Time Relaxed Round Robin Tournament and the NBA Scheduling Problem

This dissertation study was inspired by the National Basketball Association regular reason scheduling problem. NBA uses the time-relaxed round robin tournament format, which has drawn less research attention compared to the other scheduling formats. Besides NBA, the National Hockey League and many amateur leagues use the time-relaxed round robin tournament as well. This dissertation study is the first ever to examine the properties of general time-relaxed round robin tournaments. Single round, double round and multiple round time-relaxed round robin tournaments are defined. The integer programming and constraint programming models for those tournaments scheduling are developed and presented. Because of the complexity of this problem, several decomposition methods are presented as well. Traveling distance is an important factor in the tournament scheduling. Traveling tournament problem defined in the time constrained conditions has been well studied. This dissertation defines the novel problem of time-relaxed traveling tournament problem. Three algorithms has been developed and compared to address this problem. In addition, this dissertation study presents all major constraints for the NBA regular season scheduling. These constraints are grouped into three categories: structural, external and fairness. Both integer programming and constraint programming are used to model these constraints and the computation studies are presente

Data_Sheet_1_Phage-prokaryote coexistence strategy mediates microbial community diversity in the intestine and sediment microhabitats of shrimp culture pond ecosystem.docx

Emerging evidence supports that the phage-prokaryote interaction drives ecological processes in various environments with different phage life strategies. However, the knowledge of phage-prokaryote interaction in the shrimp culture pond ecosystem (SCPE) is still limited. Here, the viral and prokaryotic community profiles at four culture stages in the intestine of Litopenaeus vannamei and cultural sediment microhabitats of SCPE were explored to elucidate the contribution of phage-prokaryote interaction in modulating microbial communities. The results demonstrated that the most abundant viral families in the shrimp intestine and sediment were Microviridae, Circoviridae, Inoviridae, Siphoviridae, Podoviridae, Myoviridae, Parvoviridae, Herelleviridae, Mimiviridae, and Genomoviridae, while phages dominated the viral community. The dominant prokaryotic genera were Vibrio, Formosa, Aurantisolimonas, and Shewanella in the shrimp intestine, and Formosa, Aurantisolimonas, Algoriphagus, and Flavobacterium in the sediment. The viral and prokaryotic composition of the shrimp intestine and sediment were significantly different at four culture stages, and the phage communities were closely related to the prokaryotic communities. Moreover, the phage-prokaryote interactions can directly or indirectly modulate the microbial community composition and function, including auxiliary metabolic genes and closed toxin genes. The interactional analysis revealed that phages and prokaryotes had diverse coexistence strategies in the shrimp intestine and sediment microhabitats of SCPE. Collectively, our findings characterized the composition of viral communities in the shrimp intestine and cultural sediment and revealed the distinct pattern of phage-prokaryote interaction in modulating microbial community diversity, which expanded our cognization of the phage-prokaryote coexistence strategy in aquatic ecosystems from the microecological perspective and provided theoretical support for microecological prevention and control of shrimp culture health management.</p