We find surprisingly simple formulas for the limiting probability that the rank of a randomly selected vertex in a randomly selected phylogenetic tree or generalized phylogenetic tree is a given integer.

Cyclic timetabling for public transportation companies is usually modeled by the periodic event scheduling problem. To deduce a mixed-integer programming formulation, artificial integer variables have to be introduced. There are many ways to define these integer variables. We show that the minimal number of integer variables required to encode an instance is achieved by introducing an integer v...

A hypergraph H has tree-width k (a notion introduced by Robertson and Seymour) if k is the least integer such that H admits a tree-decomposition of tree-width k. We prove a compactness theorem for this notion, that is, if every finite subhypergraph of H has tree-width < k, then H itself has tree-width < k. This result will be used in a later paper on well-quasi-ordering infinite graphs.

We present an algorithm that for any graph G and integer k ≥ 0 in time polynomial in the size of G either nds a spanning tree with at least k internal vertices, or outputs a new graph GR on at most 3k vertices and an integer k′ such that G has a spanning tree with at least k internal vertices if and only if GR has a spanning tree with at least k ′ internal vertices. In other words, we show that...

We propose a novel solution for semantic-based XML schema matching, taking a mathematical programming approach. This method identifies the globally optimal solution for the problem of matching two XML schemas by reducing the tree-to-tree matching problem to simpler problems of pathto-path, node-to-node, and word-to-word matching. We formulate these matching problems as maximum-weighted bipartit...

Yarn's [6] algorithm solves the problem of finding an optimal code tree, optimal in the sense of minimum average cost, when the code symbols are of unequal cost and the source symbols are equiprobable. He addresses both exhaustive codes, for which the code tree is a full tree, as well as nonexhaustive codes, but only the exhaustive case will be of concern here. In particular, for code symbol co...

a set $s$ of vertices in a graph $g$ is a dominating set if every vertex of $v-s$ is adjacent to some vertex in $s$. the domination number $gamma(g)$ is the minimum cardinality of a dominating set in $g$. the annihilation number $a(g)$ is the largest integer $k$ such that the sum of the first $k$ terms of the non-decreasing degree sequence of $g$ is at most the number of edges in $g$. in this p...

We present a self-learning approach for synthesizing programs from integer sequences. Our method relies on tree search guided by learned policy. system is tested the On-Line Encyclopedia of Integer Sequences. There, it discovers, its own, solutions 27987 sequences starting basic operators and without human-written training examples.

For every integer k > 2 let [k] 1 is a subset of [k]<N of the form {w} ∪ { ww0(a0) ...wn(an) : n ∈ {0, ...,m− 1} and a0, ..., an ∈ [k] } where w is a word over k and (wn) m−1 n=0 is a finite sequence of left variable words over k. We study the behavior of a family of measurable events in a probability space index...

The paper describes a procedure for mixed integer programming that allows branches to be imposed 'by degrees', which can subsequently be revised or weeded out according to their relative influence. It is an adaptive approach in which the branch and bound tree can be maillipulated and rl'Structured. The approach also yields measures of the costs of imposing the branches that lead to integer solu...