Two Notes on the Computational Complexity of One-Dimensional Sandpiles

Two Notes on the Computational Complexity of One-Dimensional Sandpiles

Computational Complexity of Avalanches in the Kadanoff Two-dimensional Sandpile Model

In this paper we prove that the avalanche problem for Kadanoff sandpile model (KSPM) is P-complete for two-dimensions. Our proof is based on a reduction from the monotone circuit value problem by building logic gates and wires which work with configurations in KSPM. The proof is also related to the known prediction problem for sandpile which is in NC for one-dimensional sandpiles and is P-compl...

Computational Complexity of Avalanches in the Kadanoff Two-dimensional Sandpile Model

In this paper we prove that the avalanche problem for the Kadanoff sandpile model (KSPM) is P-complete for two-dimensions. Our proof is based on a reduction from the monotone circuit value problem by building logic gates and wires which work with configurations in KSPM. The proof is also related to the known prediction problem for sandpile which is in NC for one-dimensional sandpiles and is P-c...

Computational Complexity of the Avalanche Problem on One Dimensional Kadanoff Sandpiles

In this paper we prove that the general avalanche problem AP is in NC for the Kadanoff sandpile model in one dimension, answering an open problem of [2]. Thus adding one more item to the (slowly) growing list of dimension sensitive problems since in higher dimensions the problem is P-complete (for monotone sandpiles).

Image Restoration with Two-Dimensional Adaptive Filter Algorithms

Two-dimensional (TD) adaptive filtering is a technique that can be applied to many image, and signal processing applications. This paper extends the one-dimensional adaptive filter algorithms to TD structures and the novel TD adaptive filters are established. Based on this extension, the TD variable step-size normalized least mean squares (TD-VSS-NLMS), the TD-VSS affine projection algorithms (...