Rewrite systems are sets of directed equations used to compute by repeatedly replacing subterms in a given expression by equal terms until a simplest form possible (a normal form) is obtained. If a rewrite system is terminating (i.e., allows no infinite sequence of rewrites), then every expression has a normal form. A variety of orderings, called reduction orderings, have been designed for prov...

We consider the two-bar charts packing problem generalizing strongly NP-hard bin problem. prove that remains even if each chart has at least one bar higher than 1/2. If first (or second) of is 1/2, we show O(n2)-time greedy algorithm with lexicographic ordering constructs a length most OPT+1, where OPT optimum, and present an O(n2.5)-time 4/3 ・ OPT+2/3 in case

Resolving connicts between default rules is a major subtask in performing default reasoning. A declarative way of controlling the resolution of connicts is to assign priorities to default rules, and to prevent connict resolution in ways that violate the priorities. This work extends Reiter's default logic with a priority mechanism that is based on lexicographic comparison. Given a default theor...

Fast and frugal heuristics are well studied models of bounded rationality. Psychological research has proposed the take-the-best heuristic as a successful strategy in decision making with limited resources. Take-thebest searches for a sufficiently good ordering of cues (features) in a task where objects are to be compared lexicographically. We investigate the complexity of the problem of approx...

The algorithm MLS (Maximal Label Search) is a graph search algorithm that generalizes the algorithms Maximum Cardinality Search (MCS), Lexicographic Breadth-First Search (LexBFS), Lexicographic Depth-First Search (LexDFS) and Maximal Neighborhood Search (MNS). On a chordal graph, MLS computes a PEO (perfect elimination ordering) of the graph. We show how the algorithm MLS can be modified to com...

Conflict-free channel assignment is a classic and fundamental problem in wireless ad hoc networks. It seeks an assignment of the fewest channels to a given set of radio nodes with specified transmission ranges without causing either primary collision or secondary collision. It is NP-hard even when all nodes are located in a plane and have the same transmission radii. We observe that a prior ana...

A linear ordering is scattered if it does not contain a copy of the rationals. Hausdorff characterised the class of scattered linear orderings as the least family of linear orderings that includes the class B of well-orderings and reversed well-orderings, and is closed under lexicographic sums with index set in B. More generally, say that a partial ordering is κ-scattered if it does not contain...

Earlier work (Hammond, 1988a, b) on dynamically consistent “consequentialist” behaviour in decision trees was unable to treat zero probability events satisfactorily. Here the rational probability functions considered in Hammond (1994), as well as other non-Archimedean probabilities, are incorporated into decision trees. As before, the consequentialist axioms imply the existence of a preference ...

Constraint propagation algorithms implement logical inference. For efficiency, it is essential to control whether and in what order basic inference steps are taken. We provide a high-level framework that clearly differentiates between information needed for controlling propagation versus that needed for the logical semantics of complex constraints composed from primitive ones. We argue for the ...