一种求解顶点覆盖问题的混合遗传算法

顶点覆盖问题是一个NP难问题,在排序、计算机网络等现实生活中有许多的应用。使用基本遗传算法进行搜索时,存在着局部搜索能力较弱的不足,本文提出了一种新的求解最小顶点覆盖问题的混合遗传算法,将基本遗传算法与局部优化策略相结合,改善遗传算法的局部搜索能力,加快求解该问题的速度。对几种典型无向图的实验证实了新方法的有效性,其整体性能优于现有的一些顶点覆盖问题遗传算法。     

图的最小顶点覆盖问题的面上DNA解法

1994年，Adleman提出一种解决NP完全问题的新方法-DNA计算．之后又出现了许多关于DNA计算的改进操作并增加了其可靠性，其中面上操作是一种很有效的方法．本文利用DNA计算的固态处理(面上计算)解决了图论中又-NP完全问题一图的最小顶点覆盖问题．构造了含有6个顶点10条边的图的顶点集子集对应的数据池之后，进行了一系列的合成、杂交、清洗、变性等生物操作，得到所有覆盖对应的DNA序列，然后通过编址过程得到所要求的最小覆盖．     

最小顶点覆盖问题的竞争决策算法

竞争决策算法是在分析大自然生物世界特别是人类的各种竞争机制和决策原理的基础上,利用竞争造就优化、决策左右结果的特性来达到优化目的的新型寻优算法。采用竞争决策算法原理,利用竞争决策算法的通用模型,求解图的最小顶点覆盖问题。     

最小顶点覆盖问题的闭环DNA算法

提出了闭环DNA计算模型的基本概念及其基本生化实验,并给出了解决最小顶点覆盖问题的闭环DNA算法。在闭环DNA算法中,提出并实现了用删除实验直接构造顶点覆盖补集的构想;再通过电泳实验得到最小顶点覆盖的补集,由补集得到最小顶点覆盖。这使得算法的设计独特而新颖;由于算法仅用到基本的生化实验,这使得算法的实现简捷、可靠。     

化学反应优化算法求解最小顶点覆盖问题

给出了基于化学反应优化算法(CRO)求解最小顶点覆盖问题的一个新方法.首先根据最小顶点覆盖问题的无向图邻接矩阵,设计了参与化学化反应优化算法的分子编码和适应度函数;同时针对最小顶点覆盖问题的特性创造性地设计了化学反应优化算法中分子操作的四个重要算子;最后通过模拟化学反应中分子势能趋于稳定的过程,在问题的解空间中搜索其最优解.实验结果表明,通过与遗传算法(GA)、蚁群优化算法(ACO)等比较分析,所提的新方法对于求解无向图的最小顶点覆盖问题是有效的,并且与一般遗传算法相比在求解速度等方面有明显的改善.     

图的最小顶点覆盖问题的DNA表面计算模型

基于生化反应原理的DNA计算具有强大的并行运算能力,DNA计算机在求解NP问题上存在着硅计算机无法比拟的先天的优越性。采用荧光标记的策略,给出了一种新的图的最小顶点覆盖问题的DNA表面计算模型。该模型首先将问题解空间的DNA分子固定在固体载体上,然后通过进行相应的生化反应来求得图的最小顶点覆盖问题的所有解。新算法利用荧光猝灭技术,通过观察荧光来排除非解,具有编码、解读简单和错误率低的特点。     

一种求解平面图的最小顶点覆盖算法

最小顶点覆盖问题是图论中经典的组合优化问题,在实际生活中有着广泛的应用价值。根据最小顶点覆盖与最大独立集在图论中事实上是属于等价问题这一特性,从最大独立集的角度出发,根据最大独立集的特性,设计了一种求解简单平面图的最大独立集算法,从而求出最小顶点覆盖。通过实验结果的比对验证算法的正确性和有效性。     

一种增量式约简方法求解最小顶点覆盖问题

最小顶点覆盖问题是一个应用很广泛的NP难题,针对该问题给出一种增量式属性约简方法。首先将最小顶点覆盖问题转化为一个决策表的最小属性约简问题;利用增量式属性约简思想,随着图中边数的增多,提出一种更新最小顶点覆盖的增量式属性约简算法;该算法时间复杂度低于计算整个图的最小顶点覆盖的时间复杂度,同时针对大规模图问题,可随着边的增加动态更新最小顶点覆盖,因此降低了属性约简的方法求解最小顶点覆盖问题的运行时间;实验结果表明该算法的可行性和有效性。     

一种混合化学反应优化算法求解最小顶点覆盖问题

最小顶点覆盖问题是组合最优化问题,在实际应用中有较广泛的应用,是一个NP难问题。论文针对最小顶点覆盖问题给出了一种混合化学反应优化求解算法。首先根据无向图的邻接矩阵表示法,设计了参与化学化反应的分子编码和目标函数;同时把贪心算法思想创造性地融入到化学反应优化算法的四个重要反应算子中,以加快局部较优解的搜索过程;最后通过模拟化学反应中分子势能趋于稳定的过程,在问题的解空间中搜索其最优解。模拟实验结果表明,该算法对于求解无向图的最小顶点覆盖问题是有效的,并且在求解效率等方面有一定的改善。     

顶点覆盖变体问题的确定参数可解算法研究

参数复杂性作为算法研究的一个重要分支,近十年来在国际上受到了广泛的关注,确定参数可解算法是参数复杂性研究的一类重要问题,因此被广泛研究。本文主要研究了顶点覆盖问题的两个变体问题：一个是连接的顶点覆盖问题,二是含权的树型顶点覆盖问题。这两个问题都是对原始的顶点覆盖问题加入了一些限制的变体问题。本文给出了这两个问题的确定参数可解算法,并且是目前的最好结果。     

模糊需求条件下车辆路径问题的模糊模拟

研究具有模糊需求的车辆路径问题,针对具有不确定需求的单车辆单车场的车辆路径问题,建立了基于模糊可信性理论的模糊机会约束规划模型,并提出了求解该问题的一种基于模糊模拟的混合遗传算法。同时,在最小化车辆总行驶距离的目标下,通过实验研究决策者主观偏好对决策目标的影响,并给出最佳主观偏好值。     

On the parameterized vertex cover problem for graphs with perfect matching

A vertex cover of an n-vertex graph with perfect matching contains at least n/2 vertices.In this paper,we study the parameterized complexity of the problem vc-pm*that decides if a given graph with perfect matching has a vertex cover of size bounded by n/2+k.We first present an algorithm of running time O*(4k)for a variation of the vertex cover problem on K¨onig graphs with perfect matching.This algorithm combined with the iterative compression technique leads to an algorithm of running time O*(9k)for the problem vc-pm*.Our result improves the previous best algorithm of running time O*(15k)for the vc-pm*problem,which reduces the problem to the almost 2-sat problem and solves the latter by Razgon and O’Sullivan’s recent algorithm.     

Approximation algorithm for weighted weak vertex cover

The problem of efficiently monitoring the network flow is regarded as the problem to find out the minimum weighted weak vertex cover set for a given graph G = (V, E). In this paper, we give an approximation algorithm to solve it, which has the approximation ratio ln d 1, where d is the maximum degree of the vertex in graph G, and improve the previous work.     

A primal-dual approximation algorithm for the k-prize-collecting minimum vertex cover problem with submodular penalties

In this paper, we consider the k-prize-collecting minimum vertex cover problem with submodular penalties, which generalizes the well-known minimum vertex cover problem, minimum partial vertex cover problem and minimum vertex cover problem with submodular penalties. We are given a cost graph G=(V,E;c) and an integer k. This problem determines a vertex set S\subseteq V such that S covers at least k edges. The objective is to minimize the total cost of the vertices in S plus the penalty of the uncovered edge set, where the penalty is determined by a submodular function. We design a two-phase combinatorial algorithm based on the guessing technique and the primal-dual framework to address the problem. When the submodular penalty cost function is normalized and nondecreasing, the proposed algorithm has an approximation factor of 3. When the submodular penalty cost function is linear, the approximation factor of the proposed algorithm is reduced to 2, which is the best factor if the unique game conjecture holds.     

基于核心化技术的点覆盖改进算法

点覆盖是一个著名的NP难解问题,在通信网络和生物信息学等领域具有重要应用。针对点覆盖的研究主要集中在启发式或近似算法,其主要不足是无法实现全局最优。核心化是处理难解问题的一种新方法。提出融合启发式操作和核心化操作的算法框架,利用核心化技术进行点覆盖启发式算法优化。核心化操作挖掘出全局最优的顶点集,而启发式操作改变网络拓扑,使下一轮核心化操作能够继续,两者交叉执行实现解精度优化。实验结果表明,提出的算法在不同网络中均能实现不同程度的优化,在几乎所有稀疏网络实例中获得了最优解。     

A 2-approximation NC algorithm for connected vertex cover and tree cover

The connected vertex cover problem is a variant of the vertex cover problem, in which a vertex cover is additional required to induce a connected subgraph in a given connected graph. The problem is known to be NP-hard and to be at least as hard to approximate as the vertex cover problem is. While several 2-approximation NC algorithms are known for vertex cover, whether unweighted or weighted, no parallel algorithm with guaranteed approximation is known for connected vertex cover. Moreover, converting the existing sequential 2-approximation algorithms for connected vertex cover to parallel ones results in RNC algorithms of rather high complexity at best.In this paper we present a 2-approximation NC (and RNC) algorithm for connected vertex cover (and tree cover). The NC algorithm runs in O(log²n) time using O(Δ²(m+n)/logn) processors on an EREW-PRAM, while the RNC algorithm runs in O(logn) expected time using O(m+n) processors on a CRCW-PRAM, when a given graph has n vertices and m edges with maximum vertex degree of Δ.     

Parameterized algorithm for eternal vertex cover

In this paper we initiate the study of a “dynamic” variant of the classical Vertex Cover problem, the Eternal Vertex Cover problem introduced by Klostermeyer and Mynhardt, from the perspective of parameterized algorithms. This problem consists in placing a minimum number of guards on the vertices of a graph such that these guards can protect the graph from any sequence of attacks on its edges. In response to an attack, each guard is allowed either to stay in his vertex, or to move to a neighboring vertex. However, at least one guard has to fix the attacked edge by moving along it. The other guards may move to reconfigure and prepare for the next attack. Thus at every step the vertices occupied by guards form a vertex cover. We show that the problem admits a kernel of size k⁴(k+1)+2k, which shows that the problem is fixed parameter tractable when parameterized by the number of available guards k. Finally, we also provide an algorithm with running time O(²O(k²)+nm) for Eternal Vertex Cover, where n is the number of vertices and m the number of edges of the input graph. In passing we also observe that Eternal Vertex Cover is NP-hard, yet it has a polynomial time 2-approximation algorithm.     

Mean analysis of an online algorithm for the vertex cover problem

In 2005, Demange and Paschos proposed in [M. Demange, V.Th. Paschos, On-line vertex-covering, Theoret. Comput. Sci. 332 (2005) 83-108] an online algorithm (noted LR here) for the classical vertex cover problem. They shown that, for any graph of maximum degree Δ, LR constructs a vertex cover whose size is at most Δ times the optimal one (this bound is tight in the worst case).Very recently, two of the present authors have shown in [F. Delbot, C. Laforest, A better list heuristic for vertex cover, Inform. Process. Lett. 107 (2008) 125-127] that LR has interesting properties (it is a good “list algorithm” and it can easily be distributed). In addition, LR has good experimental behavior in spite of its Δ approximation (or competitive) ratio and the fact that it can be executed without the knowledge of the full instance at the beginning.In this paper we analyze it deeper and we show that LR has good “average” performances: we prove that its mean approximation ratio is strictly less than 2 for any graph and is equal to 1+e−2≈1.13 in paths. LR is then a very interesting algorithm for constructing small vertex covers, despite its bad worst case behavior.     

PTAS for connected vertex cover in unit disk graphs

This paper gives the first polynomial time approximation scheme for the connected vertex cover problem in unit disk graphs.