On some simplicial elimination schemes for chordal graphs

We present here some results on particular elimination schemes for chordal graphs, namely we show that for any chordal graph we can construct in linear time a simplicial elimination scheme starting with a pending maximal clique attached via a minimal separator maximal (resp. minimal) under inclusion among all minimal separators

Unique perfect phylogeny is NP-hard

We answer, in the affirmative, the following question proposed by Mike Steel as a $100 challenge: "Is the following problem NP-hard? Given a ternary phylogenetic X-tree T and a collection Q of quartet subtrees on X, is T the only tree that displays Q ?

A survey on algorithmic aspects of modular decomposition

The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important preprocessing step to solve a large number of combinatorial optimization problems. Since the first polynomial time algorithm in the early 70's, the algorithmic of the modular decomposition has known an important development. This paper survey the ideas and techniques that arose from this line of research

A general method for common intervals

Given an elementary chain of vertex set V, seen as a labelling of V by the set {1, ...,n=|V|}, and another discrete structure over $V$, say a graph G, the problem of common intervals is to compute the induced subgraphs G[I], such that $I$ is an interval of [1, n] and G[I] satisfies some property Pi (as for example Pi= "being connected"). This kind of problems comes from comparative genomic in bioinformatics, mainly when the graph $G$ is a chain or a tree (Heber and Stoye 2001, Heber and Savage 2005, Bergeron et al 2008). When the family of intervals is closed under intersection, we present here the combination of two approaches, namely the idea of potential beginning developed in Uno, Yagiura 2000 and Bui-Xuan et al 2005 and the notion of generator as defined in Bergeron et al 2008. This yields a very simple generic algorithm to compute all common intervals, which gives optimal algorithms in various applications. For example in the case where $G$ is a tree, our framework yields the first linear time algorithms for the two properties: "being connected" and "being a path". In the case where $G$ is a chain, the problem is known as: common intervals of two permutations (Uno and Yagiura 2000), our algorithm provides not only the set of all common intervals but also with some easy modifications a tree structure that represents this set

Graph classes and forbidden patterns on three vertices

This paper deals with graph classes characterization and recognition. A popular way to characterize a graph class is to list a minimal set of forbidden induced subgraphs. Unfortunately this strategy usually does not lead to an efficient recognition algorithm. On the other hand, many graph classes can be efficiently recognized by techniques based on some interesting orderings of the nodes, such as the ones given by traversals. We study specifically graph classes that have an ordering avoiding some ordered structures. More precisely, we consider what we call patterns on three nodes, and the recognition complexity of the associated classes. In this domain, there are two key previous works. Damashke started the study of the classes defined by forbidden patterns, a set that contains interval, chordal and bipartite graphs among others. On the algorithmic side, Hell, Mohar and Rafiey proved that any class defined by a set of forbidden patterns can be recognized in polynomial time. We improve on these two works, by characterizing systematically all the classes defined sets of forbidden patterns (on three nodes), and proving that among the 23 different classes (up to complementation) that we find, 21 can actually be recognized in linear time. Beyond this result, we consider that this type of characterization is very useful, leads to a rich structure of classes, and generates a lot of open questions worth investigating.Comment: Third version version. 38 page

Why Government Bonds Are Sold by Auction and Corporate Bonds by Posted-Price Selling

When information is costly, a seller may wish to prevent prospective buyers from acquiring information, for the cost of information acquisition is ultimately borne by the seller. A seller can achieve the desired prevention of information acquisition through posted-price selling, by offering prospective buyers a discount that is such as to deter them from gathering information. No such prevention is possible in the case of an auction. Clearly, a discount is costly to the seller. We establish the result that the seller prefers posted-price selling when the cost of information acquisition is high, and auctions when it is low. We view corporate bonds as an instance of the former case, and government bonds as an instance of the latter.Government Bonds; Corporate Bonds; Auctions; Posted-Price Selling; Costly Information

Algorithmic Aspects of Switch Cographs

This paper introduces the notion of involution module, the first generalization of the modular decomposition of 2-structure which has a unique linear-sized decomposition tree. We derive an O(n^2) decomposition algorithm and we take advantage of the involution modular decomposition tree to state several algorithmic results. Cographs are the graphs that are totally decomposable w.r.t modular decomposition. In a similar way, we introduce the class of switch cographs, the class of graphs that are totally decomposable w.r.t involution modular decomposition. This class generalizes the class of cographs and is exactly the class of (Bull, Gem, Co-Gem, C_5)-free graphs. We use our new decomposition tool to design three practical algorithms for the maximum cut, vertex cover and vertex separator problems. The complexity of these problems was still unknown for this class of graphs. This paper also improves the complexity of the maximum clique, the maximum independant set, the chromatic number and the maximum clique cover problems by giving efficient algorithms, thanks to the decomposition tree. Eventually, we show that this class of graphs has Clique-Width at most 4 and that a Clique-Width expression can be computed in linear time

An Analysis of Shareholder Agreements.

Shareholder agreements govern the relations among shareholders in privately held firms, such as joint ventures and venture capital-backed companies. We provide an economic explanation for key clauses in such agreements—namely, put and call options, tag-along and drag-along rights, demand and piggy-back rights, and catch-up clauses. In a dynamic moral hazard setting, we show that these clauses can ensure that the contract parties make efficient ex ante investments in the firm. They do so by constraining renegotiation. In the absence of the clauses, ex ante investment would be distorted by unconstrained renegotiation aimed at (i) precluding value-destroying ex post transfers, (ii) inducing value-increasing ex post investments, or (iii) precluding hold-out on value-increasing sales to a trade buyer or the IPO market.Corporate Governance; Restructuring; Investment Decision;

Negotiating over Banking Secrecy: The Case of Switzerland and the European Union

Over the period 2002 to 2003,Switzerland and the European Union (EU) were engaged in negotiations regarding banking secrecy. The EU's stated goal was for Switzerland to abolish banking secrecy. Switzerland refused and offered to impose a withholding tax on interest income instead. The two parties eventually agreed on the latter solution. We examine the effect of these negotiations on the share prices of four Swiss banks: UBS, Credit Suisse Group (CSG), Julius Baer (Baer), and Vontobel. Overall, investors believe that bank profitability will not be impacted by the imposition of the withholding tax. The event-by-event response of the share prices differs across banks. Whereas the two universal banks (UBS and CSG) primarily react to the threat of sanctions on their EU-based operations, the private banks (Baer and Vontobel) react strongly to events suggesting that banking secrecy might be abolished.Banking Secrecy; Switzerland; Event Study