On Hamilton paths in grid graphs

Abstract

In this paper we consider an approach to solve the Hamilton path problem for grid graphs. This approach is based on an explicit reduction from the problem to the satisfiability problem. Gridworlds are extensively used for design of experiments as models of real world. In particular, grid graphs are popular testbeds for different hard problems. In particular, grid graphs used for investigation of robotic planning problems (see e.g. [1]). For instance, grid graph can be considered as a map of some indoor environment. Vacuum cleaning robot needs cover the environment. The robot must visit each vertex only once to prevent a damage of the floor. It is clear that we can consider the Hamilton path problem (HP) for grid graphs as a model for this robotic problem. In this paper we consider an approach to solve HP. Note that HP is NP-complete [2]. Encoding different hard problems as instances of SAT has caused considerable interest (see e.g. PACS[3] - [15]). We consider an explicit reduction from HP to the satisfiability problem.

An Approach to Design of DNA Smart Programmable Membranes

“…Efficient satisfiability algorithms has recently caused considerable interest. We have used genetic algorithms GA [1] (see [24]), GA [2] (see [25]), GA [3] (see [26]) for the satisfiability problem. We have created a test set from random sets of DNA tiles.…”

“…It is easy to see that we can assume that P[i] is 3CNF for any 0 < i < 9 (see [24]). Let P be a conjunction of P[i] where 0 < i < 9.…”

The Problem of Sensor-Mission Assignment in Wireless Sensor Networks

“…It should be noted that many algorithmic problems can be modeled as graph problems (see e.g. [22][23][24][25][26][27][28]). In particular, the problem of sensor-mission assignment in wireless sensor networks is modeled as a weighted bipartite graph whose vertex sets consist of sensors S = {S [1]; ... ; S[n]} and missions M = {M [1]; ... ; M[m]} (see [18]).…”

“…Various manufacturing and robot tasks require environments equipped with intelligent systems of sensors (see e.g. [1][2][3][4][5]). We need to solve different placement, scheduling, and assignment problems to obtain such environments.…”

“…Also, sensor placement (see e.g. [10][11][12]) is extensively used for improved robotic navigation (see e.g. [13][14][15][16][17]).…”