On k-Column Sparse Packing Programs

We consider the class of packing integer programs (PIPs) that are column sparse, i.e. there is a specified upper bound k on the number of constraints that each variable appears in. We give an (ek+o(k))-approximation algorithm for k-column sparse PIPs, improving on recent results of $k^2\cdot 2^k$ and $O(k^2)$. We also show that the integrality gap of our linear programming relaxation is at least 2k-1; it is known that k-column sparse PIPs are $\Omega(k/ \log k)$-hard to approximate. We also extend our result (at the loss of a small constant factor) to the more general case of maximizing a submodular objective over k-column sparse packing constraints.Comment: 19 pages, v3: additional detail

Scheduling to minimize gaps and power consumption

This paper considers scheduling tasks while minimizing the power consumption of one or more processors, each of which can go to sleep at a fixed cost α . There are two natural versions of this problem, both considered extensively in recent work: minimize the total power consumption (including computation time), or minimize the number of “gaps” in execution. For both versions in a multiprocessor system, we develop a polynomial-time algorithm based on sophisticated dynamic programming. In a generalization of the power-saving problem, where each task can execute in any of a specified set of time intervals, we develop a (1+23α) -approximation, and show that dependence on α is necessary. In contrast, the analogous multi-interval gap scheduling problem is set-cover hard (and thus not o(lgn) -approximable), even in the special cases of just two intervals per job or just three unit intervals per job. We also prove several other hardness-of-approximation results. Finally, we give an O(n√) -approximation for maximizing throughput given a hard upper bound on the number of gaps.Institute for Research in Fundamental Sciences (Iran) (Grant Number CS1385-2-01)Institute for Research in Fundamental Sciences (Iran) (Grant Number CS1384-6-01

Children’s depressive symptoms and their regulation of negative affect in response to vignette-depicted emotion-eliciting events

The present study examined the relationship between sub-clinical depressive symptoms and children's anticipated cognitive and behavioral reactions to two written vignettes depicting emotion-eliciting stressors (i.e., fight with one's best friend and failure at a roller blade contest). Participants (N = 244) ranging in age between 10 and 13 were presented each vignette and then asked to rate their anticipated utilization of each of seven emotion-regulation strategies (ERs), along with the anticipated mood enhancement effects of each strategy. In addition, ratings of participants' perceived coping efficacy to manage the stressful situation were collected. Results indicated that participants were more likely to endorse ERs for which they have greater confidence in their mood enhancement effects. Moreover, marked differences were observed between ratings for conceptually distinct cognitive ERs. Consistent with expectations, results revealed that participants displaying higher levels of depressive symptoms were more likely to endorse cognitive and behavioral ERs that are negative, passive, and/or avoidant in nature. Children's ratings of the anticipated mood enhancement effects of several ERs were inversely related to their level of depressive symptoms, as was their perceived self-efficacy to manage the stressor. © 2007 The International Society for the Study of Behavioural Development