The problem of radio channel assignments with multiple levels of interference depending on distance can be modeled using graph theory. The authors previously introduced a model of labeling by real numbers. Given a graph G, possibly infinite, and real numbers k1, k2, . . . , kp ≥ 0, a L(k1, k2, . . . , kp)-labeling of G assigns real numbers f(x) ≥ 0 to the vertices x, such that the labels of ver...

A fundamental research area in relation with analyzing the complexity of optimization problems are approximation algorithms. For combinatorial optimization a vast theory of approximation algorithms has been developed, see [1]. Many natural optimization problems involve real numbers and thus an uncountable search space of feasible solutions. A uniform complexity theory for real number decision p...

Abstract Tensor shape mismatch is a common source of bugs in deep learning programs. We propose new type-based approach to detect tensor mismatches. One the main features our best-effort inference. As inference problem undecidable general, we allow static type/shape be performed only manner. If cannot guarantee absence inconsistencies, dynamic checks are inserted into program. Another feature g...