Proof: By double implication: If there is an augmenting path, then M is not maximum: OK. Suppose there is no augmenting path for M but Mopt is maximum. For each node in M Mopt (where is a xor), the degree is either 0, 1 or 2, thus M Mopt consists of disjoint paths or cycles. • The cycles must be even (otherwise M or Mopt is not a matching). • Suppose there is an odd path. Since #Mopt is maximum...

The p-median problem is one of the discrete optimization problem in location theory which aims to satisfy total demand with minimum cost. A high-level algorithmic approach can be specialized to solve optimization problem. In recent years, meta-heuristic methods have been applied to support the solution of Combinatorial Optimization Problems (COP). Collision Bodies Optimization algorithm (CBO) a...

The article addresses combinatorial optimization schemes for design of multi-layer communication network topology. The paper consists of three parts: (a) description of system issues as basic requirements, trends (e.g., evolution, upgradeability), and a ”system space” for contemporary network design; (b) brief description of some basic combinatorial optimization problems as follows: multicriter...