To any graph G can be associated a toric ideal I G. In this talk some recent joint work with Enrique Reyes and Christos Tatakis will be presented on the toric ideal of a graph. A characterization in graph theoretical terms of the elements of the Graver basis and the universal Gröbner basis of the toric ideal of a graph will be given. The Graver basis is the union of the primitive binomials of t...

In this paper we merge recent developments on exact algorithms for finding an ordering of vertices of a given graph that minimizes bandwidth (the BANDWIDTH problem) and for finding an embedding of a given graph into a line that minimizes distortion (the DISTORTION problem). For both problems we develop algorithms that work in O(9.363) time and polynomial space. For BANDWIDTH, this improves O(10...

In order to solve real world combinatorial optimization problems with a D-Wave quantum annealer it is necessary embed the problem at hand into hardware graph, namely Chimera or Pegasus. Most hard exhibit strong connectivity. For worst case scenario of complete there exists an efficient solution for embedding ideal graph. However, since machines almost always have broken qubits find We present n...

Spiking neural P systems with anti-spikes (ASN P systems, for short) are a variant of spiking neural P systems, which are inspired by inhibitory impulses/spikes or inhibitory synapses. The typical feature of ASN P systems is when a neuron contains both spikes and anti-spikes, the spikes and anti-spikes will immediately annihilate each other in a maximal way. In this work, we consider a restrict...

I Exploratory data analysis I Presenting results in concise, meaningful graphs and tables I Basics of inferenzial statistics I Organization of Experiments (Experimental Design) I Sequential statistical testing: a methdology for tuning The goal of dealing with Experimental Algorithmics is not only producing a more correct analysis but adding an important tool to the development of a good, functi...

We introduce the concept of multi-directional width-bounded geometric separators and obtain an improved separator for grid graphs. This yields an improved exact algorithm for the protein folding problem in the HP-model. For a grid graph G with n grid points P , there exists a separator A ⊆ P such that A has at most 1.02074 √ n points, and G−A has two disconnected subgraphs each with at most 2 3...

Some fast exact algorithms for the maximum weight clique problem have been proposed. Östergård’s algorithm is one of them. Kumlander says his algorithm is faster than it. But we confirmed that the straightforwardly implemented Kumlander’s algorithm is slower than Östergård’s algorithm. We propose some improvements on Kumlander’s algorithm. Keywords—Maximum weight clique, exact algorithm, branch...

We present a novel exact algorithm for the minimum graph bisection problem, whose goal is to partition a graph into two equallysized cells while minimizing the number of edges between them. Our algorithm is based on the branch-and-bound framework and, unlike most previous approaches, it is fully combinatorial. We present stronger lower bounds, improved branching rules, and a new decomposition t...

The complexity of an algorithm is usually specied by the maximum number of steps made by the algorithm, as a function of the size of the input. However, as dierent inputs of equal size can yield dramatically dierent algorithm runtime, the size of the input is not always an appropriate basis for predicting algorithm runtime. In this paper, we argue that the compressed size of the input is more a...