Reduced Ordered Binary Decision Diagram (ROBDD) is the most popular data structure for efficient representation and manipulation of Boolean functions. However, this novel data structure is very sensitive to the variable ordering, i.e. the size may vary from linear to exponential. Since finding the optimal variable ordering is an NP-complete problem and the best known algorithm has exponential r...

In many applications like verification or combinatorial optimization, OBDDs (ordered binary decision diagrams) are used as a representation or data structure for Boolean functions. Efficient algorithms exist for the important operations on OBDDs, and many functions can be represented in reasonable size if a good variable ordering is chosen. In general, it is NP-hard to compute optimal or near-o...

Word-Level Decision Diagrams (WLDDs), like *BMDs and K*BMDs, have recently been introduced as a data structure for veriication. The size of WLDDs largely depends on the chosen variable ordering , i.e. the ordering in which variables are encountered , and on the decompositions carried out in each node. In this paper we present a framework for dynamic minimization of WLDDs. We discuss the dii-cul...

Variable ordering for BDDs has been extensively investigated. Recently, sampling based ordering techniques have been proposed to overcome problems with structure based static ordering methods and sifting based dynamic reordering techniques. However, existing sampling techniques can lead to an unacceptably large deviation in the size of the final BDD. In this paper, we propose a sampling techniq...

In vector optimization with a variable ordering structure the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications it was started to develop a comprehensive theory for these vector optimization problems. Thereby also notions of proper efficiency were generalized to variable ordering structu...

This paper introduces a new kind of propositional encoding for reasoning about partial orders. The symbols in an unspecified partial order are viewed as variables which take integer values and are interpreted as indices in the order. For a partial order statement on n symbols each index is represented in dlog2 ne propositional variables and partial order constraints between symbols are modeled ...

Decision Diagrams (DDs) are often used in VLSI CAD systems for efficient representation and manipulation of Boolean functions. The most popular data structure are reduced ordered Binary Decision Diagrams (BDDs) [Bry86,DB98], also called ROBDDs. They are part of almost all courses on function representation in VLSI CAD education. BDDs are very sensitive to the variable ordering, i.e. the size of...

this paper is a research on the ordering planning of a supply chain with one supplier, multi buyer and multi deteriorating items. items have fixed life time and expire dates. the ordering period is taken as variable and must be computed the proposed models. the problem is studied via two different approaches the first is the joint replenishment, based on the hwang and chew's model [3] and ...