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Live Free or Die Hard
Published in Aida Todri-Sanial, Chuan Seng Tan, Krzysztof Iniewski, Physical Design for 3D Integrated Circuits, 2017
Yu-Guang Chen, Yiyu Shi, Shih-Chieh Chang
As the assignment graph decomposition formulation is clear now, the remaining problem is how to find its optimal solution. Simultaneously considering both graph decomposition and spanning tree formation may be very complicated for directed graphs. Trying to reduce the problem complexity, we will first solve it in an easier way by reducing the directed graph to an undirected one in Section 9.4.2.2. Actually, even with an undirected assignment graph, the decomposition problem can still be NP-hard. To prove NP-hardness, a commonly adopted technique is to show that it can be reduced from a well-known NP-complete problem in polynomial time. We choose to use Exact Cover by 3-Sets (X3C) problem to reduce to the undirected assignment graph decomposition problem. We omit the proof process since it may be out of range of topic of this chapter. Readers who are interested in the proof process can refer [27] for more details. However, doing so can make our algorithm much simpler. The reduction may prune some feasible and potentially better solutions, but will not injure the validity. Then, we will directly handle the directed assignment graph in Section 9.4.2.3.
Steganography
Published in Shivendra Shivani, Suneeta Agarwal, Jasjit S. Suri, Handbook of Image-Based Security Techniques, 2018
Shivendra Shivani, Suneeta Agarwal, Jasjit S. Suri
Some staganalysis methods run in the reverse direction. They first estimate the cover image from the stego image, after that just compare the cover and stego to find the difference and that difference is nothing but the secret message. Usually it is very difficult to find the exact cover image from the stego but the some steganalysis methods can work on an approximation of cover work only. The estimation process from the stego to cover work is called calibration.
Operational strategies for seru production system: a bi-objective optimisation model and solution methods
Published in International Journal of Production Research, 2020
Given collection S of nonempty subsets of a set X, an exact cover of X is a sub collection S* of S that satisfies the following two conditions: (1) the sets in S* are pairwise disjoint; and (2) the union of the sets in S* covers X.