Many graph problems require us to find subgraphs satisfying constraints such as no cycle, connected, degree-bounded and so on. Frontier-based search is a framework to construct a compressed data structure ZDD storing all subgraphs satisfying constraints in a given graph. Since frontier-based search processes edges one by one in a given order, we should determine an edge order of a given graph a...

In this paper is presented a parallel algorithm for computing a Lagrange interpolation on a Extended Fibonacci Cube EFC 1(n).The algorithm consists of three phases: initialisation phase, main phase in wich the Lagrange polynomials are computed and final phase in wich the terms of the interpolation formula are added together.

Exploring an unknown environment with multiple robots requires an efficient coordination method to minimize the total duration. A standard method to discover new areas is to assign frontiers (boundaries between unexplored and explored accessible areas) to robots. In this context, the frontier allocation method is paramount. This paper introduces a decentralized and computationally efficient fro...

A frontier-based tree-pruning algorithm (FBP) is proposed. The new method has comparable order of computational complexity, comparing with Cost-Complexity Pruning (CCP). Regarding tree pruning, it provides a full spectrum of information; specifically, (1) given the value of the penalization parameter λ, it gives the minimum size of a decision tree; (2) given the size of a decision tree, it prov...

Frontier-based exploration method are known to be efficient for multi-robot exploration systems. In this paper, we propose a novel, computationally inexpensive, frontier allocation method favoring a well balanced spatial distribution of robots in the environment. It is based on the computation of a position criteria. The position of a robot towards a frontier is defined by the number of robots ...

Frontier-based exploration is the most common approach to exploration, a fundamental problem in robotics. In frontier-based exploration, robots explore by repeatedly computing (and moving towards) frontiers, the segments which separate the known regions from those unknown. However, most frontier detection algorithms process the entire map data. This can be a time consuming process which slows d...

The context of this work is multi-robot exploration and mapping of unknown environments. Frontiers (boundaries between empty and unexplored areas) are points to go to in order to increase explored area. In this paper, we propose a frontier allocation method for the exploration and mapping of indoor environments using multiple robots. A wavefront propagation algorithm is used to build a local mi...

This paper focuses on wall-following exploration algorithm using two cooperating mobile robots. The aim is to decrease the exploration time and energy consumption. The new technique is a combination of wall-following exploration algorithm and frontier-based exploration algorithm. The proposed algorithm is divided into two stages: Firstly, one of the robots follows (detects) the entire of the en...