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© 2024 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG About this entry Cite this entry Mitchell, J.E. (2024). Integer Programming: Branch-and-Cut Algorithms. In: Pardalos, P.M., Prokopyev, O.A. (eds) Encyclopedia of Optim...
The abstract representations of these for the simple data structure described here are Vertex = <integer>; // v Edge = <integer,integer>; // v0, v1 Triangle <integer,integer,integer>; // v0, v1, v2 VData = <application-specific vertex data>; EData = <application-specific edge data...
We provide the first exact formulas for including recursive relations via auxiliary functions as well as concise and satisfying representations and even quasi-explicit formulas. We also discuss some of the intricate fractal-like symmetry of the sequence and the development of algorithms for computing ....
For the design of our proposed MIC decoder, we utilize MI maximizing quantization to design an information optimized processing chain that uses only quantizer labels instead of real valued representations [12]. To that end, we first review the principle idea of the MI based quantizer design approa...
The connection between polynomial optimization, maximum cliques and Turán densities is explored in [34]. (2) Maximum clique problems and their definition and solution in specific representations In [35], the maximum weighted clique problem (see Section 2) is represented by matroids and solved by ...
If the value of the integer literalthat does not havesize-suffix(since C++23)is too big to fit in any of the types allowed by suffix/base combination and the compiler supports an extended integer type (such as__int128) which can represent the value of the literal, the literal may be ...
Some portions of the preceding detailed descriptions have been presented in terms of algorithms and symbolic representations of operations on data bits within a computer memory. These algorithmic descriptions and representations are the ways used by those skilled in the data processing arts to most effe...
in each instance it requires human input in order to find a suitable set of algebraic rules to help the solver. An alternative approach using Groebner basis algorithms has been considered [39]. This is a purely algebraic approach based on polynomials. Since the language of polynomials allows one...
calculus of variations is broadly used for some disciplines such as pure mathematics, engineering, and applied mathematics. In addition, the analysts have lately revealed that the physical frameworks with dissipation can be unmistakably modeled more precisely by utilizing non-integer representations [5]....