UV/blue/green InGaN and GaN single-quantum-well structure light-emitting diodes (LEDs) were grown on epitaxially laterally overgrown GaN (ELOG) and sapphire substrates. The external quantum efficiency (EQE) of the UV InGaN LED on ELOG was much higher than that on sapphire only at high-current operation. At low-current operation, both LEDs had the same EQE. When the active layer was GaN, EQE of the LED on sapphire was much lower than that on ELOG even at low- and high-current operations due to the lack of localized energy states formed by alloy composition fluctuations. In order to improve the lifetime of laser diode (LD), ELOG had to be used because the operating current density of the LD is much higher than that of LED. A violet InGaN multi-quantum-well/GaN/AlGaN separate-confinement-heterostructure LD was grown on ELOG on sapphire. The LDs with cleaved mirror facets showed an output power as high as 40 mW under room-temperature continuous-wave (CW) operation. The stable fundamental transverse mode was observed at an output power of up to 40 mW. The estimated lifetime of the LDs at a constant output power of 10 mW was more than 2,000 hours under CW operation at an ambient temperature of 60.

It is known that all minimum cuts in an edge-weighted undirected graph with n vertices and m edges can be represented by a cactus with O(n) vertices and edges, a connected graph in which each edge is contained in an exactly one cycle. In this paper, we show that such a cactus representation can be computed in O(mn+n2log n) time and O(m) space. This improves the previously best complexity of deterministic cactus construction algorithms, and matches with the time bound of the fastest deterministic algorithm for computing a single minimum cut.