On robust cycle bases
نویسنده
چکیده
Two types of robust cycle bases are defined via recursively nice arrangements; complete and bipartite complete graphs are shown to have such bases. It is shown that a diagram in a groupoid is commutative up to natural equivalence (cutne) if for each cycle in a robust basis of the graph underlying the diagram, the composition of the morphisms is naturally equivalent to the identity. For a hypercube Qn, it is shown that the commutativity (or cutne) of a particular subset of asymptotically 4/n of the square faces forces commutativity (or cutne) of the entire diagram.
منابع مشابه
Generalized Belief Propagation on Tree Robust Structured Region Graphs
This paper provides some new guidance in the construction of region graphs for Generalized Belief Propagation (GBP). We connect the problem of choosing the outer regions of a LoopStructured Region Graph (SRG) to that of finding a fundamental cycle basis of the corresponding Markov network. We also define a new class of tree-robust Loop-SRG for which GBP on any induced (spanning) tree of the Mar...
متن کاملA note on fundamental, non-fundamental, and robust cycle bases
In many biological systems, robustness is achieved by redundant wiring, and reflected by the presence of cycles in the graphs connecting the systems’ components. When analyzing such graphs, cyclically robust cycle bases of are of interest since they can be used to generate all cycles of a given 2-connected graph by iteratively adding basis cycles. It is known that strictly fundamental (or Kirch...
متن کاملMapping of McGraw Cycle to RUP Methodology for Secure Software Developing
Designing a secure software is one of the major phases in developing a robust software. The McGraw life cycle, as one of the well-known software security development approaches, implements different touch points as a collection of software security practices. Each touch point includes explicit instructions for applying security in terms of design, coding, measurement, and maintenance of softwar...
متن کاملSIMULATED ANNEALING ALGORITHM FOR SELECTING SUBOPTIMAL CYCLE BASIS OF A GRAPH
The cycle basis of a graph arises in a wide range of engineering problems and has a variety of applications. Minimal and optimal cycle bases reduce the time and memory required for most of such applications. One of the important applications of cycle basis in civil engineering is its use in the force method to frame analysis to generate sparse flexibility matrices, which is needed for optimal a...
متن کاملA robust optimization model for distribution and evacuation in the disaster response phase
Natural disasters, such as earthquakes, affect thousands of people and can cause enormous financial loss. Therefore, an efficient response immediately following a natural disaster is vital to minimize the aforementioned negative effects. This research paper presents a network design model for humanitarian logistics which will assist in location and allocation decisions for multiple disaster per...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 11 شماره
صفحات -
تاریخ انتشار 2002