On the Usefulness of Predicates

Motivated by the pervasiveness of strong inapproximability results for Max-CSPs, we introduce a relaxed notion of an approximate solution of a Max-CSP. In this relaxed version, loosely speaking, the algorithm is allowed to replace the constraints of an instance by some other (possibly real-valued) constraints, and then only needs to satisfy as many of the new constraints as possible. To be more precise, we introduce the following notion of a predicate $P$ being \emph{useful} for a (real-valued) objective $Q$: given an almost satisfiable Max-$P$ instance, there is an algorithm that beats a random assignment on the corresponding Max-$Q$ instance applied to the same sets of literals. The standard notion of a nontrivial approximation algorithm for a Max-CSP with predicate $P$ is exactly the same as saying that $P$ is useful for $P$ itself. We say that $P$ is useless if it is not useful for any $Q$. This turns out to be equivalent to the following pseudo-randomness property: given an almost satisfiable instance of Max-$P$ it is hard to find an assignment such that the induced distribution on $k$-bit strings defined by the instance is not essentially uniform. Under the Unique Games Conjecture, we give a complete and simple characterization of useful Max-CSPs defined by a predicate: such a Max-CSP is useless if and only if there is a pairwise independent distribution supported on the satisfying assignments of the predicate. It is natural to also consider the case when no negations are allowed in the CSP instance, and we derive a similar complete characterization (under the UGC) there as well. Finally, we also include some results and examples shedding additional light on the approximability of certain Max-CSPs

Rumfitt on truth-grounds, negation, and vagueness

In The Boundary Stones of Thought, Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project

On the Online Generation of Effective Macro-operators

Macro-operator (“macro”, for short) generation is a well-known technique that is used to speed-up the planning process. Most published work on using macros in automated planning relies on an offline learning phase where training plans, that is, solutions of simple problems, are used to generate the macros. However, there might not always be a place to accommodate training. In this paper we propose OMA, an efficient method for generating useful macros without an offline learning phase, by utilising lessons learnt from existing macro learning techniques. Empirical evaluation with IPC benchmarks demonstrates performance improvement in a range of state-of-the-art planning engines, and provides insights into what macros can be generated without training

Supporting Data mining of large databases by visual feedback queries

In this paper, we describe a query system that provides visual relevance feedback in querying large databases. Our goal is to support the process of data mining by representing as many data items as possible on the display. By arranging and coloring the data items as pixels according to their relevance for the query, the user gets a visual impression of the resulting data set. Using an interactive query interface, the user may change the query dynamically and receives immediate feedback by the visual representation of the resulting data set. Furthermore, by using multiple windows for different parts of a complex query, the user gets visual feedback for each part of the query and, therefore, may easier understand the overall result. Our system allows to represent the largest amount of data that can be visualized on current display technology, provides valuable feedback in querying the database, and allows the user to find results which, otherwise, would remain hidden in the database

Using Visualization to Support Data Mining of Large Existing Databases

In this paper. we present ideas how visualization technology can be used to improve the difficult process of querying very large databases. With our VisDB system, we try to provide visual support not only for the query specification process. but also for evaluating query results and. thereafter, refining the query accordingly. The main idea of our system is to represent as many data items as possible by the pixels of the display device. By arranging and coloring the pixels according to the relevance for the query, the user gets a visual impression of the resulting data set and of its relevance for the query. Using an interactive query interface, the user may change the query dynamically and receives immediate feedback by the visual representation of the resulting data set. By using multiple windows for different parts of the query, the user gets visual feedback for each part of the query and, therefore, may easier understand the overall result. To support complex queries, we introduce the notion of approximate joins which allow the user to find data items that only approximately fulfill join conditions. We also present ideas how our technique may be extended to support the interoperation of heterogeneous databases. Finally, we discuss the performance problems that are caused by interfacing to existing database systems and present ideas to solve these problems by using data structures supporting a multidimensional search of the database