Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1401.6210

A Semi Distributed Approach for Min-Max Fair Car-Parking Slot Assignment Problem

Elisabetta Alfonsetti·Pradeep Chathuranga Weeraddana·Carlo Fischione
View original source ↗Read source document ↗Export metadata ↓

Abstract

Designing efficient car parking mechanisms that can be potentially integrated into future intelligent transportation systems is of crucial importance. Usually, the related design problems are combinatorial and the worst-case complexity of optimal solution approaches grows exponentially with the problem sizes. Therefore, such optimal approaches are not scalable and practically undesirable. As a result, almost all existing methods for parking slot assignment are simple and greedy approaches, where each car is assigned a free parking slot, which is closer to its destination. Moreover, no emphasis is placed to optimize the social benefit of the users during the parking slot assignment. In this paper, the fairness as a metric for modeling the aggregate social benefit of the users is considered and a distributed algorithm based on Lagrange duality theory is developed. The proposed algorithm is gracefully scalable compared to the optimal methods. In addition, it is shown that the proposed car parking mechanism preserves privacy in the sense that any car involved in the algorithm will not be able to discover the destination of any other car during the algorithm iterations. Numerical results illustrate the performance of the proposed algorithm compared to the optimal assignment and a greedy method. They show that our algorithm yields a good tradeoff between the implementation-level simplicity and the performance. Even though the main emphasis in this paper resides in the car parking slot assignment problem, our formulation and the algorithms, in general, can also be applied or adopted in fair agent-target assignment problems in other application domains.

Explore related subjects

math.OCcs.DS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Elisabetta Alfonsetti, Pradeep Chathuranga Weeraddana, Carlo Fischione. 2014-01-23. A Semi Distributed Approach for Min-Max Fair Car-Parking Slot Assignment Problem. https://arxiv.org/abs/1401.6210

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Symmetry-dependence in Rounding of a Convex Body

The symmetry measure of a convex body $S\subset\mathbb{R}^n$ is given by: $\mathrm{sym}(S):=\max\{α\ge0:\text{ there exists }x\in S\text{ such that }-α(S-x)\subseteq S-x\}$, where such an $x$ is called a Minkowski center. We prove that every convex body $S$ admits a $\sqrt{\frac{n}{\mathrm{sym}(S)}}$-rounding of $S$, namely, there exists an origin-centered ellipsoid $E$ and a center $c$ such that $E\subseteq S-c\subseteq\sqrt{\frac{n}{\mathrm{sym}(S)}}\,E$. This result was conjectured in 2005 by Belloni and Freund. As special cases, this recovers an $n$-rounding of $S$ (since $\mathrm{sym}(S)\ge\frac{1}{n}$), and a $\sqrt{n}$-rounding when $\mathrm{sym}(S)=1$. In the case when $S$ is a polytope given as the convex hull of points, the desired rounding is produced by a regularized minimum-volume covering ellipsoid problem where the regularization is with respect to the Minkowski center. Similarly, when $S$ is a polytope given as the intersection of halfspaces, such a rounding is produced by a regularized maximum-volume inscribed ellipsoid problem. In both of these cases, the rounding can be computed by first solving a linear optimization problem (to compute $\mathrm{sym}(S)$ and a Minkowski center), and then solving a convex optimization problem with a logarithmic determinant objective, second-order cone constraints, and one semidefinite cone constraint. We also show that the factor $\sqrt{\frac{n}{\mathrm{sym}(S)}}$ is nearly tight in its dependence on dimension and symmetry. When $\frac{n+1}{1+\mathrm{sym}(S)}$ is an integer, we show by explicit construction that the factor $\sqrt{\frac{n}{\mathrm{sym}(S)}}$ is tight. In the more general case, for every dimension $n$ and every admissible symmetry value, we construct a polytope $S$ for which every rounding factor is at least $\sqrt{\frac{2}{3}}\sqrt{\frac{n}{\mathrm{sym}(S)}}$.

math.OC↗
arXiv2026

Maximal Monotone Differential Inclusions with Volterra and One-Sided Lipschitz Perturbations under Nonlocal Initial Conditions and Applications

We investigate a class of differential inclusions governed by non-autonomous and autonomous maximal monotone operators, involving set-valued perturbations with a Volterra integral term and subject to a nonlocal condition. Under suitable assumptions on the governing operator, the set-valued perturbation, and the Volterra kernel, we establish existence results for solutions. In particular, the set-valued perturbation is assumed to satisfy a one-sided Lipschitz condition, while the Volterra kernel is required to be Lipschitz continuous. The existence of a trajectory is established by means of an iterative construction and an application of Zorn's lemma. Finally, several examples are presented to illustrate the applicability of the abstract results.

math.OC↗
arXiv2026

On Fast-Slow Mean-Field Forward-Backward Stochastic Systems

We establish an averaging principle for a class of multiscale mean-field forward-backward stochastic differential equations and identify several novel phenomena that are absent from classical fast-slow systems. In contrast with classical fast-slow systems, the effective dynamics cannot in general be obtained by simply freezing deterministic slow parameters and averaging against the invariant measure of the resulting fast equation. The appropriate averaging object is instead provided by a frozen fast dynamics in a random environment and its associated conditional invariant measures, which retain the coupling between the slow state and its distribution. The forward-backward structure creates a further obstruction: local averaging estimates need not remain stable when propagated over an arbitrary time horizon. We identify a uniform restart stability condition for the averaged system under which this obstruction can be overcome. Using a joint lifted semigroup for the state-law dynamics, together with a two-scale discretization and a Gordin-type decomposition, we prove strong averaging for both the forward and backward components with optimal convergence rate $O(\varepsilon^{1/2})$. As an application, we apply the general theory to a class of mean-field stochastic control problems and develop an efficient algorithm for solving such mean-field control problems.

math.OC↗