By Zhao Zhang, Lidong Wu, Wen Xu, Ding-Zhu Du

This booklet constitutes the refereed court cases of the eighth foreign convention on Combinatorial Optimization and purposes, COCOA 2014, hung on the island of Maui, Hawaii, united states, in December 2014. The fifty six complete papers incorporated within the ebook have been conscientiously reviewed and chosen from 133 submissions. subject matters lined comprise vintage combinatorial optimization; geometric optimization; community optimization; optimization in graphs; utilized optimization; CSoNet; and complexity, cryptography, and games.

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Section 5 concludes the paper. Randomized Online Algorithms for Set Cover Leasing Problems 2 29 Preliminaries Notations: An element j arriving at time t and requesting to be covered by p sets, is denoted as a triplet (j, t, p). Let E be the collection of all these triplets. A set S leased at time t for a period k can cover its elements over the interval T = [t, t + lk ] and incurs a cost ckS . We denote such a set as a triplet (S, k, T ). Let C be the collection of all these triplets. We refer to a leased set as active.

If he releases 1 . a new item of size 1, the game arrives at α1,1 h If the game ends at ηi for h ≤ C, then the utility of the adversary is defined ρ(ηih ). Starting from to be ρ˜(ηih ), while the utility of the packer is defined to be −˜ 0 η1 , if the packer always packs items according to Next-Fit, then obviously the adversary could choose to release a certain list of items such that the game ends at some ηih with ρ˜(ηih ) about 2. If the packer is smart enough, he would resort to an optimum online algorithm (with the competitive ratio of ρ∗ ) so that no matter how the adversary releases items, he is always able to move the game to some ηih with ρ˜(ηih ) ≤ ρ∗ .

1 One Square, Arbitrary Orientation Given a convex polygon P ,1 we want to find the enclosing rectangle whose maximum side is minimized. Let p1 , p2 , · · · , pm be the vertices of P ordered counter-clockwise (ccw). The angle of the side (pi , pi+1 ) from the horizontal 1 This polygon may be the convex hull of the points in P computed in O(n log n) time. 40 B. Bhattacharya et al. p3 cl α3 β2 p2 p4 pt β1 p1 β5 p5 β6 Y pl α < 0 α8 p8 p6 p7 (a) α7 h pr ct cb β>0 pb w θ X (b) Fig. 1. (a) Angles {αi } and {βj }; (b) Rotating the enclosing rectangle (resp.

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