Wireless Scheduling with Power Control

We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that each set satisfies the signal-to-interference-plus-noise (SINR) constraints. We give an algorithm that attains an approximation ratio of $O(\log n \cdot \log\log \Delta)$, where $n$ is the number of links and $\Delta$ is the ratio between the longest and the shortest link length. Under the natural assumption that lengths are represented in binary, this gives the first approximation ratio that is polylogarithmic in the size of the input. The algorithm has the desirable property of using an oblivious power assignment, where the power assigned to a sender depends only on the length of the link. We give evidence that this dependence on $\Delta$ is unavoidable, showing that any reasonably-behaving oblivious power assignment results in a $\Omega(\log\log \Delta)$-approximation. These results hold also for the (weighted) capacity problem of finding a maximum (weighted) subset of links that can be scheduled in a single time slot. In addition, we obtain improved approximation for a bidirectional variant of the scheduling problem, give partial answers to questions about the utility of graphs for modeling physical interference, and generalize the setting from the standard 2-dimensional Euclidean plane to doubling metrics. Finally, we explore the utility of graph models in capturing wireless interference.Comment: Revised full versio

Self-similar solutions to the mean curvature flow in the Minkowski plane R1,1\mathbf R^{1,1}

We introduce the mean curvature flow of curves in the Minkowski plane $\mathbf R^{1,1}$ and give a classification of all the self-similar solutions. In addition, we describe five other exact solutions to the flow.Comment: 31 pages, 38 figures. Two exact solutions added from previous versio

Measuring Trust: Which Measure Can Be Trusted?

The study examines the relationship of various survey measures of trust and risk taking with trusting behavior in the trust or investment game (Berg, Dickhaut, & McCabe, 1995). We conduct a series of standard trust game experiments from which we derive the standard trust measure – amount sent. We also conduct trust games in which we allow subjects in the role of trustors to make proposals for what they should send and what their counterparts (trustees) should send back, and offer the possibility of asking for costly contracts to support agreements. We use trustors’ request for such contracts as a new operationalization of behavioral trust (not asking for a contract indicates more trusting than asking for one). We compare the two behavioral measures to survey measures of trust and risk preferences. Our results confirm that the amount sent in the trust game is related to common-sense survey measures of trust but not to any measures of risk preferences. In contrast, none of the survey measures predicts asking for a contract. In addition, we investigate the association between risk preferences, gender, personality, cognitive ability and other individual characteristics and trust. We find that male subjects send significantly more than female subjects; risk attitude, the big five personality traits, cognitive ability and other variables show only limited association with the amount sent and asking for a contract. In contrast, survey trust measures are explained well by such variables. JEL classification: C72, C91, D63Trust; Trust game; Measurement