Given a finite set of closed rational points of affine space over a field, we give a Gröbner basis for the lexicographic ordering of the ideal of polynomials which vanish at all given points. Our method is an alternative to the Buchberger–Möller algorithm, but in contrast to that, we determine the set of leading terms of the ideal without solving any linear equation but by induction over the di...

Abstract. In this note we give a numerical expression for the bandwidth bw(P d n) of the dproduct of a path with n edges, P d n . We prove that this bandwidth is given by the sum of certain multinomial coefficients. We also show that bw(P d n) is bounded above and below by the largest coefficient in the expansion of (1 + x + · · ·+ x), with k ∈ {d, d + 1}. Moreover, we compare the asymptotic be...

We prove that lexicographic breadthrst search is P-complete and that a variant of the parallel perfect elimination procedure of P. Klein [24] is powerful enough to compute a semi-perfect elimination ordering in sense of [23] if certain induced subgraphs are forbidden. We present an e cient parallel breadth rst search algorithm for all graphs which have no cycle of length greater four and no hou...

Integer programming has many applications in economics and management. Applying lexicographic ordering and linear programming, we develop an iterative method for integer programming, which defines an increasing mapping from a finite lattice into itself. Given any polytope, within a finite number of iterations, the method either yields an integer point in the polytope or proves no such point exi...

We discuss a parallelization scheme for SSOR precondition-ing of Krylov subspace solvers as applied in lattice gauge theory computations. Our preconditioner is based on a locally lexicographic ordering of the lattice points leading to a parallelism adapted to the parallel system's size. By exploitation of thèEisenstat-trick' within the bi-conjugate gradient stabilized iterative solver, we achie...

We present a CAT (constant amortized time) algorithm for generating those partitions of n that are in the ice pile model IPMk(n), a generalization of the sand pile model SPM(n). More precisely, for any fixed integer k, we show that the negative lexicographic ordering naturally identifies a tree structure on the lattice IPMk(n): this lets us design an algorithm which generates all the ice piles ...

We introduce an approach to designing filtering algorithms by derivation from finite automata operating on constraint signatures. We illustrate this approach in two case studies of constraints on vectors of variables. This has enabled us to derive an incremental filtering algorithm that runs in O(n) plus amortized O(1) time per propagation event for the lexicographic ordering constraint over tw...

SkipNet is a scalable overlay network that provides controlled data placement and routing locality guarantees by organizing data primarily by lexicographic ordering of string names. A key side-effect of the SkipNet design is that all nodes from an organization form one or a few contiguous overlay segments. When an entire organization disconnects from the rest of the system, repair of only a few...

Let Ln,t be the set of all n-vertex connected graphs with clique number t (2 ≤ t ≤ n). For nvertex connected graphs with given clique number, lexicographic ordering by spectral moments (S-order) is discussed in this paper. The first ∑⌊(n−t−1)/3⌋ i=1 (n − t − 3i) + 1 graphs with 3 ≤ t ≤ n − 4, and the last few graphs, in the Sorder, among Ln,t are characterized. In addition, all graphs in Ln,n ∪...

The most general unifier (MGU) of a pair of terms can be specified by four axioms. In this paper we generalize the standard presentation of the axioms to specify the MGU of a list of equational constraints and we formally verify that the unification algorithm satisfies the axioms. Our constraints are equalities between terms in a language of simple types. We model substitutions as finite maps f...