M. Held

Publications17
h-index9
Citations5,414
Highly Influential Citations273
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The Traveling-Salesman Problem and Minimum Spanning Trees
TLDR
It is shown that maxπwπ = C* precisely when a certain well-known linear program has an optimal solution in integers.
A dynamic programming approach to sequencing problems
TLDR
A dynamic programming approach to the solution of three sequencing problems: a scheduling problem involving arbitrary cost functions, the traveling-salesman problem, and an assembly line balancing problem that admits of numerical solution through the use of a simple recursion scheme.
Validation of subgradient optimization
TLDR
It is concluded that the “relaxation” procedure for approximately solving a large linear programming problem related to the traveling-salesman problem shows promise for large-scale linear programming.
The traveling-salesman problem and minimum spanning trees: Part II
TLDR
An efficient iterative method for approximating this bound closely from below is presented, and a branch-and-bound procedure based upon these considerations has easily produced proven optimum solutions to all traveling-salesman problems presented to it.
A Dynamic Programming Approach to Sequencing Problems
Finite-State Processes and Dynamic Programming
TLDR
A formalism within which the application of dynamic programming to discrete, deterministic problems is rigorously studied is developed, and the representations of discrete decision processes by monotone sequential decision processes are characterized.
Assembly-Line Balancing---Dynamic Programming with Precedence Constraints
This paper approaches the assembly-line balancing problem as a sequencing problem involving precedence constraints that prohibit the occurrence of certain orderings. This approach permits the…
Aspects of the Traveling Salesman Problem
TLDR
A large part of the extensive research conducted by IBM in the broad area of optimization, or mathematical programming, contributed to or was inspired by aspects of this challenging problem.
Large scale optimization and the relaxation method
An algorithm is given for the maximization of any function of many variables which may be described as the envelope of a family of linear functions. It is shown how the large-scale problems of linear…
Real-Time System Prototyping Based on a Heterogeneous Multi-Processor Environment
This paper presents a design environment based on rapid prototyping to support validation and design space exploration in the area of real-time systems. The design environment is built around a…
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