We consider a class of geometric facility location problems in which the goal is to determine a set X of disks given by their centers (t j ) and radii (r j ) that cover a given set of demand points Y ⊂ R 2 at the smallest possible cost. We consider cost functions of the form ∑ j f (r j ), where f (r) = r α is the cost of transmission to radius r. Special cases arise for α = 1 (sum of radii) and α = 2 (total area); power consumption models in wireless network design often use an exponent α > 2. Different scenarios arise according to possible restrictions on the transmission centers t j , which may be constrained to belong to a given discrete set or to lie on a line, etc.We obtain several new results, including (a) exact and approximation algorithms for selecting transmission points t j on a given line in order to cover demand points Y ⊂ R 2 ; (b) approximation algorithms (and an algebraic intractability result) for selecting an optimal line on which to place transmission points to cover Y ; (c) a proof of NP-hardness for a discrete set of transmission points in R 2 and any fixed α > 1; and (d) a polynomial-time approximation scheme for the problem of computing a minimum cost covering tour (MCCT), in which the total cost is a linear combination of the transmission cost for the set of disks and the length of a tour/path that connects the centers of the disks.

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In 2011, IBM's Watson competed on the game show Jeopardy! winning against the two best players of all time, Brad Rutter and Ken Jennings (Ferrucci et al. 2010). Since this demonstration, IBM has expanded its research program in artificial intelligence (AI), including the areas of natural language processing and machine learning (Kelly and Hamm 2013). Ultimately, IBM sees the opportunity to develop cognitive computing -a unified and universal platform for computational intelligence (Modha et al. 2011). But how might cognitive computing work in real environmentsand in concert with people?In 2013, our group within IBM Research started to explore how to embed cognitive computing in physical environments. We built a Cognitive Environments Laboratory (CEL) (see figure 1) as a living lab to explore how people and cognitive computing come together.Our effort focuses not only on the physical and computational substrate, but also on the users' experience. We envision a fluid and natural interaction that extends through time across multiple environments (office, meeting room, living room, car, mobile). In this view, cognitive computing systems are always on and available to engage with people in the environment. The system appears to follow individual users, or groups of users, as they change environments, seamlessly connecting the users to available input and output devices and extending their reach beyond their own cognitive and sensory abilities.We call this symbiotic cognitive computing: computation that takes place when people and intelligent agents come together in a physical space to interact with one another. The intelligent agents use a computational substrate of "cogs" for visual object recognition, natural language parsing, probabilistic decision support, and other functions. the book The Society of Mind where Marvin Minsky likened agents to "cogs of great machines" (Minsky 1988). These cogs are available to intelligent agents through programmatic interfaces and to human participants through user interfaces.Our long-term goal is to produce a physical and computational environment that measurably improves the performance of groups on key tasks requiring large amounts of data and significant mental effort, such as information discovery, situational assessment, product design, and strategic decision making. To date, we have focused specifically on building a cognitive environment, a physical space embedded with cognitive computing systems, to support business meetings for strategic decision making. Other applications include corporate meetings exploring potential mergers and acquisitions, executive meetings on whether to purchase oil fields, and utility company meetings to address electrical grid outages. These meetings often bring together a group of participants with varied roles, skills, expertise, and points of view. They involve making decisions with a large number of high-impact choices that need to be evaluated on multiple dimensions taking into account large amounts of structured and unstructured data.While...

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We describe an inexpensive autonomous robot capable of navigating previously unseen data centers and monitoring key metrics such as air temperature 1 . The robot provides real-time navigation and sensor data to commercial IBM software, thereby enabling real-time generation of the data center layout, a thermal map and other visualizations of energy dynamics. Once it has mapped a data center, the robot can efficiently monitor it for hot spots and other anomalies using intelligent sampling. We demonstrate the robot's effectiveness via experimental studies from two production data centers.

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