A locally connected spanning tree of a graph G is a spanning tree T of G such that the set of all neighbors of v in T induces a connected subgraph of G for every v ∈ V (G). The purpose of this paper is to give linear-time algorithms for finding locally connected spanning trees on strongly chordal graphs and proper circular-arc graphs, respectively.

Lösung des jeweiligen Model-Checking Problems " nur " noch die Teilergeb-nisse zusammengesetzt werden. Auf diese Weise lösen wir die vier angespro-chenen Model-Checking Probleme für die Logik der ersten Stufe auf lokal baumartigen Strukturen (nicely locally tree-decomposable classes). Diese Algorithmen arbeiten alle in Zeit linear in der Größe der Eingabestruktur (plus der Größe der Ausgabe bei...

in this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. so the results in locally convex spaces can be translated in gradual normed linear spaces. finally, we give an examp...

A graph G is locally irregular if adjacent vertices of G have distinct degrees. An edge colouring of G is locally irregular if each of its colours induces a locally irregular subgraph of G. The irregular chromatic index of G refers to the least number of colours used by a locally irregular edge colouring of G (if any). We propose a linear-time algorithm for determining the irregular chromatic i...

We prove new upper bounds on the size of families of vectors in Zm with restricted modular inner products, when m is a large integer. More formally, if u1, . . . ,ut ∈ Zm and v1, . . . ,vt ∈ Zm satisfy 〈ui,vi〉 ≡ 0 (mod m) and 〈ui,vj〉 6≡ 0 (mod m) for all i 6= j ∈ [t], we prove that t ≤ O(m). This improves a recent bound of t ≤ m by [BDL13] and is the best possible up to the constant 8.47 when m...

Locally decodable codes (LDCs) are error correcting codes that allow for decoding of a single message bit using a small number of queries to a corrupted encoding. Despite decades of study, the optimal trade-off between query complexity and codeword length is far from understood. In this work, we give a new characterization of LDCs using distributions over Boolean functions whose expectation is ...

Despite the growing ubiquity of sensor deployments and the advances in sensor data analysis technology, relatively little attention has been paid to the spatial non-stationarity of sensed data which is an intrinsic property of the geographically distributed data. In this paper we deal with non-stationarity of geographically distributed data for the task of regression. At this purpose, we extend...

The Geographically Weighted Regression (GWR) is a method of spatial statistical analysis which allows the exploration of geographical differences in the linear effect of one or more predictor variables upon a response variable. The parameters of this linear regression model are locally determined for every point of the space by processing a sample of distance decay weighted neighboring observat...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...