Download Frontiers in Algorithmics and Algorithmic Aspects in by Jin-Yi Cai (auth.), Mikhail Atallah, Xiang-Yang Li, Binhai PDF
By Jin-Yi Cai (auth.), Mikhail Atallah, Xiang-Yang Li, Binhai Zhu (eds.)
This booklet constitutes the refereed lawsuits of the fifth foreign Frontiers of Algorithmics Workshop, FAW 2011, and the seventh overseas convention on Algorithmic points in info and administration, AAIM 2011, together held in Jinhua, China, in may perhaps 2011. The 35 revised complete papers awarded including four invited talks have been rigorously reviewed and chosen from ninety two submissions. The papers hide a variety of subject matters within the parts of algorithmics, combinatorial optimization and their purposes featuring present developments of research.
Read Online or Download Frontiers in Algorithmics and Algorithmic Aspects in Information and Management: Joint International Conference, FAW-AAIM 2011, Jinhua, China, May 28-31, 2011. Proceedings PDF
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Extra info for Frontiers in Algorithmics and Algorithmic Aspects in Information and Management: Joint International Conference, FAW-AAIM 2011, Jinhua, China, May 28-31, 2011. Proceedings
We presented lower bounds of the competitive ratio for the two subproblems. The results showed that the more travelers with full communication, the smaller the lower bound is. Based on the urban traﬃc environment, the paper studied the performance of the Retrace-Alternating strategy of the two communication situations. The results indicated that the increase of the proportion of full communication travelers does not always improve the competitive ratio, which is actually related to the structure of network.
Output the vector [n − 1, F1 , F2 , Z1 , Z2 ] that minimize the value Z = Z1 + (F1 (1 + αc ) + d − s) + (F1 (1 + αc ) + d − s)Z2 and denote the corresponding schedule as π(c). Step 5. Output the schedule π = arg min1≤c≤n Z(π(c)) as the solution, where Z(π(c)) denote the objective value of schedule π(c). To show that Algorithm H1 is an FPTAS for the problem 1, r − na|pj = αj sj | j Cj , we give the following lemmas. Lemma 5. Every state [i, F1 , F2 , Z1 , Z2 ] in the (un-reduced) state space V Si satisfies F1 ≤ F1 ≤ F1 Δi , F2 /Δi ≤ F2 ≤ F2 Δi , Z1 /Δi ≤ Z1 ≤ Z1 Δi and Z2 /Δi ≤ Z2 ≤ Z2 Δi , where the state [i, F1 , F2 , Z] is in the reduced state space V Si .
Next we describe the details about how to transform the above dynamic programming into an FPTAS by applying the framework proposed by Woeginger  with elaborate modiﬁcation. Now, we provide the Algorithm H1 as follows. Algorithm H1 Step 1. , α1 ≤ α2 ≤, · · · , ≤ αn−1 . Step 2. Let Δ = 1 + ε/(2(n − 1)), we split – the interval [t0 , s] into q1 = [t0 Δk , t0 Δk+1 ], · · · , [t0 Δq1 −1 , s]; n−1 logΔ s/t0 subintervals [t0 , t0 Δ], · · · , n−1 – the interval [1, j=1 (1 + αj )] into q2 = logΔ j=1 (1 + αj ) subintervals n−1 [1, Δ], · · · , [Δk , Δk+1 ], · · · , [Δq2 −1 , j=1 (1 + αj )]; – the interval [t0 , (n − 1)s] into q3 = logΔ (n − 1)s/t0 subintervals [t0 , t0 Δ], · · · , [t0 Δk , t0 Δk+1 ], · · · , [t0 Δq3 −1 , (n − 1)s]; Scheduling Resumable Proportionally Deteriorating Jobs 43 n−1 – and the interval [1, (n − 1) n−1 j=1 (1+αj )] into q4 = logΔ (n − 1) j=1 (1 + αj ) n−1 subintervals [1, Δ], · · · , [Δk , Δk+1 ], · · · , [Δq4 −1 , (n − 1) j=1 (1 + αj )] .