On a Construction of Digital Convex -gons of Minimum Diameter
On a dual network exterior point simplex type algorithm and its computational behavior
The minimum cost network flow problem, (MCNFP) constitutes a wide category of network flow problems. Recently a new dual network exterior point simplex algorithm (DNEPSA) for the MCNFP has been developed. This algorithm belongs to a special “exterior point simplex type” category. Similar to the classical dual network simplex algorithm (DNSA), this algorithm starts with a dual feasible tree-solution and after a number of iterations, it produces a solution that is both primal and dual feasible, i.e....
On a dual network exterior point simplex type algorithm and its computational behavior∗
The minimum cost network flow problem, (MCNFP) constitutes a wide category of network flow problems. Recently a new dual network exterior point simplex algorithm (DNEPSA) for the MCNFP has been developed. This algorithm belongs to a special “exterior point simplex type” category. Similar to the classical dual network simplex algorithm (DNSA), this algorithm starts with a dual feasible tree-solution and after a number of iterations, it produces a...
On a facet of the balanced subgraph polytope
On blockers in bounded posets.
On cycling in the simplex method of the transportation problem
This paper shows that cycling of the simplex method for the m × n transportation problem where k-1 zero basic variables are leaving and reentering the basis does not occur once it does not occur in the k × k assignment problem. A method to disprove cycling for a particular k is applied for k=2,3,4,5 and 6.
On Geometric Optimization with Few Violated Constraints.
On minimizing total tardiness in a serial batching problem
We study the problem of scheduling jobs on a serial batching machine to minimize total tardiness. Jobs of the same batch start and are completed simultaneously and the length of a batch equals the sum of the processing times of its jobs. When a new batch starts, a constant setup time occurs. This problem s-batch is known to be NP-Hard in the ordinary sense. In this paper we show that it is solvable in pseudopolynomial time by dynamic programming.
On Minimizing Total Tardiness in a Serial Batching Problem
We study the problem of scheduling jobs on a serial batching machine to minimize total tardiness. Jobs of the same batch start and are completed simultaneously and the length of a batch equals the sum of the processing times of its jobs. When a new batch starts, a constant setup time s occurs. This problem 1|s-batch | ∑Ti is known to be NP-Hard in the ordinary sense. In this paper we show that it is solvable in pseudopolynomial time by dynamic programming.
On some Interconnections Between Combinatorial Optimization and Extremal Graph Theory
On the coefficients of the max-algebraic characteristic polynomial and equation
No polynomial algorithms are known for finding the coefficients of the characteristic polynomial and characteristic equation of a matrix in max- algebra. The following are proved: (1) The task of finding the max-algebraic characteristic polynomial for permutation matrices encoded using the lengths of their constituent cycles is NP-complete. (2) The task of finding the lowest order finite term of the max-algebraic characteristic polynomial for a matrix can be converted to the assignment problem....
On the complexity of determining tolerances for ε-optimal solutions to min-max combinatorial optimization problems
This paper studies the complexity of sensitivity analysis for optimal and ε-optimal solutions to general 0-1 combinatorial optimization problems with min-max objectives. Van Hoesel and Wagelmans [9] have studied the complexity of sensitivity analysis of optimal and ε-optimal solutions to min-sum problems, and Ramaswamy et al. [17] the complexity of sensitivity analysis of optimal solutions to min-max problems. We show that under some mild assumptions the sensitivity analysis of ε-optimal solutions...
On the Pallet Loading Problem
On the solution of traveling salesman problems.
On the Steiner 2-edge connected subgraph polytope
In this paper, we study the Steiner 2-edge connected subgraph polytope. We introduce a large class of valid inequalities for this polytope called the generalized Steiner F-partition inequalities, that generalizes the so-called Steiner F-partition inequalities. We show that these inequalities together with the trivial and the Steiner cut inequalities completely describe the polytope on a class of graphs that generalizes the wheels. We also describe necessary conditions for these inequalities to...
On the structure of the quadratic Boolean problem polytope
On-Line Computation and Maximum-Weighted Hereditary Subgraph Problems
Online LIB problems : heuristics for bin covering and lower bounds for bin packing
We consider the NP Hard problems of online Bin Covering and Packing while requiring that larger (or longer, in the one dimensional case) items be placed at the bottom of the bins, below smaller (or shorter) items — we call such a version, the LIB version of problems. Bin sizes can be uniform or variable. We look at computational studies for both the Best Fit and Harmonic Fit algorithms for uniform sized bin covering. The Best Fit heuristic for this version of the problem is introduced here. The...
Online LIB problems: Heuristics for Bin Covering and lower bounds for Bin Packing
We consider the NP Hard problems of online Bin Covering and Packing while requiring that larger (or longer, in the one dimensional case) items be placed at the bottom of the bins, below smaller (or shorter) items — we call such a version, the LIB version of problems. Bin sizes can be uniform or variable. We look at computational studies for both the Best Fit and Harmonic Fit algorithms for uniform sized bin covering. The Best Fit heuristic for this version of the problem is introduced here. The...
Optimal traffic assignment in a SS/TDMA frame : a new approach by set covering and column generation