The classic view of metabolism as a collection of metabolic pathways is being questioned with the currently available possibility of studying whole networks. Novel ways of decomposing the network into modules and motifs that could be considered as the building blocks of a network are being suggested. In this work, we introduce a new definition of motif in the context of metabolic networks. Unlike in previous works on (other) biochemical networks, this definition is not based only on topological features. We propose instead to use an alternative definition based on the functional nature of the components that form the motif, which we call a reaction motif. After introducing a formal framework motivated by biological considerations, we present complexity results on the problem of searching for all occurrences of a reaction motif in a network and introduce an algorithm that is fast in practice in most situations. We then show an initial application to the study of pathway evolution. Finally, we give some general features of the observed number of occurrences in order to highlight some structural features of metabolic networks.

A MILP model for an extended version of the Flexible Job Shop Scheduling problem is proposed. The extension allows the precedences between operations of a job to be given by an arbitrary directed acyclic graph rather than a linear order. The goal is the minimization of the makespan. Theoretical and practical advantages of the proposed model are discussed. Numerical experiments show the performance of a commercial exact solver when applied to the proposed model. The new model is also compared with a simple extension of the model described by \"Ozg\"uven, \"Ozbakir, and Yavuz (Mathematical models for job-shop scheduling problems with routing and process plan flexibility, Applied Mathematical Modelling, 34:1539--1548, 2010), using instances from the literature and instances inspired by real data from the printing industry.Comment: 15 pages, 2 figures, 4 tables. Optimization Letters, 201

The MAXIMUM PLANAR SUBGRAPH problemᎏgiven a graph G, find a largest planar subgraph of Gᎏhas applications in circuit layout, facility layout, and graph drawing. No previous polynomial-time approximation algorithm for this NP-Complete problem was known to achieve a performance ratio larger than 1r3, which is achieved simply by producing a spanning tree of G. We present the first approximation algorithm for MAXIMUM PLANAR SUBGRAPH with higher Ž . performance ratio 4r9 instead of 1r3 . We also apply our algorithm to find large outerplanar subgraphs. Last, we show that both MAXIMUM PLANAR SUB-GRAPH and its complement, the problem of removing as few edges as possible to leave a planar subgraph, are Max SNP-Hard. ᮊ

No abstract

We study the problem of, given two sequences x and y over a finite alphabet, finding a repetitionfree longest common subsequence of x and y. We show several algorithmic results, a complexity result, and we describe a preliminary experimental study based on the proposed algorithms.