Extending the Accommodating Function

Boyar, Joan; Favrholdt, Lene M.; Larsen, Kim S.; Nielsen, Morten

doi:10.1007/3-540-45655-4_11

Cited by 7 publications

(17 citation statements)

References 13 publications

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“…Then, they gave upper and lower bounds on the generalized accommodating ratio for the unit price problem. Boyar et al [2] extended the above performance guarantees to more general ones for α(≤ 1) and gave several upper and lower bounds of First-Fit, Worst-Fit, and other online algorithms.…”

Section: Related Resultsmentioning

confidence: 98%

“…2). Consider the following input sequence σ = (r 1 , r 2 , r 3 , r 4 , r 5 ), where r 1 , r 2 , r 3 , r 4 , and r 5 are requests for intervals [1,2), [3,4), [1,4), [2,4), and [1, 2), respectively. Suppose that an online algorithm A assigns both r 1 and r 2 to seat 1.…”

Section: The Unit Price Problemmentioning

confidence: 99%

“…Let m and c be arbitrary positive integers, and define k = m 2 + 1 be the number of stations and n = 2cm be the number of seats. Our adversary first gives the request sequence σ 1 consisting of 2c requests for the interval [1, 2), 2c requests for the interval [2,3), . .…”

Section: Theorem 1 No Online Algorithm For the Unit Price Problem Ismentioning

confidence: 99%

“…As in the proof of Theorem 1, let m and c be arbitrary positive integers, and let k = m 2 + 1 and n = 2cm. First, we give the sequence σ 1 consisting of 2c requests for the interval [1,2), 2c requests for [2,3), . .…”

Section: Theorem 2 the Competitive Ratio Of Worst-fit For The Unit Pmentioning

confidence: 99%

“…Consider an arbitrary online algorithm A, and let k and n(= 2m for a positive integer m) be the numbers of stations and seats, respectively. The adversary first gives the sequence σ 1 consisting of m requests for the interval [1, 2) and σ 2 consisting of m requests for the interval [2,3). Let R be the set of seats to which A assigns both requests of σ 1 and σ 2 .…”

Section: An Upper Bound Theorem 3 No Online Algorithm For the Propormentioning

confidence: 99%

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Improving the Competitive Ratios of the Seat Reservation Problem

Miyazaki

Okamoto

2010

IFIP Advances in Information and Communication Technology

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Abstract. In the seat reservation problem, there are k stations, s1 through s k , and one train with n seats departing from the station s1 and arriving at the station s k . Each passenger orders a ticket from station si to station sj (1 ≤ i < j ≤ k) by specifying i and j. The task of an online algorithm is to assign one of n seats to each passenger online, i.e., without knowing future requests. The purpose of the problem is to maximize the total price of the sold tickets. There are two models, the unit price problem and the proportional price problem, depending on the pricing policy of tickets. In this paper, we improve upper and lower bounds on the competitive ratios for both models: For the unit price problem, we give an upper bound of

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Section: Related Resultsmentioning

confidence: 98%

Section: The Unit Price Problemmentioning

confidence: 99%

Section: Theorem 1 No Online Algorithm For the Unit Price Problem Ismentioning

confidence: 99%

Section: Theorem 2 the Competitive Ratio Of Worst-fit For The Unit Pmentioning

confidence: 99%

Section: An Upper Bound Theorem 3 No Online Algorithm For the Propormentioning

confidence: 99%

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Improving the Competitive Ratios of the Seat Reservation Problem

Miyazaki

Okamoto

2010

IFIP Advances in Information and Communication Technology

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Online Multi-Coloring with Advice

Christ

Favrholdt

Larsen

2015

Approximation and Online Algorithms

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We consider the problem of online graph multi-coloring with advice. Multi-coloring is often used to model frequency allocation in cellular networks. We give several nearly tight upper and lower bounds for the most standard topologies of cellular networks, paths and hexagonal graphs. For the path, negative results trivially carry over to bipartite graphs, and our positive results are also valid for bipartite graphs. The advice given represents information that is likely to be available, studying for instance the data from earlier similar periods of time.

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Online Bounded Analysis

Boyar

Epstein

Favrholdt

et al. 2016

Computer Science – Theory and Applications

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Though competitive analysis is often a very good tool for the analysis of online algorithms, sometimes it does not give any insight and sometimes it gives counter-intuitive results. Much work has gone into exploring other performance measures, in particular targeted at what seems to be the core problem with competitive analysis: the comparison of the performance of an online algorithm is made with respect to a too powerful adversary. We consider a new approach to restricting the power of the adversary, by requiring that when judging a given online algorithm, the optimal offline algorithm must perform at least as well as the online algorithm, not just on the entire final request sequence, but also on any prefix of that sequence. This is limiting the adversary's usual advantage of being able to exploit that it knows the sequence is continuing beyond the current request. Through a collection of online problems, including machine scheduling, bin packing, dual bin packing, and seat reservation, we investigate the significance of this particular offline advantage.

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Extending the Accommodating Function

Cited by 7 publications

References 13 publications

Improving the Competitive Ratios of the Seat Reservation Problem

Improving the Competitive Ratios of the Seat Reservation Problem

Online Multi-Coloring with Advice

Online Bounded Analysis

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