Given two genomic maps G1 and G2 each represented as a sequence of n gene markers, the maximal strip recovery (MSR) problem is to retain the maximum number of markers in both G1 and G2 such that the resultant subsequences, denoted as G ∗ 1 and G ∗ 2, can be partitioned into the same set of maximal strips, which are common substrings of length greater than or equal to two. The complementary maxi...

We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings. This problem has applications in a wide variety of areas, most notably in data mining, computational biology, and in understanding the complexity of genetic algorithms. We show that the basic problem of finding a small set of patterns that match one set of strings but do not match ...

We present complexity results regarding a matching-type problem related to structural controllability of dynamical systems modelled on graphs. Controllability of a dynamical system is the ability to choose certain inputs in order to drive the system from any given state to any desired state; a graph is said to be structurally controllable if it represents the structure of a controllable system....

We investigated the relationship between H2O2 metabolism and the senescence process using soluble fractions, mitochondria, and peroxisomes from senescent pea (Pisum sativum L.) leaves. After 11 d of senescence the activities of Mn-superoxide dismutase, dehydroascorbate reductase (DHAR), and glutathione reductase (GR) present in the matrix, and ascorbate peroxidase (APX) and monodehydroascorbate...

In an effort to determine the biochemical markers for identifying genotypes before sowing for drought tolerance, changes in activities of antioxidant enzymes were determined in the seedlings of five drought-tolerant and five drought-sensitive wheat (Triticum aestivum L.) genotypes, each with different genetic background growing under normal and water deficit conditions induced by 6% mannitol. I...

The problem of partitioning a partially ordered set into a minimum number of chains is a well-known problem. In this paper we study a generalization of this problem, where we not only assume that the chains have bounded size, but also that a weight wi is given for each element i in the partial order such that wi ≤ wj if i ≺ j. The problem is then to partition the partial order into a minimum-we...

We consider complexity issues and upper bounds for defensive alliances and strong global offensive alliances in graphs. We prove that it is NP-complete to decide for a given 6-regular graph G and a given integer a, whether G contains a defensive alliance of order at most a. Furthermore, we prove that determining the strong global offensive alliance number γô(G) of a graph G is APX-hard for cubi...

We investigate the computational complexity of various problems for simple recurrent neural networks (RNNs) as formal models for recognizing weighted languages. We focus on the single-layer, ReLU-activation, rationalweight RNNs with softmax, which are commonly used in natural language processing applications. We show that most problems for such RNNs are undecidable, including consistency, equiv...

We consider labeled Traveling Salesman Problems, defined upon a complete graph of n vertices with colored edges. The objective is to find a tour of maximum (or minimum) number of colors. We derive results regarding hardness of approximation, and analyze approximation algorithms for both versions of the problem. For the maximization version we give a 1 2 -approximation algorithm and show that it...

We introduce and study a combinatorial problem called preference-constrained oriented matching. This problem is defined on a directed graph in which each node has preferences over its out-neighbors, and the goal is to find a maximum-size matching on this graph that satisfies a certain preference constraint. One of our main results is a structural theorem showing that if the given graph is compl...