We give the first, as far as we know, feasible proof of König’s Min-Max Theorem (KMM), a fundamental result in combinatorial matrix theory, and we show the equivalence of KMM to various Min-Max principles, with proofs of low complexity.

Modular cut-elimination is a particular notion of ”cut-elimination in the presence of non-logical axioms” that is preserved under the addition of suitable rules. We introduce syntactic necessary and sufficient conditions for modular cut-elimination for standard calculi, a wide class of (possibly) multipleconclusion sequent calculi with generalized quantifiers. We provide a ”universal” modular c...

In this paper we consider the notions of global-fairness (G-fairness) and bounded-fairness (B-fairness) for arbitrary Petri nets (PNs). G-fairness in a PN guarantees every transition occurs infinitely often in every valid firing sequence of infinite length. B-fairness guarantees a bound on the number of times a transition in the PN can fire without some transition firing at least once. These pr...

We study continuous (strongly) minimal cut generating functions for the model where all variables are integer. We consider both the original Gomory-Johnson setting, as well as a recent extension by Cornuéjols and Yıldız. We show that for any continuous minimal or strongly minimal cut generating function, there exists an extreme cut generating function that approximates the (strongly) minimal fu...

In this paper we present a simple and efficient implementation of a min-max priority queue, reflected min-max priority queues. The main merits of our construction are threefold. First, the space utilization of the reflected min-max heaps is much better than the naive solution of putting two heaps back-to-back. Second, the methods applied in this structure can be easily used to transform ordinar...

If A ⊆ ω, n ≥ 2, and the function max({x1, . . . , xn} ∩ A) is partial recursive, it is easily seen that A is recursive. In this paper, we weaken this hypothesis in various ways (and similarly for “min” in place of “max”) and investigate what effect this has on the complexity of A. We discover a sharp contrast between retraceable and coretraceable sets, and we characterize sets which are the un...

A nonvariational generation of a min-max principle by A. Lazer is made. And it is used to prove a new existence results for a nonconservative systems of ordinary differential equations with resonance.

The high cost of supercomputers and the need for large-scale computational resources has led to the development of network of computational resources known as Grid. To better use tremendous capabilities of this large scale distributed system, effective and efficient scheduling algorithms are needed. Many such algorithms have been designed and implemented. We introduce a new scheduling algorithm...

We study min–max theory for the area functional among hypersurfaces constrained in a smooth manifold with boundary. A Schoen–Simon-type regularity result is proved integral varifolds which satisfy variational inequality and restricts to stable minimal hypersurface interior. Based on this, we show that any admissible family of sweepouts $$\Pi $$ compact boundary, there always exists closed $$C^{...