It is well known that chordal graphs are exactly the graphs of acyclic simplicial complexes . In this note we consider the analogous class of graphs associated with acyclic cubical complexes . These graphs can be characterized among median graphs by forbidden convex subgraphs . They possess a number of properties (in analogy to chordal graphs) not shared by all median graphs . In particular , w...

Classical approaches to location problems are based on the minimization of the average distance (the median concept) or the minimization of the maximum distance (the center concept) to the service facilities. The median solution concept is primarily concerned with the spatial efficiency while the center concept is focused on the spatial equity. The k-centrum model unifies both the concepts by m...

We give a TDI description for a class of polytopes which corresponds to a restricted 2-matching problem. The perfect matching polytope, triangle-free perfect 2-matching polytope and relaxations of the traveling salesman polytope are members of this class. For a class of restrictions G. Cornuéjols, D. Hartvigsen and W.R. Pulleyblank have shown that the unweighted problem is tractable; here we sh...

Results: The mean Lysholm score improved from 45.6 (range, 11-76) to 71.9 (range, 30-91). The median preoperative Tegner activity scale score was 3 (range, 1-7), while the median postoperative score was 4 (range, 1-9). The median Western Ontario and McMaster Universities Arthritis Index (WOMAC) total score improved from 38 (range, 1-57) preoperatively to 6 postoperatively (range, 0-52). The mea...

When we have several results of measuring or estimating the same quantities, it is desirable to aggregate them into a single estimate for the desired quantities. A natural requirement is that if the majority of estimates has some property, then the aggregate estimate should have the same property. It turns out that it is not possible to require this for all possible properties – but we can requ...

Policymakers are often interested in understanding how the receipt of a subsidy affects economic behavior. In the case of housing assistance, they may want to understand how cost savings (if they exist) from the receipt of a rental subsidy affects their spending on other goods. This paper analyzes Consumer Expenditure (CE) Survey data to investigate the relationship between rental assistance an...

Let M(m,n) be the complexity of checking whether a graph G with m edges and n vertices is a median graph. We show that the complexity of checking whether G is triangle-free is at most M(m,m). Conversely, we prove that the complexity of checking whether a given graph is a median graph is at most O(m log n) + T (m log n, n), where T (m,n) is the complexity of finding all triangles of the graph. W...

Given a set of graphs, the median graph has been theoretically presented as a useful concept to infer a representative of the set. However, the computation of the median graph is a highly complex task and its practical application has been very limited up to now. In this work we present a new genetic algorithm for the median graph computation. A set of experiments on real data, where none of th...

In this paper we consider two existing methods to generate a representative of a given set of graphs, that satisfy the following two conditions. On the one hand, that they are applicable to graphs with any kind of labels in nodes and edges and on the other hand, that they can handle relatively large amount of data. Namely, the approximated algorithms to compute the Median Graph via graph embedd...