Publications of Giovanni Rinaldi

This page shows all publications that appeared in the IASI annual research reports. Authors currently affiliated with the Institute are always listed with the full name.

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IASI Research Report n. 244  (Previous    Next)


Naddef D., Giovanni Rinaldi

The graphical relaxation: a new framework for the symmetric traveling salesman polytope.

ABSTRACT
A present trend in the study of the Symmetric Traveling Salesman Polytope (STSP(n)) is to use, as a relaxation of the polytope, the graphical relaxation (GTSP(n)) rather than the traditional monotone relaxation which seems to have attained its limits. In this paper, we show the very close relationship between STSP(n) and GTSP(n). In particular, we prove that every nontrival facet of STSP(n) is the intersection of n + 1 facets of GTSP(n), n of which are induced by the degree inequalities. This fact permits us to define a standard form for the facet-inducing inequalities for STSP(n), that we call tight triangular, and to devise a proof technique that can be used to show that many known facet-inducing inequalities for GTSP(n) induce also facets of STSP(n). In addition, we give conditions that permit to obtain facet-inducing inequalities by composition of facet-inducing inequalities for STSP(n) and general lifting theorems to derive facet-inducing inequalities for STSP(n + k) from inequalities inducing facets of STSP(n).
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