2 research outputs found
A heuristic approach for dividing graphs into bi-connected components with a size constraint
In this paper we propose a new problem of finding the maximal bi-connected
partitioning of a graph with a size constraint (MBCPG-SC). With the goal of
finding approximate solutions for the MBCPG-SC, a heuristic method is developed
based on the open ear decomposition of graphs. Its essential part is an
adaptation of the breadth first search which makes it possible to grow
bi-connected subgraphs. The proposed randomized algorithm consists of growing
several subgraphs in parallel. The quality of solutions generated in this way
is further improved using a local search which exploits neighboring relations
between the subgraphs. In order to evaluate the performance of the method, an
algorithm for generating pseudo-random unit disc graphs with known optimal
solutions is created. The conducted computational experiments show that the
proposed method frequently manages to find optimal solutions and has an average
error of only a few percent to known optimal solutions. Further, it manages to
find high quality approximate solutions for graphs having up to 10.000 nodes in
reasonable time
A Heuristic Method for Solving the Problem of Partitioning Graphs with Supply and Demand
In this paper we present a greedy algorithm for solving the problem of the
maximum partitioning of graphs with supply and demand (MPGSD). The goal of the
method is to solve the MPGSD for large graphs in a reasonable time limit. This
is done by using a two stage greedy algorithm, with two corresponding types of
heuristics. The solutions acquired in this way are improved by applying a
computationally inexpensive, hill climbing like, greedy correction procedure.
In our numeric experiments we analyze different heuristic functions for each
stage of the greedy algorithm, and show that their performance is highly
dependent on the properties of the specific instance. Our tests show that by
exploring a relatively small number of solutions generated by combining
different heuristic functions, and applying the proposed correction procedure
we can find solutions within only a few percent of the optimal ones