On fractionality of the path packing problem

In this paper, we study fractional multiflows in undirected graphs. A fractional multiflow in a graph G with a node subset T, called terminals, is a collection of weighted paths with ends in T such that the total weights of paths traversing each edge does not exceed 1. Well-known fractional path packing problem consists of maximizing the total weight of paths with ends in a subset S of TxT over all fractional multiflows. Together, G,T and S form a network. A network is an Eulerian network if all nodes in N\T have even degrees. A term "fractionality" was defined for the fractional path packing problem by A. Karzanov as the smallest natural number D so that there exists a solution to the problem that becomes integer-valued when multiplied by D. A. Karzanov has defined the class of Eulerian networks in terms of T and S, outside which D is infinite and proved that whithin this class D can be 1,2 or 4. He conjectured that D should be 1 or 2 for this class of networks. In this paper we prove this conjecture.Comment: 18 pages, 5 figures in .eps format, 2 latex files, main file is kc13.tex Resubmission due to incorrectly specified CS type of the article; no changes to the context have been mad

Necessary and sufficient optimality conditions for scheduling unit time jobs on identical parallel machines

In this paper we characterize optimal schedules for scheduling problems with parallel machines and unit processing times by providing necessary and sufficient conditions of optimality. We show that the optimality conditions for parallel machine scheduling are equivalent to detecting negative cycles in a specially defined graph. For a range of the objective functions, we give an insight into the underlying structure of the graph and specify the simplest types of cycles involved in the optimality conditions. Using our results we demonstrate that the optimality check can be performed by faster algorithms in comparison with existing approaches based on sufficient conditions

On providing semantic alignment and unified access to music library metadata

A variety of digital data sources—including insti- tutional and formal digital libraries, crowd-sourced commu- nity resources, and data feeds provided by media organisa- tions such as the BBC—expose information of musicological interest, describing works, composers, performers, and wider historical and cultural contexts. Aggregated access across such datasets is desirable as these sources provide comple- mentary information on shared real-world entities. Where datasets do not share identifiers, an alignment process is required, but this process is fraught with ambiguity and difficult to automate, whereas manual alignment may be time-consuming and error-prone. We address this problem through the application of a Linked Data model and frame- work to assist domain experts in this process. Candidate alignment suggestions are generated automatically based on textual and on contextual similarity. The latter is determined according to user-configurable weighted graph traversals. Match decisions confirming or disputing the candidate sug- gestions are obtained in conjunction with user insight and expertise. These decisions are integrated into the knowledge base, enabling further iterative alignment, and simplifying the creation of unified viewing interfaces. Provenance of the musicologist’s judgement is captured and published, support- ing scholarly discourse and counter-proposals. We present our implementation and evaluation of this framework, con- ducting a user study with eight musicologists. We further demonstrate the value of our approach through a case study providing aligned access to catalogue metadata and digitised score images from the British Library and other sources, and broadcast data from the BBC Radio 3 Early Music Show