2964234
Random Trees and the Analysis of Branch and Bound Procedures
Branch and bound procedures are the most efficient known means for solving many NP-hard problems A special class of branch and bound procedures called relaxation-gutded procedures ig presented. While for some branch and bound procedures a worst-case complexity bound is known, the average case complexity is usually unknown, despite the fact that it may g~ve more useful information about the performance of the algorithm. A random process which generates labeled trees is introduced as a model of the kind of trees that a relaxatlon-gutded procedure generates over random instances of a problem Results concerning the expected time and space complexity of searching these random trees are derived with respect to several search strategies. The best-bound search strategy is shown to be optimal in both time and space. These results are illustrated by data from random traveling salesman instances Evidence ~s presented that the asymmetric traveling salesman problem can be solved exactly in time O(n31n(n)) on the average. Categories and Subject Descnptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumencal Algorithms and Problems, G.2.1 [Discrete Mathematics]: Combinatorics; G.I.6 [Numerical Analysis]. OpUmlzatlon General Terms: Algorithms, Theory Addlttonal
7947888
Constructing Specification Morphisms
Specification morphisms underlie the refinement of algebraic specifications and provide the logical foundations for algorithm and data structure design. We present four techniques for formally, even mechanically, constructing specification morphisms. The first two techniques, verifying a manually constructed signature morphism and composition of specification morphisms are well-known. The remaining two techniques exploit the axioms of the source specification to help infer the translation of sort and function symbols from the source specification. The third, unskolemization, finds the translation of a function symbol by replacing occurrences of it in an axiom by an existentially quantified variable. A constructive proof of the translated axiom yields a witness to the existential that serves as the desired translation of the function symbol. The fourth technique, connections between specifications, allows the transfer of structure from one specification morphism to another. The unskolemization and connection techniques arose as abstractions from the algorithm design tactics implemented in the KIDS program transformation system (Smith (1990)). They suggest a more general approach to providing mechanized support for applying design knowledge expressed axiomatically.
44957593
Toward a Classification Approach to Design
This paper addresses the problem of how to construct refinements of specifications formally and incrementally. The key idea is to use a taxonomy of abstract design concepts, each represented by a design theory An abstract design concept is applied by constructing a specification morphism from its design theory to a requirement specification. Procedures for propagating constraints, computing colimits, and constructing specification morphisms provide computational support for this approach. Although we conjecture that classification generally applies to the incremental application of knowledge represented in a taxonomy of design theories, this paper mainly focuses on algorithm design theories and presents several examples of design by classification.
12681881
Synthesis of Constraint Algorithms
206511487
Composition and refinement of behavioral specifications
This paper presents a mechanizable framework for specifying, developing, and reasoning about complex systems. The framework combines features from algebraic specifications, abstract state machines, and refinement calculus, all couched in a categorical setting. In particular, we show how to extend algebraic specifications to evolving specifications (especs) in such a way that composition and refinement operations extend to capture the dynamics of evolving, adaptive, and self-adaptive software development, while remaining efficiently computable. The framework is partially implemented in the Epoxi system.
17878068
Guarded Transitions in Evolving Specifications
We represent state machines in the category of specifications, where assignment statements correspond exactly to interpretations between theories [7, 8]. However, the guards on an assignment require a special construction. In this paper we raise guards to the same level as assignments by treating each as a distinct category over a shared set of objects. A guarded assignment is represented as a pair of arrows, a guard arrow and an assignment arrow. We give a general construction for combining arrows over a factorization system, and show its specialization to the category of specifications. This construction allows us to define the fine structure of state machine morphisms with respect to guards. Guards define the flow of control in a computation, and how they may be translated under refinement is central to the formal treatment of safety, liveness, concurrency, and determinism.
7534908
Building a hypertextual digital library in the humanities: a case study on London
This paper describes the creation of a new humanities digital library collection: 11,000,000 words and 10,000 images representing books, images and maps on pre-twentieth century London and its environs. The London collection contained far more dense and precise information than the materials from the Greco-Roman world on which we had previously concentrated. The London collection thus allowed us to explore new problems of data structure, manipulation, and visualization. This paper contrasts our model for how humanities digital libraries are best used with the assumptions that underlie many academic digital libraries on the one hand and more literary hypertexts on the other. Since encoding guidelines such as those from the TEI provide collection designers with far more options than any one project can realize, this paper describes what structures we used to organize the collection and why. We particularly emphasize the importance of mining historical authority lists (encyclopedias, gazetteers, etc.) and then generating automatic span-to-span links within the collection.
26954991
Optimally Reliable Graphs for Both Vertex and Edge Failures
218,462. Pink, F. June 9, 1923. Separating by gravity. -Apparatus for separating liquids of different densities such as oil and water comprises a vessel of horizontally elongated form in which, as the mixture flows therethrough, the lighter liquid rises and collects in a part of the vessel, which is provided with a discharge valve actuated by the rise or fall of the level of the heavier liquid. The mixture enters a tank 1, provided with baffles 4, by an inlet 3. The lighter liquid rises between the baffles and flows backward along the top to a collecting- compartment 19, while the heavier liquid is discharged through a rising pipe 25 . The discharge valve 14 for the lighter liquid may be operated by a float 9 which is raised to close the valve by the heavier liquid, but falls and opens the valve when surrounded by the lighter liquid. The float may be directly connected to the valve 14 or may operate a slide valve controlling the supply of pressure fluid to a piston 12 which operates the valve 14. Or the float may control an electric switch to energize a solenoid or actuate a motor for opening and closing the valve 14. Alternatively, the float may be omitted and the compartment 19 provided with electrodes between which a current passes when the electrodes are immersed in impure, water but not when they are immersed in oil; the circuit includes a solenoid or motor for actuating the valve. A relief valve 22 for the discharge of air or oil may be provided. Heating coils 24 may also be provided. The baffles 4 may be mounted on vertical or horizontal pivots, or one part of each baffle may be fixed while another is pivoted. Apparatus is described in which the baffles extend to the top of the tank, and pipes are provided to conduct the lighter liquid from the compartments so formed to the compartment 19. The apparatus may be built into a ship as a part thereof, or the double bottom of a ship may be adapted for use as a separating chamber.
18928754
An improved algorithm to determine lower bounds for the fixed spectrum frequency assignment problem
Frequencies have to be assigned to transmitters whenever a radio network is established or modified. This is ideally done is a way which minimises interference in the network. Lower bounds are necessary to establish the effectiveness of the heuristic algorithms used for this task and to assess the quality of the assignments obtained. 
 
In the fixed spectrum frequency assignment problem the available frequencies are known in advance. The constraints are often binary constraints, specifying the necessary frequency separation between given pairs of transmitters. There may be penalties (or weights) associated with the violation of each constraint; it is then either necessary to minimise the number of constraints violated or, increasingly often, to minimise the sum of the weights associated with violated constraints. 
 
A technique for generating lower bounds for these quantities is presented. This is an evolution of a technique which has recently appeared in the literature. It produces better quality bounds, is in general significantly faster and allows larger problems to be handled.
8267445
Explaining design plans
The paper describes a methodology for generating quality explanations from design plans. In selecting items of information for inclusion in an explanation, the methodology considers the rationales behind the strategic knowledge and object-level knowledge specified in a design plan. Rhetorical structure theory and discourse focus tracking are utilised to determine textual structure, and to maintain discourse coherence and cohesion. Using a simple system of user modelling, it is shown how the methodology flexibly includes consideration of a user's knowledge, thus resulting in more focused and convincing explanations. The methodology is used to investigate follow-up explanations, and the generation of explanations from plans which contain a misconception on the part of the designer.
11953962
Detecting events with date and place information in unstructured text
Digital libraries of historical documents provide a wealth of information about past events, often in unstructured form. Once dates and place names are identified and disambiguated, using methods that can differ by genre, we examine collocations to detect events. Collocations can be ranked by several measures, which vary in effectiveness according to type of events, but the log-likelihood measure (-2 log λ) offers a reasonable balance between frequently and infrequently mentioned events and between larger and smaller spatial and temporal ranges. Significant date-place collocations can be displayed on timelines and maps as an interface to digital libraries. More detailed displays can highlight key names and phrases associated with a given event.