Combinatorial design problems arise in many application areas and are naturally modelled in terms of set variables and constraints. Traditionally, the domain of a set variable is specified by two sets (R,E) and denotes all sets containing R and disjoint from E. This representation has inherent difficulties in handling cardinality and lexicographic constraints so important in combinatorial desig...

Since the first investigations on web graph compression, it has been clear that the ordering of the nodes of the graph has a fundamental influence on the compression rate (usually expressed as the number of bits per link). The author of the LINK database [1], for instance, investigated three different approaches: an extrinsic ordering (URL ordering) and two intrinsic (or coordinate-free) orderi...

Since the first investigations on web graph compression, it has been clear that the ordering of the nodes of the graph has a fundamental influence on the compression rate (usually expressed as the number of bits per link). The authors of the LINK database [2], for instance, investigated three different approaches: an extrinsic ordering (URL ordering) and two intrinsic orderings based on the row...

In this article we introduce the notion of a generalized system of fundamental sequences and we define its associated slow-growing hierarchy. We claim that these concepts are genuinely related to the classification of the complexity—the derivation length— of rewrite systems for which termination is provable by a standard termination ordering. To substantiate this claim, we re-obtain multiple re...

This paper presents a numerically robust algorithm for solving linear complementarity problems (LCPs), and applies it to simulation of frictional contacts of articulated rigid bodies each modeled as a general polygonal object. We first point out two problems of the popular pivot-based LCP solver called Lemke Algorithm and its extension with lexicographic ordering, due to numerical errors especi...

Existing methods of breaking all variable symmetries by adding lexicographic ordering constraints can require a factorial number of constraints. This adds an unacceptable overhead to the solving process. In certain cases, for example when the variables are constrained to take distinct values, a reduction to a linear set of constraints is possible. This paper studies some commonly-occuring famil...

It is known that an ordinal is the order type of the lexicographic ordering of a regular language if and only if it is less than ωω . We design a polynomial time algorithm that constructs, for each well-ordered regular language L with respect to the lexicographic ordering, given by a deterministic finite automaton, the Cantor Normal Form of its order type. It follows that there is a polynomial ...

This paper models collective decision-making scenarios by using a priority-based aggregation procedure, the so-called lexicographic method, in order to represent a form of reliability-based ‘deliberation’. More precisely, it considers agents with a preference ordering over a set of objects and a reliability ordering over the agents themselves, providing a logical framework describing the way in...