The Returning Secretary

In the online random-arrival model, an algorithm receives a sequence of $n$ requests that arrive in a random order. The algorithm is expected to make an irrevocable decision with regard to each request based only on the observed history. We consider the following natural extension of this model: each request arrives k times, and the arrival order is a random permutation of the kn arrivals; the algorithm is expected to make a decision regarding each request only upon its last arrival. We focus primarily on the case when k=2, which can also be interpreted as each request arriving at, and departing from the system, at a random time. We examine the secretary problem: the problem of selecting the best secretary when the secretaries are presented online according to a random permutation. We show that when each secretary arrives twice, we can achieve a competitive ratio of 0.767974... (compared to 1/e in the classical secretary problem), and that it is optimal. We also show that without any knowledge about the number of secretaries or their arrival times, we can still hire the best secretary with probability at least 2/3, in contrast to the impossibility of achieving a constant success probability in the classical setting. We extend our results to the matroid secretary problem, introduced by Babaioff et al. [3], and show a simple algorithm that achieves a 2-approximation to the maximal weighted basis in the new model (for k=2). We show that this approximation factor can be improved in special cases of the matroid secretary problem; in particular, we give a 16/9-competitive algorithm for the returning edge-weighted bipartite matching problem

Letter From Francis Mairs Huntington-Wilson to Charles Norton, June 29, 1909

The document is a carbon copy of a typed letter from the Assistant Secretary of State to Charles Norton, returning a letter to Norton and replying for the Secretary of State about an invitation.https://digitalcommons.ursinus.edu/fmhw_other/1137/thumbnail.jp

Modrall Sperling interviews Kevin Washburn about Indian law and returning to New Mexico

Reflections on Service as Assistant Secretary-Indian Affairs, the State of Indian Law in 2016, and Returning Home to New Mexic

Packing Returning Secretaries

We study online secretary problems with returns in combinatorial packing domains with $n$ candidates that arrive sequentially over time in random order. The goal is to accept a feasible packing of candidates of maximum total value. In the first variant, each candidate arrives exactly twice. All $2n$ arrivals occur in random order. We propose a simple 0.5-competitive algorithm that can be combined with arbitrary approximation algorithms for the packing domain, even when the total value of candidates is a subadditive function. For bipartite matching, we obtain an algorithm with competitive ratio at least $0.5721 - o(1)$ for growing $n$, and an algorithm with ratio at least $0.5459$ for all $n \ge 1$. We extend all algorithms and ratios to $k \ge 2$ arrivals per candidate. In the second variant, there is a pool of undecided candidates. In each round, a random candidate from the pool arrives. Upon arrival a candidate can be either decided (accept/reject) or postponed (returned into the pool). We mainly focus on minimizing the expected number of postponements when computing an optimal solution. An expected number of $\Theta(n \log n)$ is always sufficient. For matroids, we show that the expected number can be reduced to $O(r \log (n/r))$, where $r \le n/2$ is the minimum of the ranks of matroid and dual matroid. For bipartite matching, we show a bound of $O(r \log n)$, where $r$ is the size of the optimum matching. For general packing, we show a lower bound of $\Omega(n \log \log n)$, even when the size of the optimum is $r = \Theta(\log n)$.Comment: 23 pages, 5 figure

Immigration: Policy Considerations Related to Guest Worker Programs

[Excerpt] At present, the United States has two main programs for temporarily importing low-skilled workers, sometimes referred to as guest workers. Agricultural guest workers enter through the H-2A visa program, and other guest workers enter through the H-2B visa program. Employers interested in importing workers under either program must first apply to the U.S. Department of Labor for a certification that U.S. workers capable of performing the work are not available and that the employment of alien workers will not adversely affect the wages and working conditions of similarly employed U.S. workers. Other requirements of the programs differ. A variety of bills have been introduced in recent Congresses to make changes to the H-2A and H-2B programs and the “H” visa category generally, and to establish new temporary worker visas. The 109th Congress revised the H-2B program in the FY2005 Emergency Supplemental Appropriations Act (P.L. 109-13). Among the changes, a temporary provision was added to the Immigration and Nationality Act (INA) to exempt certain returning H-2B workers from the H-2B annual numerical cap of 66,000. The FY2007 Department of Defense authorization bill (P.L. 109-364) extended this exemption through FY2007. The exemption expired on September 30, 2007. A number of bills before the 110th Congress (S. 988, S. 2839, H.R. 1843, H.R. 5233, H.R. 5495, H.R. 5849) would reenact an H-2B returning worker exemption. Other guest worker bills introduced in the 110th Congress include proposals to reform the H-2A program (S. 237/S. 340/H.R. 371, S. 1639, H.R. 1645, H.R. 1792) and the H-2B program (S. 1639, S. 2094), and to establish new temporary worker visas (S. 330, S. 1639, H.R. 1645, H.R. 2413). Some of these bills also would establish mechanisms for certain foreign workers to become legal permanent residents (LPRs). The Senate debated, but failed to invoke cloture on, S. 1639 in June 2007. President George W. Bush proposed a new, expanded temporary worker program in January 2004 when he announced his principles for immigration reform, and has since reiterated his support for such a program. In August 2007, following the unsuccessful cloture vote in the Senate on S. 1639, the Bush Administration announced that it would seek to streamline the existing H-2A and H-2B programs within current law. In February 2008, the U.S. Department of Labor (DOL) and the U.S. Department of Homeland Security (DHS) published proposed rules to significantly amend their respective H-2A regulations. The current discussion of guest worker programs takes place against a backdrop of historically high levels of unauthorized migration to the United States, and one question that often arises about proposals for new guest worker programs is whether they would enable participants to obtain LPR status. Other issues raised in connection with guest worker proposals include how new program requirements would compare with those of the H-2A and H-2B programs and how the eligible population would be defined. This report will be updated as legislative developments occur

For Our Information, Winter & June 1964, Vol. XVI, no. 2-3

An official publication of the ILR School, Cornell University, “for the information of all faculty, staff and students.