An Activity Profile Model and dynamic-matching results for social networks regarding wellness applications

Health-care costs are spiraling out of control. There are more than one billion obese people in the world and that number is growing alarmingly fast. We must find a way to motivate unhealthy people to take care of themselves, so as to put less strain on economies around the world, less strain on natural resources, less strain on the health-care system, and, most importantly, to save lives and to reduce suffering. We have gone from hunters and gathers to sitters and twitterers. While eating high-caloric foods, many (apparently at least a billion) people watch TV or play with the Internet all day long. In fact, the popularity of social networking is astounding. Nations around the world have a significant percentage of their populations engaged in social-networking sites such as Facebook, Flickr, Friendster, hi5, LinkedIn, MySpace, Orkut, Qzone, and so on. In this paper we develop an Activity Profile Model that captures network members' characteristics, preferences, activities vitals, and other relevant information. We formulate dynamic-matching problems whose focus is to find groups of individuals with similar desires and time constraints, so that they can participate in activities together. We examine the complexity of the problems from both the sequential and parallel perspectives. We give a polynomial-time algorithm for one of the problems; prove a problem is P-hard, show another is NP-hard, and yet another NP-complete. Most people need help reducing their weight; they can not do it alone - diets and exercise plans often fail. Our model is a step toward producing an environment in which groups of individuals can be matched in real time to engage in joint activities and motivate each other to stay healthy. The problems defined here involve a new type of dynamic matching, as opposed to traditional matching as is done in many of the current Internet social-networking sites and traditional graph theory.