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Online Node-Weighted Problems

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  • First Online:
Encyclopedia of Algorithms

  • 150 Accesses

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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Recommended Reading

  1. Alon N, Awerbuch B, Azar Y, Buchbinder N, Naor J (2009) The online set cover problem. SIAM J Comput 39(2):361–370

    Article  MathSciNet  MATH  Google Scholar 

  2. 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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  3. Goemans MX, Williamson DP (1995) A general approximation technique for constrained forest problems. SIAM J Comput 24(2):296–317

    Article  MathSciNet  MATH  Google Scholar 

  4. Hajiaghayi MT, Liaghat V, Panigrahi D (2013) Online node-weighted steiner forest and extensions via disk paintings. In: FOCS, Berkeley, pp 558–567

    Google Scholar 

  5. Hajiaghayi MT, Liaghat V, Panigrahi D (2014) Near-optimal online algorithms for prize-collecting steiner problems. In: ICALP (1), Copenhagen, pp 576–587

    Google Scholar 

  6. Korman S (2005) On the use of randomization in the online set cover problem. M.S. thesis, Weizmann Institute of Science

    Google Scholar 

  7. Naor J, Panigrahi D, Singh M (2011) Online node-weighted steiner tree and related problems. In: FOCS, Palm Springs, pp 210–219

    MATH  Google Scholar 

  8. Qian J, Williamson DP (2011) An O(logn)-competitive algorithm for online constrained forest problems. In: ICALP (1), Zurich, pp 37–48

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Duke University, Durham, NC, USA

    Debmalya Panigrahi

Authors
  1. Debmalya Panigrahi
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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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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