Online matching problems have garnered significant attention in recent years due to numerous applications in e-commerce, online advertisements, ride-sharing, etc. Many of them capture the uncertainty in the real world by including stochasticity in both the arrival and matching processes. The Online Stochastic Matching with Timeouts problem introduced by Bansal, et al., (Algorithmica, 2012) models matching markets (e.g., E-Bay, Amazon). Buyers arrive from an independent and identically distributed (i.i.d.) known distribution on buyer profiles and can be shown a list of items one at a time. Each buyer has some probability of purchasing each item and a limit (timeout) on the number of items they can be shown.Bansal et al., (Algorithmica, 2012) gave a 0.12-competitive algorithm which was improved by Adamczyk, et al., (ESA, 2015) to 0.24. We present several online attenuation frameworks that use an algorithm for offline stochastic matching as a black box. On the upper bound side, we show that one framework, combined with a black-box adapted from Bansal et al., (Algorithmica, 2012), yields an online algorithm which nearly doubles the ratio to 0.46. Additionally, our attenuation frameworks extend to the more general setting of fractional arrival rates for online vertices. On the lower bound side, we show that no algorithm can achieve a ratio better than 0.632 using the standard LP for this problem. This framework has a high potential for further improvements since new algorithms for offline stochastic matching can directly improve the ratio for the online problem.Our online frameworks also have the potential for a variety of extensions. For example, we introduce a natural generalization: Online Stochastic Matching with Two-sided Timeouts in which both online and offline vertices have timeouts. Our frameworks provide the first algorithm for this problem achieving a ratio of 0.30. We once again use the algorithm of Bansal et al., (Algorithmica, 2012) as a black-box and plug it into one of our frameworks. * This is the full version of the paper that appeared in AAMAS-2017 [10]. There was an error in one of the offline black-box. This version fixes all the ratios in the theorems.

Risk assessment instrument (RAI) datasets, particularly ProPublica's COMPAS dataset, are commonly used in algorithmic fairness papers due to benchmarking practices of comparing algorithms on datasets used in prior work. In many cases, this data is used as a benchmark to demonstrate good performance without accounting for the complexities of criminal justice (CJ) processes. We show that pretrial RAI datasets contain numerous measurement biases and errors inherent to CJ pretrial evidence and due to disparities in discretion and deployment, are limited in making claims about real-world outcomes, making the datasets a poor fit for benchmarking under assumptions of ground truth and real-world impact. Conventional practices of simply replicating previous data experiments may implicitly inherit or edify normative positions without explicitly interrogating assumptions. With context of how interdisciplinary fields have engaged in CJ research, algorithmic fairness practices are misaligned for meaningful contribution in the context of CJ, and would benefit from transparent engagement with normative considerations and values related to fairness, justice, and equality. These factors prompt questions about whether benchmarks for intrinsically socio-technical systems like the CJ system can exist in a beneficial and ethical way.

Online matching has received significant attention over the last 15 years due to its close connection to Internet advertising. As the seminal work of Karp, Vazirani, and Vazirani has an optimal (1−1/e) competitive ratio in the standard adversarial online model, much effort has gone into developing useful online models that incorporate some stochasticity in the arrival process. One such popular model is the "known I.I.D. model" where different customer-types arrive online from a known distribution. We develop algorithms with improved competitive ratios for some basic variants of this model with integral arrival rates, including: (a) the case of general weighted edges, where we improve the best-known ratio of 0.667 due to Haeupler, Mirrokni and Zadimoghaddam [12] to 0.705; and (b) the vertex-weighted case, where we improve the 0.7250 ratio of Jaillet and Lu [13] to 0.7299.We also consider an extension of stochastic rewards, a variant where each edge has an independent probability of being present. For the setting of stochastic rewards with non-integral arrival rates, we present a simple optimal non-adaptive algorithm with a ratio of 1 − 1/e. For the special case where each edge is unweighted and has a uniform constant probability of being present, we improve upon 1 − 1/e by proposing a strengthened LP benchmark.One of the key ingredients of our improvement is the following (offline) approach to bipartitematching polytopes with additional constraints. We first add several valid constraints in order to get a good fractional solution f; however, these give us less control over the structure of f. We next remove all these additional constraints and randomly move from f to a feasible point on the matching polytope with all coordinates being from the set {0, 1/k, 2/k, . . . , 1} for a chosen integer k. The structure of this solution is inspired by Jaillet and Lu (Mathematics of Operations Research, 2013) and is a tractable structure for algorithm design and analysis. The appropriate random move preserves many of the removed constraints (approximately with high probability and exactly in expectation). This underlies some of our improvements and could be of independent interest. * A preliminary version of this appeared in the European Symposium on Algorithms (ESA), 2016 † Claim 4. For a large edge e, EW 1 [h] (3) with parameter h achieves a competitive ratio of R[EW 1 , 2/3] = 0.67529 + (1 − h) * 0.00446. Claim 5. For a small edge e of type Γ 1 , EW 1 [h] (3) achieves a competitive ratio of R[EW 1 , 1/3] = 0.751066, regardless of the value h. Claim 6. For a small edge e of type Γ 2 , EW 1 [h] (3) achieves a competitive ratio of R[EW 1 , 1/3] = 0.72933 + h * 0.040415. By setting h = 0.537815, the two types of small edges have the same ratio and we get that EW 1 [h] achieves (R[EW 1 , 2/3], R[EW 1 , 1/3]) = (0.679417, 0.751066). Thus, this proves Lemma 2. Proof of Claim 4Proof. Consider a large edge e = (u, v 1 ) in the graph G F . Let e ′ = (u, v 2 ) be the other small edge incident to u. Edges e and e ′ can appear in [M ...

In this paper, we show an improved bound and new algorithm for the online square-into-square packing problem. This twodimensional packing problem involves packing an online sequence of squares into a unit square container without any two squares overlapping. The goal is to find the largest area α such that any set of squares with total area α can be packed. We show an algorithm that can pack any set of squares with total area α ≤ 3/8 into a unit square in an online setting, improving the previous bound of 11/32. ⋆ This work has been supported partially by NSF award CCF-1218620. I also want to thank my mentor Prof. Gandhi for all his support.

Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation algorithms for some well-known families of such problems. As three main examples, we attain the integrality gap, up to lower-order terms, for known LP relaxations for k-column sparse packing integer programs (Bansal et al., Theory of Computing, 2012) and stochastic k-set packing (Bansal et al., Algorithmica, 2012), and go "half the remaining distance" to optimal for a major integrality-gap conjecture of Füredi, Kahn and Seymour on hypergraph matching (Combinatorica, 1993).