In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

There are many complex combinatorial problems which involve searching for an undirected graph satisfying given constraints. Such problems are often highly challenging because of the large number of isomorphic representations of their solutions. This paper introduces effective and compact, complete symmetry breaking constraints for small graph search. Enumerating with these symmetry breaks generates all and only non-isomorphic solutions. For small search problems, with up to 10 vertices, we compute instance independent symmetry breaking constraints. For small search problems with a larger number of vertices we demonstrate the computation of instance dependent constraints which are complete. We illustrate the application of complete symmetry breaking constraints to extend two known sequences from the OEIS related to graph enumeration.
Breaking Symmetries in Graph Search with Canonizing Sets

Standard belief change assumes an underlying logic containing full classical propositional logic. However, there are good reasons for considering belief change in less expressive logics as well. In this paper we build on recent investigations by Delgrande on contraction for Horn logic. We show that the standard basic form of contraction, partial meet, is too strong in the Horn case. This result stands in contrast to Delgrande's conjecture that orderly maxichoice is the appropriate form of contraction for Horn logic. We then define a more appropriate notion of basic contraction for the Horn case, influenced by the convexity property holding for full propositional logic and which we refer to as infra contraction. The main contribution of this work is a result which shows that the construction method for Horn contraction for belief sets based on our infra remainder sets corresponds exactly to Hansson's classical kernel contraction for belief sets, when restricted to Horn logic. This result is obtained via a detour through contraction for belief bases. We prove that kernel contraction for belief bases produces precisely the same results as the belief base version of infra contraction. The use of belief bases to obtain this result provides evidence for the conjecture that Horn belief change is best viewed as a 'hybrid' version of belief set change and belief base change. One of the consequences of the link with base contraction is the provision of a representation result for Horn contraction for belief sets in which a version of the Core-retainment postulate features.
On the Link between Partial Meet, Kernel, and Infra Contraction and its Application to Horn Logic

An increasing amount of analytics is performed on data that is procured in a real-time fashion to make real-time decisions. Such tasks include simple reporting on streams to sophisticated model building. However, the practicality of such analyses are impeded in several domains because they are faced with a fundamental trade-off between data collection latency and analysis accuracy. In this paper, we study this trade-off in the context of a specific domain, Cellular Radio Access Networks (RAN). Our choice of this domain is influenced by its commonalities with several other domains that produce real-time data, our access to a large live dataset, and their real-time nature and dimensionality which makes it a natural fit for a popular analysis technique, machine learning (ML). We find that the latency accuracy trade-off can be resolved using two broad, general techniques: intelligent data grouping and task formulations that leverage domain characteristics. Based on this, we present CellScope, a system that addresses this challenge by applying a domain specific formulation and application of Multi-task Learning (MTL) to RAN performance analysis. It achieves this goal using three techniques: feature engineering to transform raw data into effective features, a PCA inspired similarity metric to group data from geographically nearby base stations sharing performance commonalities, and a hybrid online-offline model for efficient model updates. Our evaluation of CellScope shows that its accuracy improvements over direct application of ML range from 2.5 to 4.4 while reducing the model update overhead by up to 4.8. We have also used CellScope to analyze a live LTE consisting of over 2 million subscribers for a period of over 10 months, where it uncovered several problems and insights, some of them previously unknown.
Fast and Accurate Performance Analysis of LTE Radio Access Networks