The curvature of a polytope, deflned as the largest possible total curvature of the associated central path, can be regarded as the continuous analogue of its diameter. We prove the analogue of the result of Klee and Walkup. Namely, we show that if the order of the curvature is less than the dimension d for all polytope deflned by 2d inequalities and for all d, then the order of the curvature i...

We further study the effect of odd cycle inequalities in the description of the polytopes associated with the p-median and uncapacitated facility location problems. We show that the obvious integer linear programming formulation together with the odd cycle inequalities completely describe these polytopes for the class of restricted Y-graphs. This extends our results for the class of Y-free grap...

The curvature of a polytope, defined as the largest possible total curvature of the associated central path, can be regarded as a continuous analogue of its diameter. We prove an analogue of the result of Klee and Walkup. Namely, we show that if the order of the curvature is less than the dimension d for all polytopes defined by 2d inequalities and for all d , then the order of the curvature is...

We propose in this paper a tour of the symmetric traveling salesman polytope, focusing on inequalities that can be deened on sets. The most known inequalities are all of this type. Many papers have appeared which give more and more complex valid inequalities for this polytope, but no intuitive idea on why these inequalities are valid has ever been given. In order to help in understanding these ...

Dimension-independent Harnack inequalities are derived for a class of subordinate semigroups. In particular, for a diffusion satisfying the BakryEmery curvature condition, the subordinate semigroup with power α satisfies a dimension-free Harnack inequality provided α ∈ ` 1 2 , 1 ́ , and it satisfies the log-Harnack inequality for all α ∈ (0, 1). Some infinite-dimensional examples are also presen...

A new notion of partition-determined functions is introduced, and several basic inequalities are developed for the entropy of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these functions. Here a compound set means a set obtained by varying each argument of a function of several variables over a set associated with that argument, wh...

The Internet is constantly growing but the available resources, i.e. bandwidth, are limited. Using bandwidth efficiently to provide high quality of service to users is referred to as traffic engineering. This is of utmost importance. Traffic in IP networks is commonly routed along shortest paths with respect to auxiliary link weights, e.g. using the OSPF or IS-IS protocol. Here, shortest path r...

In this paper we investigate separation problems for classes of inequalities valid for the polytope associated with the Steiner tree packing problem , a problem that arises, e. g., in VLSI routing. The separation problem for Steiner partition inequalities is NP-hard in general. We show that it can be solved in polynomial time for those instances that come up in switchbox routing. Our algorithm ...

Given a combinatorial optimization problem Π and an increasing finite sequence c of natural numbers, we obtain a cardinality constrained version Πc of Π by permitting only those feasible solutions of Π whose cardinalities are members of c. We are interested in polyhedra associated with those problems, in particular in inequalities that cut off solutions of forbidden cardinality. Maurras [11] an...