953 research outputs found
The Complexity of Approximately Counting Stable Roommate Assignments
We investigate the complexity of approximately counting stable roommate
assignments in two models: (i) the -attribute model, in which the preference
lists are determined by dot products of "preference vectors" with "attribute
vectors" and (ii) the -Euclidean model, in which the preference lists are
determined by the closeness of the "positions" of the people to their
"preferred positions". Exactly counting the number of assignments is
#P-complete, since Irving and Leather demonstrated #P-completeness for the
special case of the stable marriage problem. We show that counting the number
of stable roommate assignments in the -attribute model () and the
3-Euclidean model() is interreducible, in an approximation-preserving
sense, with counting independent sets (of all sizes) (#IS) in a graph, or
counting the number of satisfying assignments of a Boolean formula (#SAT). This
means that there can be no FPRAS for any of these problems unless NP=RP. As a
consequence, we infer that there is no FPRAS for counting stable roommate
assignments (#SR) unless NP=RP. Utilizing previous results by the authors, we
give an approximation-preserving reduction from counting the number of
independent sets in a bipartite graph (#BIS) to counting the number of stable
roommate assignments both in the 3-attribute model and in the 2-Euclidean
model. #BIS is complete with respect to approximation-preserving reductions in
the logically-defined complexity class #RH\Pi_1. Hence, our result shows that
an FPRAS for counting stable roommate assignments in the 3-attribute model
would give an FPRAS for all of #RH\Pi_1. We also show that the 1-attribute
stable roommate problem always has either one or two stable roommate
assignments, so the number of assignments can be determined exactly in
polynomial time
A Simply Exponential Upper Bound on the Maximum Number of Stable Matchings
Stable matching is a classical combinatorial problem that has been the
subject of intense theoretical and empirical study since its introduction in
1962 in a seminal paper by Gale and Shapley. In this paper, we provide a new
upper bound on , the maximum number of stable matchings that a stable
matching instance with men and women can have. It has been a
long-standing open problem to understand the asymptotic behavior of as
, first posed by Donald Knuth in the 1970s. Until now the best
lower bound was approximately , and the best upper bound was . In this paper, we show that for all , for some
universal constant . This matches the lower bound up to the base of the
exponent. Our proof is based on a reduction to counting the number of downsets
of a family of posets that we call "mixing". The latter might be of independent
interest
10481 Abstracts Collection -- Computational Counting
From November 28 to December 3 2010, the Dagstuhl Seminar 10481 ``Computational Counting\u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
FPTAS for #BIS with Degree Bounds on One Side
Counting the number of independent sets for a bipartite graph (#BIS) plays a
crucial role in the study of approximate counting. It has been conjectured that
there is no fully polynomial-time (randomized) approximation scheme
(FPTAS/FPRAS) for #BIS, and it was proved that the problem for instances with a
maximum degree of is already as hard as the general problem. In this paper,
we obtain a surprising tractability result for a family of #BIS instances. We
design a very simple deterministic fully polynomial-time approximation scheme
(FPTAS) for #BIS when the maximum degree for one side is no larger than .
There is no restriction for the degrees on the other side, which do not even
have to be bounded by a constant. Previously, FPTAS was only known for
instances with a maximum degree of for both sides.Comment: 15 pages, to appear in STOC 2015; Improved presentations from
previous version
Solving Hard Stable Matching Problems Involving Groups of Similar Agents
Many important stable matching problems are known to be NP-hard, even when
strong restrictions are placed on the input. In this paper we seek to identify
structural properties of instances of stable matching problems which will allow
us to design efficient algorithms using elementary techniques. We focus on the
setting in which all agents involved in some matching problem can be
partitioned into k different types, where the type of an agent determines his
or her preferences, and agents have preferences over types (which may be
refined by more detailed preferences within a single type). This situation
would arise in practice if agents form preferences solely based on some small
collection of agents' attributes. We also consider a generalisation in which
each agent may consider some small collection of other agents to be
exceptional, and rank these in a way that is not consistent with their types;
this could happen in practice if agents have prior contact with a small number
of candidates. We show that (for the case without exceptions), several
well-studied NP-hard stable matching problems including Max SMTI (that of
finding the maximum cardinality stable matching in an instance of stable
marriage with ties and incomplete lists) belong to the parameterised complexity
class FPT when parameterised by the number of different types of agents needed
to describe the instance. For Max SMTI this tractability result can be extended
to the setting in which each agent promotes at most one `exceptional' candidate
to the top of his/her list (when preferences within types are not refined), but
the problem remains NP-hard if preference lists can contain two or more
exceptions and the exceptional candidates can be placed anywhere in the
preference lists, even if the number of types is bounded by a constant.Comment: Results on SMTI appear in proceedings of WINE 2018; Section 6
contains work in progres
The Cowl - v.78 - n.23 - May 1, 2014
The Cowl - student newspaper of Providence College. Volume 78 - No. 23 - May 1, 2014. 32 pages
Spartan Daily, February 4, 1983
Volume 80, Issue 5https://scholarworks.sjsu.edu/spartandaily/6987/thumbnail.jp
Effect of Black- or White-Sounding Name and Impact of Intergroup Contact with Black Individuals on Auditor Judgments
The accounting profession in the United States continues to reflect a gap in racial diversity, with the majority of accountants being white. Implicit racial bias results in discrimination in the U.S. today, specifically against Black individuals. Within accounting, the auditing specialty requires exercising professional judgment that could present opportunities for implicit racial bias to affect the financial statements. This study aims to fill gaps in the existing research by answering the following questions: 1) How does the race of the CFO affect the accounting judgments of auditors? 2) How does intergroup contact with Black individuals impact auditors’ accounting judgments when working with a Black CFO? The participants included individuals in the U.S. who have a bachelor’s degree in accounting, the majority of whom were CPAs with auditing experience. Participants completed a computerized experiment, responded to a short questionnaire, and answered manipulation, attention-check, and demographic questions. Data for the first hypothesis, based on the first research question, was analyzed using an independent sample t-test. H1 was not supported. H2, analyzed using both Pearson and Spearman correlations, was also not supported. Supplemental analysis was conducted based on additional demographic data collected for the sample using multiple two-way ANOVAs. Post-hoc analysis using Scheffé post-hoc criterion for significance indicated a potential difference in the write-down amounts for non-Hispanic/Latino white participants compared to both Hispanic/Latino participants and participants of two or more races. Similar analysis indicated a potential difference in the write- down amounts for participants who spent their childhood in the Midwest compared to those who did not provide the location where they spent their childhood. While the study results do not provide support for the effect of Black- or white-sounding name or impact of intergroup contact on auditor judgments, the study was limited by a number of factors that may have impacted the results. Future research should continue to explore the presence and impacts of implicit bias generally, and implicit racial bias specifically, in the auditing field
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