This paper proposes a new algorithm for the linear least squares problem where the unknown variables are constrained to be in a finite set. The factor graph that corresponds to this problem is very loopy; in fact, it is a complete graph. Hence, applying the Belief Propagation (BP) algorithm yields very poor results. The algorithm described here is based on an optimal tree approximation of the G...

The tree-depth problem can be seen as finding an elimination tree of minimum height for a given input graph G. We introduce bicriteria generalization in which additionally the width needs to bounded by some integer b. are interested case when G is line tree, proving that \(\mathcal {NP}\)-hard and obtaining polynomial-time additive 2b-approximation algorithm. This particular class graphs receiv...

This report describes the implementation of bonsaiG, a program for mixed-integer linear programming (MILP). bonsaiG is a research code, designed to explore the utility and power of arc consistency as a general technique for solving MILP problems, and to provide a foundation for exploring other techniques. It strives to provide maximum flexibility, control, and robustness, while retaining a reas...

Multistage stochastic mixed-integer programming is a powerful modeling paradigm appropriate for many problems involving a sequence of discrete decisions under uncertainty; however, they are difficult to solve without exploiting special structures. We present scenario-tree decomposition to establish bounds for unstructured multistage stochastic mixed-integer programs. Our method decomposes the s...

A long line of research on fixed parameter tractability integer programming culminated with showing that programs $n$ variables and a constraint matrix dual tree-depth $d$ largest entry $\Delta$ are solvable in time $g(d,\Delta){poly}(n)$ for some function $g$. However, the is not preserved by row operations, i.e., given program can be equivalent to another smaller tree-depth, thus does reflect...

An algorithm for solving linear programming problems can be used as a subroutine in methods for more complicated problems. Such methods usually involve solving a sequence of related linear programming problems, where the solution to one linear program is close to the solution to the next, that is, it provides a warm start for the next linear program. The branch and cut method for solving intege...

Tree theory, partitions of integer numbers, combinatorial mathematics and computer algebra are the basis for the construction of a powerful and efficient symbolic package for the derivation of Runge Kutta order conditions and principal truncation error terms.

We give a derived equivalence classification of algebras of the form Â/〈φ〉 for some piecewise hereditary algebra A of tree type and some automorphism φ of  such that φ(A) = A for some positive integer n.

The equitable tree-coloring can formulate a structure decomposition problem on the communication network with some security considerations. Namely, an tree-k-coloring of graph is vertex coloring using k distinct colors such that every color class induces forest and sizes any two classes differ by at most one. In this paper, we show theoretical results graphs proving d-degenerate maximum degree ...

We investigate the topological complexity of non Borel recognizable tree languages with regard to the difference hierarchy of analytic sets. We show that, for each integer n ≥ 1, there is a Dωn(Σ 1 1)-complete tree language Ln accepted by a (non deterministic) Muller tree automaton. On the other hand, we prove that a tree language accepted by an unambiguous Büchi tree automaton must be Borel. T...