In a matrix-completion problem the aim is to specify the missing entries of a matrix in order to produce a matrix with particular properties. In this paper we survey results concerning matrix-completion problems where...In a matrix-completion problem the aim is to specify the missing entries of a matrix in order to produce a matrix with particular properties. In this paper we survey results concerning matrix-completion problems where we look for completions of various types for partial matrices supported on a given pattern. We see that the existence of completions of the required type often depends on the chordal properties of graphs associated with the pattern.展开更多
Small cells have been regarded as an appealing technique to boost resource reuse ratio. On the other hand, their large-scale and self-organised tendency would complicate the interference environment of mobile networks...Small cells have been regarded as an appealing technique to boost resource reuse ratio. On the other hand, their large-scale and self-organised tendency would complicate the interference environment of mobile networks. Meanwhile, traffic class is booming in recent years, which leads to higher demand for net- work designers on Quality of Service （QoS） provision, and therefore users＇ diverse re- quirements may not be guaranteed in sucff＇an interference limited scenario. To maximise the number of users with QoS demands as well as resource reuse ratio, we formulate the resource allocation problem into a multi-objective l0 norm form. It is shown to be NP hard, and an iterative method is employed to approach the optimal solution. Because of its limit of being not adaptive to large-scale networks, we also design a heuristic method based on chordal graph, which, however, could result in per- formance loss when the size of networks is small. Finally, by combining these two meth- ods, we devise a hybrid algorithm such that the allocation performs both efficiently and effectively. Simulation results illustrate the performance of our proposed methods in terms of outage probability and resource reuse ratio.展开更多
文摘In a matrix-completion problem the aim is to specify the missing entries of a matrix in order to produce a matrix with particular properties. In this paper we survey results concerning matrix-completion problems where we look for completions of various types for partial matrices supported on a given pattern. We see that the existence of completions of the required type often depends on the chordal properties of graphs associated with the pattern.
基金ACKNOWLEDGEMENT First, thanks for the invitation from the organ- isers of IEEE/CIC ICCC 2013 held in Xi＇an, China. This work was supported by the Na- tional Natural Science Foundation of China under Grants No. 60972047, No. 61231008 the National Science and Technology Major Project under Grams No. 2011ZX03005-004, No. 2011ZX03004-003, No. 2011ZX03005- 003-03, No. 2013ZX03004007-003+4 种基金 the Shannxi 13115 Project under Grant No. 2010ZDKG-26 the National Basic Research Program of China （973 Program） under Grant No. 2009CB320404 the Program for Changjiang Scholars and Inn- ovative Research Team in University under Gr- ant No. IRT0852 the 111 Project under Grant No. B08038 and the State Key Laboratory Fou- ndation under Grants No. ISN1002005, No. ISN090305.
文摘Small cells have been regarded as an appealing technique to boost resource reuse ratio. On the other hand, their large-scale and self-organised tendency would complicate the interference environment of mobile networks. Meanwhile, traffic class is booming in recent years, which leads to higher demand for net- work designers on Quality of Service （QoS） provision, and therefore users＇ diverse re- quirements may not be guaranteed in sucff＇an interference limited scenario. To maximise the number of users with QoS demands as well as resource reuse ratio, we formulate the resource allocation problem into a multi-objective l0 norm form. It is shown to be NP hard, and an iterative method is employed to approach the optimal solution. Because of its limit of being not adaptive to large-scale networks, we also design a heuristic method based on chordal graph, which, however, could result in per- formance loss when the size of networks is small. Finally, by combining these two meth- ods, we devise a hybrid algorithm such that the allocation performs both efficiently and effectively. Simulation results illustrate the performance of our proposed methods in terms of outage probability and resource reuse ratio.
