Incremental Medians via Online Bidding

Chrobák, Marek; Kenyon, Claire; Noga, John; Young, Neal E.

doi:10.1007/s00453-007-9005-x

Cited by 34 publications

(50 citation statements)

References 26 publications

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“…This approach allows us to focus specifically on the limits posed by the lack of complete information about the input. Similar considerations played a role in some earlier work on online computation, for example for online medians [6,7,12], minimum-latency tours [5], and several other online optimization problems (see [8]). …”

Section: Introductionmentioning

confidence: 60%

Competitive Strategies for Online Clique Clustering

Chrobák

Dürr

Nilsson

2015

Lecture Notes in Computer Science

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Abstract.A clique clustering of a graph is a partitioning of its vertices into disjoint cliques. The quality of a clique clustering is measured by the total number of edges in its cliques. We consider the online variant of the clique clustering problem, where the vertices of the input graph arrive one at a time. At each step, the newly arrived vertex forms a singleton clique, and the algorithm can merge any existing cliques in its partitioning into larger cliques, but splitting cliques is not allowed. We give an online strategy with competitive ratio 15.645 and we prove a lower bound of 6 on the competitive ratio, improving the previous respective bounds of 31 and 2.

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Section: Introductionmentioning

confidence: 60%

Competitive Strategies for Online Clique Clustering

Chrobák

Dürr

Nilsson

2015

Lecture Notes in Computer Science

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“…In this section we show a connection between the performance guarantee for sequencing jobs on a single machine without release dates and an online bidding problem investigated by Chrobak et al [7]. This allows us to prove tight lower bounds for our problem.…”

Section: Lower Boundsmentioning

confidence: 67%

“…Note that by letting C = R + 1, we get exactly the well known sequence defined by the recurrence b i = C(b i−1 − b i−2 ); see, e.g., [7]. For this sequence, it is known that since C < 4, no matter what the initial conditions are exactly (but 0 < b 1 < b 2 ), there exists an integer n such that b 1 < b 2 < · · · < b n , while 0 < b n+1 ≤ b n .…”

Section: Theorem 12mentioning

confidence: 95%

“…Chrobak et al [7] gave lower bounds of 4 − and e − , for any > 0, for deterministic and randomized algorithms, respectively.…”

Section: Lower Boundsmentioning

confidence: 99%

“…We also show that our upper bounds are best possible for universal sequencing. This is done by establishing an interesting connection between our problem and a certain online bidding problem [7].…”

Section: Introductionmentioning

confidence: 99%

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Universal Sequencing on an Unreliable Machine

Mestre

Megow

2015

Encyclopedia of Algorithms

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We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. We aim for a universal solution that performs well without adaptation for any possible machine behavior. Our objective is to minimize w j f (C j ) for any non-decreasing, nonnegative, differentiable cost function f (C j ). We design a deterministic algorithm that finds a universal scheduling sequence with a solution value within 4 times the value of an optimal clairvoyant algorithm that knows the machine behavior in advance. A randomized version of this algorithm attains in expectation a ratio of e. We also show that both results are best possible among all universal solutions. Our algorithms can be adapted to run in polynomial time with slightly increased cost.When jobs have individual release dates, the situation changes drastically. Even if all weights are equal, there are instances for which any universal solution is a factor of Ω(log n/ log log n) worse than an optimal sequence for any unbounded cost function. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a non-trivial algorithm with a small constant performance guarantee.

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An incremental algorithm for the uncapacitated facility location problem

2015

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We study the incremental facility location problem, wherein we are given an instance of the uncapacitated facility location problem (UFLP) and seek an incremental sequence of opening facilities and an incremental sequence of serving customers along with their fixed assignments to facilities open in the partial sequence. We say that a sequence has a competitive ratio of k, if the cost of serving the first ℓ customers in the sequence is at most k times the optimal solution for serving any ℓ customers for all possible values of ℓ. We provide an incremental framework that computes a sequence with a competitive ratio of at most eight and a worst‐case instance that provides a lower bound of three for any incremental sequence. We also present the results of our computational experiments carried out on a set of benchmark instances for the UFLP. The problem has applications in multistage network planning. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(4), 306–311 2015

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Incremental Medians via Online Bidding

Cited by 34 publications

References 26 publications

Competitive Strategies for Online Clique Clustering

Competitive Strategies for Online Clique Clustering

Universal Sequencing on an Unreliable Machine

An incremental algorithm for the uncapacitated facility location problem

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