Given a directed graph D = (N, A) and a sequence of positive integers 1 ≤ c1 < c2 < · · · < cm ≤ |N |, we consider those path and cycle polytopes that are defined as the convex hulls of simple paths and cycles of D of cardinality cp for some p ∈ {1, . . . , m}, respectively. We present integer characterizations of these polytopes by facet defining linear inequalities for which the separation pr...

Flow cover inequalities are among the most effective valid inequalities for capacitated fixed-charge network flow problems. These valid inequalities are based on implications for the flow quantity on the cut arcs of a two-partitioning of the network, depending on whether some of the cut arcs are open or closed. As the implications are only on the cut arcs, flow cover inequalities can be obtaine...

We present novel Markov-type and Nikolskii-type inequalities for multivariate polynomials associated with arbitrary downward closed multi-index sets in any dimension. Moreover, we show how the constant of these inequalities changes, when the polynomial is expanded in series of tensorized Legendre or Chebyshev or Gegenbauer or Jacobi orthogonal polynomials indexed by a downward closed multi-inde...

We discuss three natural pseudodistances and pseudometrics on a bounded domain in IR based on polynomial inequalities.

Parikh’s Theorem says that the commutative image of every context free language is the commutative image of some regular set. Pilling has shown that this theorem is essentially a statement about least solutions of polynomial inequalities. We prove the following general theorem of commutative Kleene algebra, of which Parikh’s and Pilling’s theorems are special cases: Every finite system of polyn...

We consider the multilinear polytope which arises naturally in binary polynomial optimization. Del Pia and Di Gregorio introduced class of odd $$\beta $$ -cycle inequalities valid for this polytope, showed that these generally have Chvátal rank 2 with respect to standard relaxation that, together flower inequalities, they yield a perfect formulation cycle hypergraph instances. Moreover, describ...

The complexity of linear programming is discussed in the "integer" and "real number" models of computation. Even though the integer model is widely used in theoretical computer science, the real number model is more useful for estimating an algorithm's running time in actual computation. Although the ellipsoid algorithm is a polynomial-time algorithm in the integer model, we prove that it has u...

We consider spatial databases and queries definable using first-order logic and real polynomial inequalities. We are interested in topological queries: queries whose result only depends on the topological aspects of the spatial data. Two spatial databases are called topologically elementary equivalent if they cannot be distinguished by such topological first-order queries. Our contribution is a...

We develop the theory of twisted L-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on H(M, R) and they generalize the standard notions. A new feature of the twisted L-cohomology theory is that in addition to satisfying the standard L Morse inequalities, they also satisfy certain asymptotic L Morse inequalities. These...

In this paper we discuss the generation of strong valid inequalities for (mixed) integer knapsack sets based on lifting of valid inequalities for basic knapsack sets with two integer variables (and one continuous variable). The description of the basic polyhedra can be made in polynomial time. We use superadditive valid functions in order to obtain sequence independent lifting.