# The parking permit problem

@article{Meyerson2005ThePP,
title={The parking permit problem},
journal={46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)},
year={2005},
pages={274-282}
}
• A. Meyerson
• Published 2005
• Computer Science
• 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)
We consider online problems where purchases have time durations which expire regardless of whether the purchase is used or not. The parking permit problem is the natural analog of the well-studied ski rental problem in this model, and we provide matching upper and lower bounds on the competitive ratio for this problem. By extending the techniques thus developed, we give an online-competitive algorithm for the problem of renting steiner forest edges with time durations.
66 Citations

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#### References

SHOWING 1-10 OF 15 REFERENCES
Approximation via cost-sharing: a simple approximation algorithm for the multicommodity rent-or-buy problem
• Computer Science, Mathematics
• 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.
• 2003
This paper gives a conceptually simple 12-approximation algorithm for the multicommodity rent-or-buy problem, and is the first to show the converse - those ideas from cost sharing can be fruitfully applied in the design and analysis of approximation algorithms. Expand
A constant-factor approximation algorithm for the multicommodity rent-or-buy problem
• Computer Science, Mathematics
• The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
• 2002
This work considers the rent-or-buy problem, a type of multicommodity buy-at-bulk network design in which there are two ways to install capacity on any given edge, and proposes a novel primal-dual algorithm, the first constant factor approximation algorithm for network design with multiple commodities and economies of scale. Expand
Improved Combinatorial Algorithms for Single Sink Edge Installation Problems.
• Mathematics
• 2000
We present the first constant approximation to the single sink buy-at-bulk network design problem, where we have to design a network by buying pipes of different costs and capacities per unit lengthExpand
• Computer Science
• Proceedings 38th Annual Symposium on Foundations of Computer Science
• 1997
O(log/sup 2/n) randomized approximation algorithm is provided for the buy-at-bulk network design problem, solving the open problem and solving additional natural variations of the problem, such as multi-sink network design, as well as selective network design. Expand
Improved algorithms for the data placement problem
• Computer Science, Mathematics
• SODA '02
• 2002
This work studies the data placement problem, where the goal is to place certain data objects in fixed capacity caches in a network to optimize latency of access, and presents a constant approximation, while blowing up the cache capacities by a constant factor. Expand
Buy-at-bulk network design: approximating the single-sink edge installation problem
• Computer Science
• SODA '97
• 1997
The algorithmic study of an important but NP-hard problem that arises commonly in network design, an undirected graph with one sink node and multiple source nodes, and a small set of cable types, where each cable type is specified by its capacity and its cost per unit length. Expand
Placement Algorithms for Hierarchical Cooperative Caching
• Computer Science, Mathematics
• J. Algorithms
• 1999
The main result is a simple constant-factor approximation algorithm for the hierarchical placement problem that admits an efficient distributed implementation and does not appear to be practical for large problem sizes. Expand
On-line algorithms for Steiner tree problems (extended abstract)
• Mathematics, Computer Science
• STOC '97
• 1997
This work presents an algorithm for the on-line Generalized Steiner Tree (GST) problem, and two other problems: Rectilinear Steiner Arborescence(RSA) and Symmetric Rectil inear Steer arborescence (SRSA), with performance ratios of O(log n). Expand
A tight bound on approximating arbitrary metrics by tree metrics
• Mathematics, Computer Science
• STOC '03
• 2003
In this paper, we show that any n point metric space can be embedded into a distribution over dominating tree metrics such that the expected stretch of any edge is O(log n). This improves upon theExpand
Web caching using access statistics
• Computer Science
• SODA '01
• 2001
This work considers the problem of caching web pages with the objective of minimizing latency of access, and presents a constant factor approximation to the optimum average latency while exceeding capacity constraints by a logarithmic factor. Expand