
Online VertexWeighted Bipartite Matching: Beating 11/e with Random Arrivals
We introduce a weighted version of the ranking algorithm by Karp et al. ...
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Metrical Task Systems with Online Machine Learned Advice
Machine learning algorithms are designed to make accurate predictions of...
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Extreme Flow Decomposition for MultiSource Multicast with IntraSession Network Coding
Network coding (NC), when combined with multipath routing, enables a lin...
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The PrimalDual method for Learning Augmented Algorithms
The extension of classical online algorithms when provided with predicti...
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Online Primal Dual Meets Online Matching with Stochastic Rewards: Configuration LP to the Rescue
Mehta and Panigrahi (FOCS 2012) introduce the problem of online matching...
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Online Generalized Network Design Under (Dis)Economies of Scale
We consider a general online network design problem where a sequence of ...
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Online and Offline Greedy Algorithms for Routing with Switching Costs
Motivated by the use of high speed circuit switches in large scale data ...
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Online Directed Spanners and Steiner Forests
We present online algorithms for directed spanners and Steiner forests. These problems fall under the unifying framework of online covering linear programming formulations, developed by Buchbinder and Naor (MOR, 34, 2009), based on primaldual techniques. Our results include the following: For the pairwise spanner problem, in which the pairs of vertices to be spanned arrive online, we present an efficient randomized Õ(n^4/5)competitive algorithm for graphs with general lengths, where n is the number of vertices. With uniform lengths, we give an efficient randomized Õ(n^2/3+ϵ)competitive algorithm, and an efficient deterministic Õ(k^1/2+ϵ)competitive algorithm, where k is the number of terminal pairs. These are the first online algorithms for directed spanners. In the offline setting, the current best approximation ratio with uniform lengths is Õ(n^3/5 + ϵ), due to Chlamtac, Dinitz, Kortsarz, and Laekhanukit (TALG 2020). For the directed Steiner forest problem with uniform costs, in which the pairs of vertices to be connected arrive online, we present an efficient randomized Õ(n^2/3 + ϵ)competitive algorithm. The stateoftheart online algorithm for general costs is due to Chakrabarty, Ene, Krishnaswamy, and Panigrahi (SICOMP 2018) and is Õ(k^1/2 + ϵ)competitive. In the offline version, the current best approximation ratio with uniform costs is Õ(n^26/45 + ϵ), due to Abboud and Bodwin (SODA 2018). A small modification of the online covering framework by Buchbinder and Naor implies a polynomialtime primaldual approach with separation oracles, which a priori might perform exponentially many calls. We convert the online spanner problem and the online Steiner forest problem into online covering problems and round in a problemspecific fashion.
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