We propose a novel approach, called Progressive Parameterizations , to compute foldover-free parameterizations with low isometric distortion on disk topology meshes. Instead of using the input mesh as a reference to define the objective function, we introduce a progressive reference that contains bounded distortion to the parameterized mesh and is as close as possible to the input mesh. After optimizing the bounded distortion energy between the progressive reference and the parameterized mesh, the parameterized mesh easily approaches the progressive reference, thereby also coming close to the input. By iteratively generating the progressive reference and optimizing the bounded distortion energy to update the parameterized mesh, our algorithm achieves high-quality parameterizations with strong practical reliability and high efficiency. We have demonstrated that our algorithm succeeds on a massive test data set containing over 20712 complex disk topology meshes. Compared to the state-of-the-art methods, our method has achieved higher computational efficiency and practical reliability.

Pervasive computing environments typically change frequently in terms of available resources and their properties. Applications in pervasive computing use contexts to capture these changes and adapt their behaviors accordingly. However, contexts available to these applications may be abnormal or imprecise due to environmental noises. This may result in context inconsistencies, which imply that contexts conflict with each other. The inconsistencies may set such an application into a wrong state or lead the application to misadjust its behavior. It is thus desirable to detect and resolve the context inconsistencies in a timely way. One popular approach is to detect context inconsistencies when contexts breach certain consistency constraints. Existing constraint checking techniques recheck the entire expression of each affected consistency constraint upon context changes. When a changed context affects only a constraint's subexpression, rechecking the entire expression can adversely delay the detection of other context inconsistencies. This article proposes a rigorous approach to identifying the parts of previous checking results that are reusable without entire rechecking. We evaluated our work on the Cabot middleware through both simulation experiments and a case study. The experimental results reported that our approach achieved over a fifteenfold performance improvement on context inconsistency detection than conventional approaches.

Exception handling resolves inconsistency by backward or forward error recovery methods or both in Business-to-Business (B2B) process collaboration. To avoid committing irrevocable tasks followed by exceptions, B2B processes, which guarantee the atomicity sphere property, are attractive. While atomicity sphere ensures its outcomes to be either all or nothing, conflicting local recoveries may lead to global B2B inconsistencies. Existing (global) analysis techniques however mandate every process unveiling all individual tasks. Such an analysis is infeasible when some business parties refuse to disclose their process details for privacy or business reasons. To address this problem, we propose a process algebraic technique to prove, construct, and check atomicity-equivalent public views from B2B processes. By checking atomicity spheres in the composition of these public views, business parties can identify suitable services that respect their individual and overall atomicity requirements. An example based on a real-life multilateral supply chain process is included.