Cut elimination is the main tool in proof theoretical research. The emphasis there, however, is on the cut–elimination procedure, i.e., the dynamical aspect of cut–elimination. In this paper we want to show that also the statical aspect, i.e., the mere existence of cut–free derivations, has consequences which may be viewed to belong to Descriptive Set Theory or Generalized Recursion Theory. We ...

We explore the structure of the maximum vertex independence sets in fullerenes: plane trivalent graphs with pentagonal and hexagonal faces. At the same time, we will consider benzenoids: plane graphs with hexagonal faces and one large outer face. In the case of fullerenes, a maximum vertex independence set may constructed as follows: (i) Pair up the pentagonal faces. (ii) Delete the edges of a ...

We study the convex set L n deened by L n := fX j X = (x ij) positive semideenite n n matrix; x ii = 1 for all ig: We describe several geometric properties of L n. In particular, we show that L n has 2 n?1 vertices, which are its rank one matrices, corresponding to all bipartitions of the set f1; 2; : : : ; ng. Our main motivation for investigating the convex set L n comes from com-binatorial o...

We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them fixedparameter tractable and which are easy to compute. This tractability tends either to be the result of a simple dynamic program or of a decomposition which has...

We discuss the effectiveness of branch and cut for solving large instances of the independent set problem. Typical LP formulations, even strengthened by clique inequalities, yield poor bounds for this problem. We prove that a strong bound is obtained by the use of the so called “rank inequalities”, which generalize the clique inequalities. For some problems the clique inequalities imply the ran...

Consider the problem of routing the electrical connections among two large terminal sets in circuit layout. A realistic model for this problem is given by the vertex-disjoint packing of two Steiner trees (2VPST), which is known to be NP-complete. This work presents an investigation on the 2VPST polyhedra. The main idea is to depart from facet-deening inequalities for a vertex-weighted Steiner t...

Marco Trubian Dipartimento di Scienze dell’Informazione Università degli studi di Milano 20135 Milan, Italy Phone:+39 02 503 16230, Fax:+39 02 503 16253 [email protected] Abstract Multiple combinations of hardware and network components can be selected to design an information technology (IT) infrastructure that satisfies performance requirements. The professional criterion to deal with thes...

• Probabilistic method and applications • " Tail Bounds " • Chernoff bounds In this lecture, we complete the introduction to approximation algorithms and by using the max-cut and dominating set problem, we introduce the probabilistic method of solving problems. We also study some techniques for bounding the probability that a random variable takes value far from its expectation, known as tail b...

If C is a clutter with n vertices and q edges whose clutter matrix has column vectors A = {v1, . . . , vq}, we call C an Ehrhart clutter if {(v1, 1), . . . , (vq , 1)} ⊂ {0, 1} n+1 is a Hilbert basis. Letting A(P ) be the Ehrhart ring of P = conv(A), we are able to show that if A is the clutter matrix of a uniform, unmixed MFMC clutter C, then C is an Ehrhart clutter and in this case we provide...

The Valued Constraint Satisfaction Problem (VCSP) is a general framework encompassing many optimisation problems. We discuss precisely what it means for a problem to be modelled in the VCSP framework. Using our analysis, we show that some optimisation problems, such as (s, t)-Min-Cut and Submodular Function Minimisation, can be modelled using a restricted set of valued constraints which are tra...