By Yuting Liu, Zhi-Ming Ma (auth.), Bo Chen (eds.)

ISBN-10: 3642143555

ISBN-13: 9783642143557

While the parts of knowledge administration and administration technological know-how are packed with algorithmic demanding situations, the proliferation of information has known as for the layout of e?cient and e?ective algorithms and information constructions for his or her administration and processing. The foreign convention on Algorithmic elements in details and Management(AAIM) is meant for originalalgorithmicresearchon instant functions and/or primary difficulties pertinent to info mana- ment and administration technology to be greatly construed. The convention goals at bringing jointly researchers in laptop technological know-how, operations examine, utilized arithmetic, economics, and similar disciplines. This quantity includes papers awarded at AAIM 2010: the sixth foreign convention on Algorithmic features in info and administration, which used to be held in the course of July 19-21, 2010, in Weihai, China. We obtained a complete of fifty s- missions.Eachsubmissionwasreviewedbythreemembersof the ProgramC- mittee or their deputies at the caliber, originality, soundness, and signi?cance of its contribution. The committee determined to simply accept 31 papers. this system additionally incorporated invited keynote talks. The luck of the convention resulted from the enter of many folks. we wish ?rst of all to thank all of the contributors of this system Committee for his or her professional evaluate of the submissions. The neighborhood organizers within the tuition of machine technological know-how and expertise, Shandong collage, did a rare task, for which we're very thankful. We thank the nationwide normal technology origin of China, Montana nation collage (USA), college of Warwick (UK), and Shandong collage (China) for his or her sponsorship.

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**Additional info for Algorithmic Aspects in Information and Management: 6th International Conference, AAIM 2010, Weihai, China, July 19-21, 2010. Proceedings**

**Example text**

Suppose that there exists an optimal solution for SP3 problem such that xt 0 < x1t < xt and x1t = W W1 . According to Theorem 6, if x1t is an FTL 1 shipment, there exists at most one n0 ∈ S1 with xn0 t > 0, and xnt = 0 for all n ∈ S1 \ {n0 }. If x1t is an FTL shipment, and there is no n ∈ S1 with xnt > 0, then we have xnt = 0 for all n ∈ S1 . If x1t is an LTL shipment, we have xnt = 0 for all n ∈ S1 . The above two cases mean that x1t = xt , which contradicts the fact 0 < x1t < xt . xt Now we assume that x1t is an FTL shipment but x1t = W W1 , and there is 1 only one n0 ∈ S1 with xn0 t > 0.

Call this tree T2 . Note that in T2 , each subtree of nodes of Vk hanging on R is a path of length exactly k, except for possibly one shorter path. An example of T2 is shown in Figure 2 top-right. 3. “Uncontract” the node R in T2 , obtaining a forest in which each connected component is a rooted-spider, a node in r ∪ VK with paths of nodes from Vk , all of length k except possibly for one shorter path. Let F2 denote the forest created from T2 edges after the ’uncontraction’ . Consider Figure 2 middle-left for an example of F2 , where the bold nodes denote r ∪ VK .

It follows easily from the triangle inequality that a star (where all the nodes are directly connected to the root) is a K-approximation. Lemma 1. The matching solution described for the case K = 2 is a (K − 1)approximation. 3 The (K, 1) Problem with General K We present now an approximation algorithm for the general (K, 1) problem. Algorithm (K, 1) Tree 1. Compute a minimum weight matching M from the nodes of Vk to VK ∪ {r} such that each node in VK may be assigned at most K − 1 nodes, and all the remaining nodes are assigned to r.

### Algorithmic Aspects in Information and Management: 6th International Conference, AAIM 2010, Weihai, China, July 19-21, 2010. Proceedings by Yuting Liu, Zhi-Ming Ma (auth.), Bo Chen (eds.)

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