In this paper, we consider the problem of partitioning a given collection of node sets into k collections such that the average size of collections is the largest, where the size of a collection is defined as the cardinarity of the union of the subsets contained in the collection. More concretely, we give an upper bound on the performance ratio of an approximation algorithm proposed by Abrams et al., which is known to have a performance ratio of at least 1-1/e≅0.6321 where e is Napier's constant. The proposed upper bound is 1-(2-d+1√2)d+1/2 for any d≥1 provided that k=o(n) which approaches to 0.75 as d increases.

Some key challenges remain to be overcome before spectrum sensing can be widely used to identify spectrum opportunities in the TV bands. To fulfill the strict sensing requirement specified by FCC, a comprehensive sensing algorithm, which produces high SNR gain and maintains sensing robustness under complex noise conditions, needs to be implemented. In addition, carefully designed physical features and improvement on cost performance ratio are also essential if a prototype is to be commercialized. To the best of our knowledge, no success has ever been announced in developing a sensing prototype that fulfills both FCC sensing requirement and the above mentioned features. In this paper, we introduce a recently developed sensing prototype for Japanese digital TV signals of ISDB-T. The prototype operates in the Japanese UHF TV band of 470-770MHz and can reliably identify presence/absence of an ISDB-T signal at the level of -114dBm in a 6MHz channel. Moreover, it has constrained size and weight, and is capable of accurately measuring power of an ISDB-T signal at an extremely low level. Efforts on reducing cost have also been made by avoiding the use of electronic components/devices of high price. Both laboratory and field tests are performed to evaluate its sensing performance and power measurement capability. In the laboratory test, sensing performance under conditions of adjacent channel interference and frequency offset, and power measurement accuracy, are checked. In field tests, the prototype is attached in a vehicle and is checked for its capability to identify the presence of purposely broadcasted ISDB-T signals at some fixed locations and also during movement of the vehicle.

This study examined the performance improvement of a photovoltaic (PV) array and inverter as well as their design, construction, and post-operation and management, which will become the key elements in future PV systems. In addition, it evaluated the performance characteristics of a 50 kW grid-connection PV system in Korea. According to the result of the evaluation, the PV array showed approximately 10% efficiency. The inverter was indicated to operate at > 90% efficiency regularly at > 400 W/m2 irradiation. The capture losses (Lc), system losses (Ls) and performance ratio were approximately 0.9 h/d, 0.3 h/d, and > 70%, respectively, indicating that the system was operating stably. In addition, while the Ls decreased rapidly due to the efficiency of the inverter, the performance ratio decreased markedly with increasing Lc due to the increase in temperature when the reference yield was > 5.0 h/d.

The 2-vertex-connectivity augmentation problem for specified vertices (2VCA-SV) is defined as follows: Given an undirected graph G=(V,E), a subgraph G0=(V,E') of G, a specified set of vertices S V and a weight function w:E R^+ (nonnegative real numbers), find a set E" E-E' with the minimum total weight, such that G0+E"=(V,E' E") has at least two internally disjoint paths between any pair of vertices in S. In this paper, we propose an O(|V||E|+ |V|2 log |V|) time algorithm 2-ABIS, whose performance ratio is 2 (3, respectively), for 2VCA-SV if G0 has a connected component containing S (otherwise).