Years and Authors of Summarized Original Work
2011; Naor, Panigrahi, Singh
2013; Hajiaghayi, Liaghat, Panigrahi
2014; Hajiaghayi, Liaghat, Panigrahi
Problem Definition
We are given an undirected graph G = (V, E) offline, where node v has a given weight w v . Initially, the output graph H ⊆ G is the empty graph. In the generic online Steiner network design problem, each online step has a connectivity request C i and the online algorithm must augment the output graph H to meet the new request. We will consider the following problems in this domain:
Steiner tree. Each connectivity request C i comprises a new vertex t i ∈ V (called a terminal) that must be connected in H to all previous terminals. (The first terminal t0 is often called the root and the constraint C i can then be restated as connecting terminal t i to the root.)
Steiner forest. Each connectivity request C i comprises a new vertex pair (s i , t i ) (called a terminal pair) that must be connected in H.
Group Steiner tree....
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Alon N, Awerbuch B, Azar Y, Buchbinder N, Naor J (2009) The online set cover problem. SIAM J Comput 39(2):361–370
Demaine ED, Hajiaghayi MT, Klein PN (2009) Node-weighted steiner tree and group steiner tree in planar graphs. In: ICALP (1), Rhodes, pp 328–340
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Panigrahi, D. (2016). Online Node-Weighted Problems. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_761
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DOI: https://doi.org/10.1007/978-1-4939-2864-4_761
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