5,958 research outputs found
Stable marriage and roommates problems with restricted edges: complexity and approximability
In the Stable Marriage and Roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents. A matching is a set of disjoint pairs of mutually acceptable agents. If any two agents mutually prefer each other to their partner, then they block the matching, otherwise, the matching is said to be stable. We investigate the complexity of finding a solution satisfying additional constraints on restricted pairs of agents. Restricted pairs can be either forced or forbidden. A stable solution must contain all of the forced pairs, while it must contain none of the forbidden pairs.
Dias et al. (2003) gave a polynomial-time algorithm to decide whether such a solution exists in the presence of restricted edges. If the answer is no, one might look for a solution close to optimal. Since optimality in this context means that the matching is stable and satisfies all constraints on restricted pairs, there are two ways of relaxing the constraints by permitting a solution to: (1) be blocked by as few as possible pairs, or (2) violate as few as possible constraints n restricted pairs.
Our main theorems prove that for the (bipartite) Stable Marriage problem, case (1) leads to View the MathML source-hardness and inapproximability results, whilst case (2) can be solved in polynomial time. For non-bipartite Stable Roommates instances, case (2) yields an View the MathML source-hard but (under some cardinality assumptions) 2-approximable problem. In the case of View the MathML source-hard problems, we also discuss polynomially solvable special cases, arising from restrictions on the lengths of the preference lists, or upper bounds on the numbers of restricted pairs
Stable Roommate Problem with Diversity Preferences
In the multidimensional stable roommate problem, agents have to be allocated
to rooms and have preferences over sets of potential roommates. We study the
complexity of finding good allocations of agents to rooms under the assumption
that agents have diversity preferences [Bredereck et al., 2019]: each agent
belongs to one of the two types (e.g., juniors and seniors, artists and
engineers), and agents' preferences over rooms depend solely on the fraction of
agents of their own type among their potential roommates. We consider various
solution concepts for this setting, such as core and exchange stability, Pareto
optimality and envy-freeness. On the negative side, we prove that envy-free,
core stable or (strongly) exchange stable outcomes may fail to exist and that
the associated decision problems are NP-complete. On the positive side, we show
that these problems are in FPT with respect to the room size, which is not the
case for the general stable roommate problem. Moreover, for the classic setting
with rooms of size two, we present a linear-time algorithm that computes an
outcome that is core and exchange stable as well as Pareto optimal. Many of our
results for the stable roommate problem extend to the stable marriage problem.Comment: accepted to IJCAI'2
Locally Stable Marriage with Strict Preferences
We study stable matching problems with locality of information and control.
In our model, each agent is a node in a fixed network and strives to be matched
to another agent. An agent has a complete preference list over all other agents
it can be matched with. Agents can match arbitrarily, and they learn about
possible partners dynamically based on their current neighborhood. We consider
convergence of dynamics to locally stable matchings -- states that are stable
with respect to their imposed information structure in the network. In the
two-sided case of stable marriage in which existence is guaranteed, we show
that the existence of a path to stability becomes NP-hard to decide. This holds
even when the network exists only among one partition of agents. In contrast,
if one partition has no network and agents remember a previous match every
round, a path to stability is guaranteed and random dynamics converge with
probability 1. We characterize this positive result in various ways. For
instance, it holds for random memory and for cache memory with the most recent
partner, but not for cache memory with the best partner. Also, it is crucial
which partition of the agents has memory. Finally, we present results for
centralized computation of locally stable matchings, i.e., computing maximum
locally stable matchings in the two-sided case and deciding existence in the
roommates case.Comment: Conference version in ICALP 2013; to appear in SIAM J. Disc Mat
The Stability of the Roommate Problem Revisited
The lack of stability in some matching problems suggests that alternative solution concepts to the core might be applied to find predictable matchings. We propose the absorbing sets as a solution for the class of roommate problems with strict preferences. This solution, which always exists, either gives the matchings in the core or predicts some other matchings when the core is empty. Furthermore, it satisfies an interesting property of outer stability. We also characterize the absorbing sets, determine their number and, in case of multiplicity, we find that they all share a similar structure.roommate problem, core, absorbing sets
The stability of the roommate problem revisited
The lack of stability in some matching problems suggests that alternative solution concepts to the core might be a step towards furthering our understanding of matching market performance. We propose absorbing sets as a solution for the class of roommate problems with strict preferences. This solution, which always exists, either gives the matchings in the core or predicts other matchings when the core is empty. Furthermore, it satisfies the interesting property of outer stability. We also determine the matchings in absorbing sets and find that in the case of multiple absorbing sets a similar structure is shared by all.roommate problem, core, absorbing sets
Linguistic Intuitions: Error Signals and the Voice of Competence
Linguistic intuitions are a central source of evidence across a variety of linguistic domains. They have also long been a source of controversy. This chapter aims to illuminate the etiology and evidential status of at least some linguistic intuitions by relating them to error signals of the sort posited by accounts of on-line monitoring of speech production and comprehension. The suggestion is framed as a novel reply to Michael Devitt’s claim that linguistic intuitions are theory-laden “central systems” responses, rather than endorsed outputs of a modularized language faculty (the “Voice of Competence”). Along the way, it is argued that linguistic intuitions may not constitute a natural kind with a common etiology; and that, for a range of cases, the process by which intuitions used in linguistics are generated amounts to little more than comprehension
Farsighted Stability for Roommate Markets
Using a bi-choice graph technique (Klaus and Klijn, 2009), we show that a matching for a roommate market indirectly dominates another matching if and only if no blocking pair of the former is matched in the latter (Proposition 1). Using this characterization of indirect dominance, we investigate von Neumann-Morgenstern farsightedly stable sets. We show that a singleton is von Neumann-Morgenstern farsightedly stable if and only if the matching is stable (Theorem 1). We also present roommate markets with no and with a non-singleton von Neumann-Morgenstern farsightedly stable set (Examples 1 and 2).core, farsighted stability, one- and two-sided matching, roommate markets, von Neumann-Morgenstern stability.
Spartan Daily, February 4, 2016
Volume 146, Issue 3https://scholarworks.sjsu.edu/spartan_daily_2016/1001/thumbnail.jp
Self-Disclosure Within Intimate Romantic Relationships: Determining Relevant Relational Factors
The Romantic Intimacy Survey assessed the value of self-disclosure in intimate romantic relationships. Males and females place a stronger disclosure importance in specific intimate relationships, such as mom/female guardian, friends from college, friends from high school, previous romantic partners, dad/male guardian, cross-gender friends, and siblings. In addition, females place more disclosure importance than males on specific intimate relationships. These specific relationships included siblings, current roommates, instructors, and peers within social organizations. Males and females categorize relationships into different factors when assessed by a factor analysis. Males and females also thought different relationships had disclosure importance. Males thought adult friends should not be disclosed, whereas youth friends should be disclosed to a romantic partner. Females thought youth friends should not be disclosed, whereas adult friends should be disclosed to a romantic partner. The subjects included 108 female and 51 male undergraduate students
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