Online Maximum Independent Set of Hyperrectangles

The maximum independent set problem is a classical NP-hard problem in theoretical computer science. In this work, we study a special case where the family of graphs considered is restricted to intersection graphs of sets of axis-aligned hyperrectangles and the input is provided in an online fashion. We prove bounds on the competitive ratio of an optimal online algorithm under the adaptive offline, adaptive online, and oblivious adversary models, for several classes of hyperrectangles and restrictions on the order of the input. We are the first to present results on this problem under the oblivious adversary model. We prove bounds on the competitive ratio for unit hypercubes, $\sigma$-bounded hypercubes, unit-volume hypercubes, arbitrary hypercubes, and arbitrary hyperrectangles, in both arbitrary and non-dominated order. We are also the first to present results under the adaptive offline and adaptive online adversary models with input in non-dominated order, proving bounds on the competitive ratio for the same classes of hyperrectangles; for input in arbitrary order, we present the first results on $\sigma$-bounded hypercubes, unit-volume hyperrectangles, arbitrary hypercubes, and arbitrary hyperrectangles. For input in dominating order, we show that the performance of the naive greedy algorithm matches the performance of an optimal offline algorithm in all cases. We also give lower bounds on the competitive ratio of a probabilistic greedy algorithm under the oblivious adversary model. We conclude by discussing several promising directions for future work.Comment: 27 pages, 12 figure

Maximizing Neutrality in News Ordering

The detection of fake news has received increasing attention over the past few years, but there are more subtle ways of deceiving one's audience. In addition to the content of news stories, their presentation can also be made misleading or biased. In this work, we study the impact of the ordering of news stories on audience perception. We introduce the problems of detecting cherry-picked news orderings and maximizing neutrality in news orderings. We prove hardness results and present several algorithms for approximately solving these problems. Furthermore, we provide extensive experimental results and present evidence of potential cherry-picking in the real world.Comment: 14 pages, 13 figures, accepted to KDD '2

Efficient Algorithms for Constructing an Interpolative Decomposition

Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix properties such as sparsity and non-negativity. It also helps save space in memory. In this work, we introduce two optimized algorithms to construct an interpolative decomposition along with numerical evidence that they outperform the current state of the art.Comment: Disclaimer: we do not have any experiments on very large matrices, so these findings are only conclusive for relatively small matrice