30701744
Single change covering designs
A single-change covering designSC (v, k, b) on av-setV is a sequence ofb k-sets (blocks) onV which together cover every pair of elements ofV at least once, such that two successive blocks havek−1 elements in common. It is desirable to minimizeb. Some constructions and lower bounds forb are given.
36095353
Extremal Regular Graphs with Prescribed Odd Girth
The odd girth of a graph G gives the length of a shortest odd cycle in G. Let ?(k, g) denote the smallest n such that there exists a k-regular graph of order n and odd girth g. It is known that ?(k, g) ? kg/2 and that ?(k, g) = kg/2 if k is even. The exact values of ?(k, g) are also known if k = 3 or g = 5. Let ?x?e denote the smallest even integer no less than x, ?(g) = (?1)g ? 1/2, and s(k) = min {p + q | k = pq, where p and q are both positive integers}. It is proved that if k ? 5 and g ? 7 are both odd, then formula] with the exception that ?(5, 7) = 20.
37771428
Some New Bounds on Single-Change Covering Designs
A single-change covering design SCD(v, k, b) on a c-set V is a sequence of b k-sets (blocks) on V that together cover every pair of elements of V at least once, such that two successive blocks have k-1 elements in common. Let f(v,k) denote the smallest b for which there exists an SCD(v, k, b). Some new upper and lower bounds for f(v,k) are given.
41994930
On the partition and coloring of a graph by cliques
Abstract We first introduce the concept of the k -chromatic index of a graph, and then discuss some of its properties. A characterization of the clique partition number of the graph G ⋁ K c m for any simple graph G is given, together with some of its applications. Graphs with maximum valency 3 are also considered.
38503566
Pseudo-one-factorizations of regular graphs of odd order - II. products of graphs
Abstract We study the pseudo-one-factorization of regular graphs of odd order. It is shown that some classes of products (including composition and cartesian product) of graphs are pseudo-one- factorizable. In particular, we prove that a complete regular t -partite graph of odd order has this property.
13992541
Enhancing relevance scoring with chronological term rank
We introduce a new relevance scoring technique that enhances existing relevance scoring schemes with term position information. This technique uses chronological term rank (CTR) which captures the positions of terms as they occur in the sequence of words in a document. CTR is both conceptually and computationally simple when compared to other approaches that use document structure information, such as term proximity, term order and document features. CTR works well when paired with Okapi BM25. We evaluate the performance of various combinations of CTR with Okapi BM25 in order to identify the most effective formula. We then compare the performance of the selected approach against the performance of existing methods such as Okapi BM25, pivoted length normalization and language models. Significant improvements are seen consistently across a variety of TREC data and topic sets, measured by the major retrieval performance metrics. This seems to be the first use of this statistic for relevance scoring. There is likely to be greater retrieval improvements possible using chronological term rank enhanced methods in future work.
5343000
Constraints in Nonmonotonic Reasoning
We report on the use of constraints to govern partial models of rst-order logic. These models are constructed using systems of default rules, as in the default logic of Reiter, but where Reiter's rules build logical theories, our rules build models. Our approach takes advantage of domain-theoretic notions. A system of default rules is a straightforward generalization of Scott's notion of information system, already an important tool in understanding constraint programming. We apply our theory to resolve an anomaly due to Poole on the meaning of defaults. Using nite default models, constraints, and a constructive, rule-based notion of conditional degree of belief, we give a probabilistic way of interpreting default statements.
42909091
Combining path relinking and genetic algorithms for the multiple-level warehouse layout problem
Path relinking is a method to generate new solution by exploring trajectories that connect high quality solutions. In this paper, a class of new hybrid heuristics are proposed by combining a genetic algorithm and path relinking and applying these to a multiple-level warehouse layout problem. Parallel and series combinations to integrate crossover and mutation operations of a genetic algorithm with path relinking are investigated. We proposed position and sequence based path relinking methods to connect two solutions, which are either elites or ones selected randomly. Extensive experiments are carried out to compare the performance of the new heuristics.
43741261
Parallel Product of Event Structures
Event structures were introduced by Nielsen, Plotkin and Winskel [5] as a model for computational processes. These were essentially sets of events with relations expressing causal dependence and conflicts between them. These structures, also called prime event structures, were shown to be connected both with a class of acyclic Petri nets (called by the authors occurrence nets) and with a class of domains (finitary prime algebraic coherent domains). Though a very pleasant model of computation, prime event structures can lead to tedious definitions for more sophisticated constructions such as parallel product or exponentiation. In subsequent papers [8,9], Winskel introduced a more general class of event structures called stable event structures, for which such constructions are defined categorically. Although stable event structures themselves are slightly more complicated than prime event structures, constructions on them can be defined in an elegant way. In general, category theory has proven very useful for computer science. When constructions are formulated in categorical terms, not only can the required universal properties provide some guideline in the definitions, the associated morphisms may contain suggestions of computational interest as well. Moving to more general structures, however, can sometimes shield the intuitions about the model. In the case of stable event structures, the causality relation on events is not explicitly given, but is derived from an enabling relation on events. This makes such event structures a little hard to visualize, and one may wonder whether a more manageable notion could be devised. Moreover, unlike prime event structures, it is not clear if stable event structures correspond to a class of Petri nets, in the sense of [5]. Flow event structures were proposed in [2] as an intermediate between prime event structures and stable event structures, suitable both for graphical representation and for an easy definition of process operators. Among these operators the critical one is the
15701939
Disjunctive Systems and L-Domains
Disjunctive systems are a representation of L-domains. They use sequents of the form X⊢Y, with X finite and Y pairwise disjoint. We show that for any disjunctive system, its elements ordered by inclusion form an L-domain. On the other hand, via the notion of stable neighborhoods, every L-domain can be represented as a disjunctive system. More generally, we have a categorical equivalence between the category of disjunctive systems and the category of L-domains. A natural classification of domains is obtained in terms of the style of the entailment: when ¦X¦=2 and ¦Y¦=0 disjunctive systems determine coherent spaces; when ¦Y¦≤1 they represent Scott domains; when either ¦X¦=1 or ¦Y¦=0 the associated cpos are distributive Scott domains; and finally, without any restriction, disjunctive systems give rise to L-domains.