The Online Set Aggregation Problem

Carrasco, Rodrigo A.; Pruhs, Kirk; Stein, Clifford; Verschae, José

doi:10.1007/978-3-319-77404-6_19

Cited by 2 publications

(4 citation statements)

References 17 publications

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“…. 16 if q is still pending then connect q to facility at u b u . If this lls the counter of v, the exploration of u is paused, and a new exploration of v is started, in a DFS manner.…”

Section: Algorithm For Hstsmentioning

confidence: 99%

“…4 Declare T . Add(e) 13 set b e ← w(e) 14 while b e = 0 and there remain pending requests in T e do 15 let H be the live cut under e. 16 let Q be the set of pending requests in T e . 17 let t be the earliest time such that there exists a set of requests Q ⊆ Q that saturates T e for some e ∈ H. 18 call Invest(e,e ) 19 if c e = w(e ) then set c e = 0 ; call Explore(e ).…”

Section: Algorithm 4: Online Multilevel Aggregation With Delaymentioning

confidence: 99%

“…Additional problems with delay exist other than those over a metric space. The set aggregation problem, presented in [16], is a variant of set cover with delay. The problem of bin packing with delay is presented in [3].…”

Section: Related Workmentioning

confidence: 99%

“…Proposition 4. 16. Let e be an edge, and let H be a cut in T e that does not include e. Let Q ⊆ h∈H T h be a set of pending requests and t be a time such that d Q (t) ≥ w(T Q e ) − w(e).…”

Section: Lower Bounding Optmentioning

confidence: 99%

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General Framework for Metric Optimization Problems with Delay or with Deadlines

Azar

Touitou

2019

2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)

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In this paper, we present a framework used to construct and analyze algorithms for online optimization problems with deadlines or with delay over a metric space. Using this framework, we present algorithms for several di erent problems. We present an O(D 2 )-competitive deterministic algorithm for online multilevel aggregation with delay on a tree of depth D, an exponential improvement over the O(D 4 2 D )-competitive algorithm of Bienkowski et al. (ESA '16). We also present an O(log 2 n)competitive randomized algorithm for online service with delay over any general metric space of n points, improving upon the O(log 4 n)-competitive algorithm by Azar et al. (STOC '17).In addition, we present the problem of online facility location with deadlines. In this problem, requests arrive over time in a metric space, and need to be served until their deadlines by facilities that are opened momentarily for some cost. We also consider the problem of facility location with delay, in which the deadlines are replaced with arbitrary delay functions. For those problems, we present O(log 2 n)-competitive algorithms, with n the number of points in the metric space.The algorithmic framework we present includes techniques for the design of algorithms as well as techniques for their analysis. arXiv:1904.07131v1 [cs.DS] 15 Apr 20192. An O(log 2 n)-competitive randomized algorithm for online service with delay over a metric space with n points. This improves upon the O(log 4 n)-competitive randomized algorithm in [5].3. An O(log 2 n)-competitive randomized algorithm for online facility location with deadlines over a metric space with n points.4. An O(log 2 n)-competitive randomized algorithm for online facility location with delay over a metric space with n points.Our algorithms all share a common framework, which we present. The framework provides general structure to both the algorithm and its analysis.Such an improvement for the online multilevel aggregation problem is only known for the special case of deadlines, as given in [13].The algorithms for online facility location with deadlines and with delay can be easily extended to the case in which the cost of opening a facility is di erent for each point in the metric space. This changes the competitiveness of the algorithms to O(log 2 ∆ + log ∆ log n), where ∆ is the aspect ratio of the metric space. Our TechniquesAll of our algorithms are based on corresponding competitive algorithms for HSTs. The randomized algorithms for general metric spaces are obtained through randomized HST embedding. The O(D 2 )competitive deterministic algorithm for online multilevel aggregation with delay on a tree is based on decomposing the tree into a forest of HSTs. This decomposition is similar to that used in [13] for the case of deadlines.The framework -algorithm design. In designing algorithms for the problems over HSTs, we use a certain framework. In an algorithm designed using the framework, there is a counter for every node (in the case of facility location) or every edge (in the case of online m...

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“…. 16 if q is still pending then connect q to facility at u b u . If this lls the counter of v, the exploration of u is paused, and a new exploration of v is started, in a DFS manner.…”

Section: Algorithm For Hstsmentioning

confidence: 99%