficient algorithm for sparse difference resultant