In many real world applications, data are organized by coverings, not partitions. Covering-based rough sets have been proposed to cope with this type of data. Covering-based rough set theory is more general than rough set theory, then there is a need to employ sophisticated theories to make it more adaptive to real world application. The covering is one of core concepts in covering-based rough ...

Given a set N with n elements and a family F of subsets, we show how to partition N into k such subsets in 2nnO(1) time. We also consider variations of this problem where the subsets may overlap or are weighted, and we solve the decision, counting, summation, and optimisation versions of these problems. Our algorithms are based on the principle of inclusion–exclusion and the zeta transform. In ...

Given a set S with real-valued members, associated with each member one of two possible types; a multi-partitioning of S is a sequence of the members of S such that if x, y ∈ S have different types and x < y, x precedes y in the multi-partitioning of S. We give two distribution-sensitive algorithms for the set multi-partitioning problem and a matching lower bound in the algebraic decision-tree ...

Embedded zerotree wavelet (EZW) coding, introduced by J. M. Shapiro, is a very eeective and computationally simple technique for image compression. Here we ooer an alternative explanation of the principles of its operation, so that the reasons for its excellent performance can be better understood. These principles are partial ordering by magnitude with a set partitioning sorting algorithm, ord...

Article history: Available online 23 April 2008

JCSE-SPIHT, an algorithm of joint compression and selective encryption based on set partitioning in hierarchical trees (SPIHT), is proposed to achieve image encryption and compression simultaneously. It can protect SPIHT compressed images by only fast scrambling a tiny portion of crucial data during the vailable online 29 March 2014

In the last years mobile terminals diffusion has fostered the development of new audio–visual services. Thus the possibility to employ wireless devices to exchange multimedia informations is becoming real. Beyond these attractive motivations, some critical factors are hidden: the design of wireless terminals, in fact, has to deal with limited power budgets and reduced resources availability. Th...