An artificial-free simplex-type algorithm for general LP models

An Intro to LP and the Simplex Algorithm Primal Simplex

Towards Hardware Implementation of the Simplex Algorithm for LP Decoding

Combining methods of mathematical optimization theory and applications from communications engineering recently led to new approaches for error correction in data transmission systems. In this new discipline, also called LP decoding, researchers so far focussed on theoretical aspects. In this paper, we study how these new algorithms from mathematical theory can be accelerated using dedicated ha...

An Efficient Extension of Network Simplex Algorithm

In this paper, an efficient extension of network simplex algorithm is presented. In static scheduling problem, where there is no change in situation, the challenge is that the large problems can be solved in a short time. In this paper, the Static Scheduling problem of Automated Guided Vehicles in container terminal is solved by Network Simplex Algorithm (NSA) and NSA+, which extended the stand...

A Counterexample to H. Arsham’s “initialization of the Simplex Algorithm: an Artificial-free Approach”∗

In “An artificial-free simplex-type algorithm for general LP models” [Math. Comput. Model., 25 (1997), pp. 107–123] and “Initialization of the simplex algorithm: An artificial-free approach” [SIAM Rev., 39 (1997), pp. 736–744], Arsham presents a new Phase 1 algorithm for the simplex method of linear programming, which allegedly obviates the use of artificial variables. He claims in [SIAM Rev., ...

An LP-Designed Algorithm for Constraint Satisfaction

The class Max (r, 2)-CSP consists of constraint satisfaction problems with at most two r-valued variables per clause. For instances with n variables and m binary clauses, we present an O(nr)-time algorithm. It is the fastest algorithm for most problems in the class (including Max Cut, Max 2-Sat, and weighted Maximum Independent Set), and in combination with “Generalized CSPs” introduced in a co...