Efficient algorithms for generalized Stable Marriage and Roommates problems

Fleiner, Tamás; Irving, Robert W.; Manlove, David F.

doi:10.1016/j.tcs.2007.04.029

Cited by 44 publications

(43 citation statements)

References 23 publications

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“…We hence need to find a way to remove the rotations from the possible overlapping coalition agreements. As observed in [6], [18], [22], [49], a stable matching is associated with a unique set of rotations referred as the observable rotations. Therefore, if the rotation detection and removal sequence can be uniquely decided, the set of observable rotations as well as the stable matching will also be fixed.…”

Section: D2d Selection Algorithmmentioning

confidence: 99%

A Bayesian Overlapping Coalition Formation Game for Device-to-Device Spectrum Sharing in Cellular Networks

Xiao

Chen

Yuen

et al. 2015

IEEE Trans. Wireless Commun.

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We consider the spectrum sharing problem between a set of device-to-device (D2D) links and multiple co-located cellular networks. Each cellular network is controlled by an operator which can provide service to a number of subscribers. Each D2D link can either access a sub-band occupied by a cellular subscriber or obtain an empty sub-band for its exclusive use. We introduce a new spectrum sharing mode for D2D communications in cellular networks by allowing two or more D2D links with exclusive use of sub-bands to share their sub-bands with each other without consulting the operators. We establish a new game theoretic model called Bayesian non-transferable utility overlapping coalition formation (BOCF) game. We show that our proposed game can be used to model and analyze the above spectrum sharing problem. However, we observe that the core of the BOCF game can be empty, and we derive a sufficient condition for which the core is non-empty. We propose a hierarchical matching algorithm which can detect whether the sufficient condition is satisfied and, if it is satisfied, achieve a stable and unique matching structure which coincides with the overlapping coalition agreement profile in the core of the BOCF game. .sg) L. A. DaSilva is with CTVR, Trinity College Dublin, Ireland (e-mail: dasilval@tcd.ie). L. A. DaSilva is also with Virginia Tech, VA, USA.infrastructure (e.g., base station) even when the sources and destinations are close to each other. This not only increases communication delay and energy consumption but also reduces the reliability of the networks. For example, in cellular networks, failure of a base station can lead to mobile service outage for the entire coverage area of the corresponding cell. Device-to-device (D2D) communication without relying on the base station to forward the traffic provides an efficient way to increase the network capacity and reliability. Another issue is that the traditional exclusive spectrum ownership model used in existing cellular networks has resulted in inefficient spectrum utilization for a significant portion of the time [2], [3]. One technique that promises to address this problem is spectrum sharing, which allows under-utilized licensed spectrum to be shared by unlicensed devices. Allowing both D2D communication and spectrum sharing in cellular networks can improve network capacity, reliability and spectrum utilization efficiency. However, D2D links are generally established autonomously and cannot be fully controlled by the base station. In addition, choosing the wrong spectrum sharing pair of D2D links and cellular subscribers can result in high cross-interference, which may adversely affect both D2D links and cellular subscribers.This motivates the work in this paper, where we investigate the joint optimization of spectrum sharing approaches and sub-band allocation problem for a set of D2D links in an area with multiple co-located cellular networks. Each cellular network is controlled by an operator. We propose a general analytical framework in which each D2D link...

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Section: D2d Selection Algorithmmentioning

confidence: 99%

A Bayesian Overlapping Coalition Formation Game for Device-to-Device Spectrum Sharing in Cellular Networks

Xiao

Chen

Yuen

et al. 2015

IEEE Trans. Wireless Commun.

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“…Fleiner et al [15] showed that any sr instance with forbidden edges can be converted into another stable matching problem involving ties that can be solved in O(m) time [16] and the transformation has the same time complexity as well. Forced edges can easily be eliminated by forbidding all edges adjacent to them, therefore we can state the following result.…”

Section: Theorem 12 (Dias Et Al [10]) the Problem Of Finding A Stamentioning

confidence: 99%

“…Forced edges can easily be eliminated by forbidding all edges adjacent to them, therefore we can state the following result. Theorem 1.3 (Fleiner et al [15]). The problem of finding a stable matching in an sr instance with forced and forbidden edges or reporting that none exists is solvable in O(m) time.…”

Section: Theorem 12 (Dias Et Al [10]) the Problem Of Finding A Stamentioning

confidence: 99%

“…Hence to solve sr min restricted violations dec we generate all subsets S of P ∪ Q of size k, for each k ≤ K. Then we run the algorithm of [15] to determine in O(m) time whether there is a stable matching containing no edge in (P \ S) ∪ (Q ∩ S) and containing all edges in (P ∩ S) ∪ (Q \ S). We now show how to use the above approach in order to solve sr min restricted violations.…”

Section: Bounded Parametersmentioning

confidence: 99%

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Stable Marriage and Roommates Problems with Restricted Edges: Complexity and Approximability

Cseh

Manlove

2015

Algorithmic Game Theory

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a b s t r a c tIn 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 NP-hardness and inapproximability results, whilst case (2) can be solved in polynomial time. For non-bipartite Stable Roommates instances, case (2) yields an NP-hard but (under some cardinality assumptions) 2-approximable problem. In the case of NP-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.

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“…Algorithms for solving this problem have found many real-world applications, including in economics and in college admission. Many variants, e.g., with restrictions on the preference lists, have been studied since (see, for example, Fleiner et al 12 and the references therein).…”

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confidence: 99%

Planar Matchings for Weighted Straight Skeletons

Biedl

Huber

Palfrader

2014

Algorithms and Computation

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We introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist.Using our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings.

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Efficient algorithms for generalized Stable Marriage and Roommates problems

Cited by 44 publications

References 23 publications

A Bayesian Overlapping Coalition Formation Game for Device-to-Device Spectrum Sharing in Cellular Networks

A Bayesian Overlapping Coalition Formation Game for Device-to-Device Spectrum Sharing in Cellular Networks

Stable Marriage and Roommates Problems with Restricted Edges: Complexity and Approximability

Planar Matchings for Weighted Straight Skeletons

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