Maximal Area Triangles in a Convex Polygon

The widely known linear time algorithm for computing the maximum area triangle in a convex polygon was found incorrect recently by Keikha et. al.(arXiv:1705.11035). We present an alternative algorithm in this paper. Comparing to the only previously known correct solution, ours is much simpler and more efficient. More importantly, our new approach is powerful in solving related problems

Characterizing interference in wireless mesh networks.

Hui, Ka Hung.Thesis (M.Phil.)--Chinese University of Hong Kong, 2007.Includes bibliographical references (leaves 123-126).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.ivChapter 1 --- Introduction / Motivation --- p.1Chapter 2 --- Literature Review --- p.6Chapter 2.1 --- Introduction --- p.6Chapter 2.2 --- The Capacity-Finding Problem --- p.6Chapter 2.3 --- Interference Models --- p.8Chapter 2.4 --- Considering Interference in the Capacity-Finding Problem with Perfect Scheduling --- p.9Chapter 2.4.1 --- Conflict Graph --- p.10Chapter 2.4.2 --- Independent Set Constraints --- p.11Chapter 2.4.3 --- Row Constraints --- p.11Chapter 2.4.4 --- Clique Constraints --- p.12Chapter 2.4.5 --- Using the physical model --- p.13Chapter 2.5 --- Considering Interference in the Capacity-Finding Problem with Random Access --- p.15Chapter 2.6 --- Chapter Summary --- p.17Chapter 3 --- Partial Interference - Basic Idea --- p.18Chapter 3.1 --- Introduction --- p.18Chapter 3.2 --- Deficiencies in Previous Models --- p.18Chapter 3.2.1 --- Multiple Interferers --- p.19Chapter 3.2.2 --- Non-binary Behavior of Interference --- p.19Chapter 3.2.3 --- Impractical Perfect Scheduling --- p.21Chapter 3.3 --- Refining the Relationship between Interference and Throughput Degradation --- p.21Chapter 3.4 --- Capacity Gain by Exploiting Partial Interference . --- p.23Chapter 3.5 --- Chapter Summary --- p.28Chapter 4 --- Partial Interference in 802.11 --- p.29Chapter 4.1 --- Introduction --- p.29Chapter 4.2 --- The 802.11 Model --- p.29Chapter 4.2.1 --- Assumptions --- p.30Chapter 4.2.2 --- Transmission Probability Calculation --- p.31Chapter 4.2.3 --- Packet Corruption Probability Calculation --- p.34Chapter 4.2.4 --- Loading Calculation --- p.35Chapter 4.2.5 --- Summary --- p.36Chapter 4.3 --- Some Analytical Results --- p.37Chapter 4.4 --- A TDM A/CDMA Analogy --- p.40Chapter 4.5 --- Admissible (Stability) Region --- p.42Chapter 4.6 --- Chapter Summary --- p.44Chapter 5 --- Partial Interference in Slotted ALOHA --- p.45Chapter 5.1 --- Introduction --- p.45Chapter 5.2 --- The Finite-Link Slotted ALOHA Model --- p.46Chapter 5.2.1 --- Assumptions --- p.46Chapter 5.2.2 --- Stability of Slotted ALOHA --- p.46Chapter 5.3 --- Stability Region of 2-Link Slotted ALOHA under Partial Interference --- p.47Chapter 5.4 --- Some Illustrations --- p.50Chapter 5.5 --- Generalization to the M-Link Case --- p.53Chapter 5.6 --- Chapter Summary --- p.58Chapter 6 --- FRASA --- p.59Chapter 6.1 --- Introduction --- p.59Chapter 6.2 --- The FRASA Model --- p.60Chapter 6.3 --- Validation of the FRASA Model --- p.66Chapter 6.3.1 --- Simulation Results --- p.66Chapter 6.3.2 --- Comparison to Previous Bounds --- p.72Chapter 6.4 --- Convex Hull Bound --- p.75Chapter 6.5 --- p-Convexity --- p.80Chapter 6.6 --- Supporting Hyperplane Bound --- p.86Chapter 6.7 --- Extension to Partial Interference --- p.89Chapter 6.7.1 --- FRASA under Partial Interference --- p.90Chapter 6.7.2 --- Convex Hull Bound --- p.93Chapter 6.7.3 --- p-Convexity --- p.97Chapter 6.7.4 --- Supporting Hyperplane Bound --- p.101Chapter 6.8 --- Chapter Summary --- p.102Chapter 7 --- Conclusion and Future Works --- p.110Chapter 7.1 --- Conclusion --- p.110Chapter 7.2 --- Future Works --- p.111Chapter A --- Proof of (4.13) in Chapter 4 --- p.113Bibliography --- p.12