A theory of flow network typings and its optimization problems

Many large-scale and safety critical systems can be modeled as flow networks. Traditional approaches for the analysis of flow networks are whole-system approaches in that they require prior knowledge of the entire network before an analysis is undertaken, which can quickly become intractable as the size of network increases. In this thesis we study an alternative approach to the analysis of flow networks, which is modular, incremental and order-oblivious. The formal mechanism for realizing this compositional approach is an appropriately defined theory of network typings. Typings are formalized differently depending on how networks are specified and which of their properties is being verified. We illustrate this approach by considering a particular family of flow networks, called additive flow networks. In additive flow networks, every edge is assigned a constant gain/loss factor which is activated provided a non-zero amount of flow enters that edge. We show that the analysis of additive flow networks, more specifically the max-flow problem, is NP-hard, even when the underlying graph is planar. The theory of network typings gives rise to different forms of graph decomposition problems. We focus on one problem, which we call the graph reassembling problem. Given an abstraction of a flow network as a graph G = (V,E), one possible definition of this problem is specified in two steps: (1) We cut every edge of G into two halves to obtain a collection of |V| one-vertex components, and (2) we splice the two halves of all the edges, one edge at a time, in some order that minimizes the complexity of constructing a typing for G, starting from the typings of its one-vertex components. One optimization is minimizing “maximum” edge-boundary degree of components encountered during the reassembling of G (denoted as α measure). Another is to minimize the “sum” of all edge-boundary degrees encountered during this process (denoted by β measure). Finally, we study different variations of graph reassembling (with respect to minimizing α or β) and their relation with problems such as Linear Arrangement, Routing Tree Embedding, and Tree Layout

A compositional approach to network algorithms

We present elements of a typing theory for flow networks, where “types”, “typings”, and “type inference” are formulated in terms of familiar notions from polyhedral analysis and convex optimization. Based on this typing theory, we develop an alternative approach to the design and analysis of network algorithms, which we illustrate by applying it to the max-flow problem in multiple-source, multiple-sink, capacited directed planar graphs.National Science Foundation (CCF-0820138, CNS-1135722

A compositional approach to network algorithms

We present elements of a typing theory for flow networks, where “types”, “typings”, and “type inference” are formulated in terms of familiar notions from polyhedral analysis and convex optimization. Based on this typing theory, we develop an alternative approach to the design and analysis of network algorithms, which we illustrate by applying it to the max-flow problem in multiple-source, multiple-sink, capacited directed planar graphs.National Science Foundation (CCF-0820138, CNS-1135722

Report on shape analysis and matching and on semantic matching

In GRAVITATE, two disparate specialities will come together in one working platform for the archaeologist: the fields of shape analysis, and of metadata search. These fields are relatively disjoint at the moment, and the research and development challenge of GRAVITATE is precisely to merge them for our chosen tasks. As shown in chapter 7 the small amount of literature that already attempts join 3D geometry and semantics is not related to the cultural heritage domain. Therefore, after the project is done, there should be a clear ‘before-GRAVITATE’ and ‘after-GRAVITATE’ split in how these two aspects of a cultural heritage artefact are treated.This state of the art report (SOTA) is ‘before-GRAVITATE’. Shape analysis and metadata description are described separately, as currently in the literature and we end the report with common recommendations in chapter 8 on possible or plausible cross-connections that suggest themselves. These considerations will be refined for the Roadmap for Research deliverable.Within the project, a jargon is developing in which ‘geometry’ stands for the physical properties of an artefact (not only its shape, but also its colour and material) and ‘metadata’ is used as a general shorthand for the semantic description of the provenance, location, ownership, classification, use etc. of the artefact. As we proceed in the project, we will find a need to refine those broad divisions, and find intermediate classes (such as a semantic description of certain colour patterns), but for now the terminology is convenient – not least because it highlights the interesting area where both aspects meet.On the ‘geometry’ side, the GRAVITATE partners are UVA, Technion, CNR/IMATI; on the metadata side, IT Innovation, British Museum and Cyprus Institute; the latter two of course also playing the role of internal users, and representatives of the Cultural Heritage (CH) data and target user’s group. CNR/IMATI’s experience in shape analysis and similarity will be an important bridge between the two worlds for geometry and metadata. The authorship and styles of this SOTA reflect these specialisms: the first part (chapters 3 and 4) purely by the geometry partners (mostly IMATI and UVA), the second part (chapters 5 and 6) by the metadata partners, especially IT Innovation while the joint overview on 3D geometry and semantics is mainly by IT Innovation and IMATI. The common section on Perspectives was written with the contribution of all