9,613 research outputs found
An Order-based Algorithm for Minimum Dominating Set with Application in Graph Mining
Dominating set is a set of vertices of a graph such that all other vertices
have a neighbour in the dominating set. We propose a new order-based randomised
local search (RLS) algorithm to solve minimum dominating set problem in
large graphs. Experimental evaluation is presented for multiple types of
problem instances. These instances include unit disk graphs, which represent a
model of wireless networks, random scale-free networks, as well as samples from
two social networks and real-world graphs studied in network science. Our
experiments indicate that RLS performs better than both a classical greedy
approximation algorithm and two metaheuristic algorithms based on ant colony
optimisation and local search. The order-based algorithm is able to find small
dominating sets for graphs with tens of thousands of vertices. In addition, we
propose a multi-start variant of RLS that is suitable for solving the
minimum weight dominating set problem. The application of RLS in graph
mining is also briefly demonstrated
The Weighted Independent Domination Problem: ILP Model and Algorithmic Approaches
This work deals with the so-called weighted independent domination problem, which is an -hard combinatorial optimization problem in graphs. In contrast to previous work, this paper considers the problem from a non-theoretical perspective. The first contribution consists in the development of three integer linear programming models. Second, two greedy heuristics are proposed. Finally, the last contribution is a population-based iterated greedy metaheuristic which is applied in two different ways: (1) the metaheuristic is applied directly to each problem instance, and (2) the metaheuristic is applied at each iteration of a higher-level framework---known as construct, merge, solve \& adapt---to sub-instances of the tackled problem instances. The results of the considered algorithmic approaches show that integer linear programming approaches can only compete with the developed metaheuristics in the context of graphs with up to 100 nodes. When larger graphs are concerned, the application of the populated-based iterated greedy algorithm within the higher-level framework works generally best. The experimental evaluation considers graphs of different types, sizes, densities, and ways of generating the node and edge weights
Industry applications of neutral-atom quantum computing solving independent set problems
Architectures for quantum computing based on neutral atoms have risen to
prominence as candidates for both near and long-term applications. These
devices are particularly well suited to solve independent set problems, as the
combinatorial constraints can be naturally encoded in the low-energy Hilbert
space due to the Rydberg blockade mechanism. Here, we approach this connection
with a focus on a particular device architecture and explore the ubiquity and
utility of independent set problems by providing examples of real-world
applications. After a pedagogical introduction of basic graph theory concepts
of relevance, we briefly discuss how to encode independent set problems in
Rydberg Hamiltonians. We then outline the major classes of independent set
problems and include associated example applications with industry and social
relevance. We determine a wide range of sectors that could benefit from
efficient solutions of independent set problems -- from telecommunications and
logistics to finance and strategic planning -- and display some general
strategies for efficient problem encoding and implementation on neutral-atom
platforms.Comment: 28 pages, 9 example application
The Directed Dominating Set Problem: Generalized Leaf Removal and Belief Propagation
A minimum dominating set for a digraph (directed graph) is a smallest set of
vertices such that each vertex either belongs to this set or has at least one
parent vertex in this set. We solve this hard combinatorial optimization
problem approximately by a local algorithm of generalized leaf removal and by a
message-passing algorithm of belief propagation. These algorithms can construct
near-optimal dominating sets or even exact minimum dominating sets for random
digraphs and also for real-world digraph instances. We further develop a core
percolation theory and a replica-symmetric spin glass theory for this problem.
Our algorithmic and theoretical results may facilitate applications of
dominating sets to various network problems involving directed interactions.Comment: 11 pages, 3 figures in EPS forma
Adaptive Scatter Search to Solve the Minimum Connected Dominating Set Problem for Efficient Management of Wireless Networks
An efficient routing using a virtual backbone (VB) network is one of the most significant improvements in the wireless sensor network (WSN). One promising method for selecting this subset of network nodes is by finding the minimum connected dominating set (MCDS), where the searching space for finding a route is restricted to nodes in this MCDS. Thus, finding MCDS in a WSN provides a flexible low-cost solution for the problem of event monitoring, particularly in places with limited or dangerous access to humans as is the case for most WSN deployments. In this paper, we proposed an adaptive scatter search (ASS-MCDS) algorithm that finds the near-optimal solution to this problem. The proposed method invokes a composite fitness function that aims to maximize the solution coverness and connectivity and minimize its cardinality. Moreover, the ASS-MCDS methods modified the scatter search framework through new local search and solution update procedures that maintain the search objectives. We tested the performance of our proposed algorithm using different benchmark-test-graph sets available in the literature. Experiments results show that our proposed algorithm gave good results in terms of solution quality
Improving Local Search for Minimum Weighted Connected Dominating Set Problem by Inner-Layer Local Search
The minimum weighted connected dominating set (MWCDS) problem is an important variant of connected dominating set problems with wide applications, especially in heterogenous networks and gene regulatory networks. In the paper, we develop a nested local search algorithm called NestedLS for solving MWCDS on classic benchmarks and massive graphs. In this local search framework, we propose two novel ideas to make it effective by utilizing previous search information. First, we design the restart based smoothing mechanism as a diversification method to escape from local optimal. Second, we propose a novel inner-layer local search method to enlarge the candidate removal set, which can be modelled as an optimized version of spanning tree problem. Moreover, inner-layer local search method is a general method for maintaining the connectivity constraint when dealing with massive graphs. Experimental results show that NestedLS outperforms state-of-the-art meta-heuristic algorithms on most instances
A novel multi-objective evolutionary algorithm based on space partitioning
To design an e ective multi-objective optimization evolutionary algorithms (MOEA), we need to address the following issues: 1) the sensitivity to the shape of true Pareto front (PF) on decomposition-based MOEAs; 2) the loss of diversity due to paying so much attention to the convergence on domination-based MOEAs; 3) the curse of dimensionality for many-objective optimization problems on grid-based MOEAs. This paper proposes an MOEA based on space partitioning (MOEA-SP) to address the above issues. In MOEA-SP, subspaces, partitioned by a k-dimensional tree (kd-tree), are sorted according to a bi-indicator criterion de ned in this paper. Subspace-oriented and Max-Min selection methods are introduced to increase selection pressure and maintain diversity, respectively. Experimental studies show that MOEA-SP outperforms several compared algorithms on a set of benchmarks
- …