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Concepts and Algorithms of Optimization – Series 4

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Dr. Maximilian Merkert Benjamin Peters M.Sc.

Winter term 2019/2020

Concepts and Algorithms of Optimization – Series 4

www.math.uni-magdeburg.de/institute/imo/teaching/wise19/cao/

November 8, 2019

Exercise 1

Consider the following graphG= (V, E) with given edge costs ce for all e∈E.

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(a) Determine a spanning treeT in Gwith minimal costs c(T). (b) Give a general description of the algorithm applied in (a).

(c) Determine all cliquesCi inG with 󳈌Ci󳈌 ≥3.

(d) Find a stable set S∗ in G with maximal weight w(S∗) regarding the node weights wv =1 for all v∈V.

(e) Decide whether the graph Gis bipartite.

(Hint: This corresponds to finding a stable set with maximal cardinality in G.)

p. 1/??

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