In this paper, we study two classic optimization problems: minimum geometric dominating set and set cover. In the dominating set problem, for a given set of objects as input, the objective is to choose minimum number of input objects such that every input object is dominated by the chosen set of objects. Here, one object is dominated by the other if both of them have non-empty intersection regi...

In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

We show that hitting set and set cover problems with half-strips oriented in two opposite directions are NPcomplete.

This paper studies a learning approach to geometric shaping (GS) for concatenated two-level multi-level codes (MLC). Unlike standard bit-interleaved coded modulation (BICM), the proposed MLC protects only least reliable bits (LRBs) by an inner code, and thereby efficiently reduces complexity associated with soft-decision (SD) decoding compared BICM without performance degradation. We propose ne...

For robots to solve real world tasks, they often require the ability to reason about both symbolic and geometric knowledge. We present a framework, called KABouM, for integrating knowledge-level task planning and motion planning in a bounding geometry. By representing symbolic information at the knowledge level, we can model incomplete information, sensing actions and information gain; by repre...

The discipline of mathematics is characterized by a small, fundamental set of operators which, when taken in concert, support complex manipulations and analyses. In a similar sense, higher levels of spatial applications programming are founded upon a fundamental set of spatial operators. The tendency to focus upon geometric elements and operators based upon the dimensionality of space is perhap...