Center for Discrete Mathematics and Theoretical Computer Science

About: Center for Discrete Mathematics and Theoretical Computer Science is a facility organization based out in Piscataway, New Jersey, United States. It is known for research contribution in the topics: Local search (optimization) & Optimization problem. The organization has 140 authors who have published 175 publications receiving 2345 citations.

Mixed-cell-height placement with complex minimum-implant-area constraints

Abstract: Mixed-cell-height standard cells are prevailingly used in advanced technologies to achieve better design trade-offs among timing, power, and routability. As feature size decreases, placement of cells with multiple threshold voltages may violate the complex minimum-implant-area (MIA) layer rule arising from the limitations of patterning technologies. Existing works consider the mixed-cell-height placement problem only during legalization, or handle the MIA constraints during detailed placement. In this paper, we address the mixed-cell-height placement problem with MIA constraints into two major stages: post global placement and MIA-aware legalization. In the post global placement stage, we first present a continuous and differentiable cost function to address the Vdd/Vss alignment constraints, and add weighted pseudo nets to MIA violation cells dynamically. Then, we propose a proximal optimization method based on the given global placement result to simultaneously consider Vdd/Vss alignment constraints, MIA constraints, cell distribution, cell displacement, and total wirelength. In the MIA-aware legalization stage, we develop a graph-based method to cluster cells of specific threshold voltages, and apply a strip-packing-based binary linear programming to reshape cells. Then, we propose a matching-based technique to resolve intra-row MIA violations and reduce filler insertion. Furthermore, we formulate inter-row MIA-aware legalization as a quadratic programming problem, which is efficiently solved by a modulus-based matrix splitting iteration method. Finally, MIA-aware cell allocation and refinement are performed to further improve the result. Experimental results show that, without any extra area overhead, our algorithm still can achieve 8.5% shorter final total wirelength than the state-of-the-art work.

A simple function that requires exponential size read-once branching programs

Abstract: We present a Boolean function in n variables that is computable in depth 2 monotone AC0 but requires 2 Ω(√n) size read-once branching programs. The function we consider is defined by the blocking sets of a finite projective plane.

Systems approach to studying animal sociality: individual position versus group organization in dynamic social network models.

Abstract: Social networks can be used to represent group structure as a network of interacting components, and also to quantify both the position of each individual and the global properties of a group. In a series of simulation experiments based on dynamic social networks, we test the prediction that social behaviors that help individuals reach prominence within their social group may conflict with their potential to benefit from their social environment. In addition to cases where individuals were able to benefit from improving both their personal relative importance and group organization, using only simple rules of social affiliation we were able to obtain results in which individuals would face a trade-off between these factors. While selection would favor (or work against) social behaviors that concordantly increase (or decrease, respectively) fitness at both individual and group level, when these factors conflict with each other the eventual selective pressure would depend on the relative returns individuals get from their social environment and their position within it. The presented results highlight the importance of a systems approach to studying animal sociality, in which the effects of social behaviors should be viewed not only through the benefits that those provide to individuals, but also in terms of how they affect broader social environment and how in turn this is reflected back on an individual's fitness.

Disproportional effects in populations of concern for pandemic influenza: insights from seasonal epidemics in Wisconsin, 1967-2004.

Abstract: Please cite this paper as: Lofgren et al. (2010) Disproportional effects in populations of concern for pandemic influenza: insights from seasonal epidemics in Wisconsin, 1967–2004. Influenza and Other Respiratory Viruses 4(4), 205–212. Background Influenza infections pose a serious burden of illness in the United States. We explored age, influenza strains, and seasonal epidemic curves in relation to influenza-associated mortality. Methods The state of Wisconsin death records for the years 1967–2004 were analyzed for three distinct populations: children, general population, and elderly. Yearly parameters of duration, intensity, and peak timing were obtained from Annual Harmonic Regression coefficients. Results Overall, elderly had the highest rate and intensity of influenza mortality. The children and infant subpopulations showed an earlier and wider range in duration of peak timing than elderly. During A/Hong Kong/1/68 pandemic years, the elderly subpopulation showed no change in mortality rates while a sharp increase was observed for the children and infant subpopulations. In epidemic years such as 1966–1969, children and infants showed a dramatic decrease in the severity of influenza outbreaks over time. The elderly had increased baseline mortality in years (1986–1987) where predominant strain was characterized as A/Singapore/6/86. Conclusions Our findings indicate that the younger populations may have benefited from the lack of a major shift in viral strains for a number of decades. Furthermore, we demonstrate considerable heterogeneity in the spread of seasonal influenza across age categories, with implications both for the modeling of influenza seasonality, risk assessment, and effective distribution and timing of vaccine and prophylactic interventions.

Tight lower bounds for linear 2-query LCCs over finite fields

Abstract: A Locally Correctable Code (LCC) is an error correcting code that has a probabilistic self-correcting algorithm that, with high probability, can correct any coordinate of the codeword by looking at only a few other coordinates, even if a ? fraction of the coordinates is corrupted. LCCs are a stronger form of LDCs (Locally Decodable Codes) which have received a lot of attention recently due to their many applications and surprising constructions. In this work, we show a separation between linear 2-query LDCs and LCCs over finite fields of prime order. Specifically, we prove a lower bound of the form pΩ(?d) on the length of linear 2-query LCCs over Fp, that encode messages of length d. Our bound improves over the known bound of 2Ω(?d) [8,10,6] which is tight for LDCs. Our proof makes use of tools from additive combinatorics which have played an important role in several recent results in theoretical computer science. We also obtain, as corollaries of our main theorem, new results in incidence geometry over finite fields. The first is an improvement to the Sylvester-Gallai theorem over finite fields [14] and the second is a new analog of Beck's theorem over finite fields. The paper also contains an appendix, written by Sergey Yekhanin, showing that there do exist nonlinear LCCs of size 2O(d) over Fp, thus highlighting the importance of the linearity assumption for our result.