P2-Packing问题参数算法的改进

P_2-Packing问题是一个典型的NP难问题.目前这个问题的最好结果是时间复杂度为O(2~(5.301k))的参数算法,其核的大小为15k.通过对P_2-packing问题的结构作进一步分析,提出了改进的核心化算法,得到大小为7k的核,并在此基础上提出了一种时间复杂度为O(2~(4.142k))的参数算法,大幅度改进了目前文献中的最好结果.     

加权3-Set Packing 的改进算法

Packing问题构成了一类重要的NP难问题.对于加权3-SetPacking问题,把问题转化成加权3-SetPacking Augmentation问题进行求解,即主要讨论如何从一个已知的最大加权k-packing求得一个权值最大的(k+1)-packing.通过对问题结构的分析,结合Color-Coding技术,首先给出了一种时间复杂度为O*(10.63k)的参数算法,极大地改进了目前文献中的最好结果O*(12.83k).通过对(k+1)-packing结构的进一步分析,利用集合划分技术将上述结果降到O*(7.563k).     

一种基于链暗示技术的Min-CVCB问题的精确算法

随着VLSI(超大规模集成电路)技术的发展,关于可重构阵列二分图的受约束最小点覆盖(Min-CVCB)问题受到了很多文献的关注.作为点覆盖问题的子问题,该问题已被证明是NP-完全问题.人们利用核心化和分支即使给出了时间复杂度为O((ku k1)|G| 1.26ku k1)的目前最好算法,然而仍不能满足实际工程的需要.通过进一步深入分析二分图的结构,对含有权值大于或等于3的块的连通子图分析其可能连接情况后充分利用"链暗示"技术和分枝搜索技术来建立起新的搜索递推关系;对于分枝后的块提出了一种动态规划算法,其可在多项式时间内完成处理.整个参数算法的运行时间为O((ku k1)|G| 1.1892ku k1),极大地改进了目前的最好结果.     

加权3D-Matching的改进算法

Matching问题构成了一类重要的NP难问题.此类问题在诸多领域中有着重要的应用,如调度、代码优化等领域.对于加权3D-matching问题,通过深入分析问题的结构特性,可以转化成加权3D-matching augmentation问题进行求解,即从一个最大加权的k-matching着手构造权值最大的(k+1)-matching.从问题的特殊结构特性出发,给出了加权3D-matching augmentation问题特有的性质: k- matching中存在2列使得该2列至少有2k/3元素被包含在(k+1)-matching中所对应的2列中.基于给出的性质,通过运用color-coding和动态规划技术,给出了一个时间复杂度为O* (4.823k)的参数算法,最终求解加权3D-matching问题.该算法较目前文献中的最好结果O* (5.473k)有了极大的改进.     

基于立方体剖分的传感器网络快速三维k-覆盖判定算法

提出了一种传感器网络中基于立方体剖分的三维k 覆盖快速判定算（CP-RTCDA）和三维最大k 覆盖问题的快速求解算法（CP-RTMCDA）。算法首先把感兴趣区域剖分为立方体区域，从而将复杂的空间区域覆盖问题转化为简单的立方体区域覆盖问题。理论分析与仿真实验表明, 针对具有n个节点的传感器网络, 新算法的计算时间复杂度为O(n)，远低于已有算法O(n3logn)的计算时间复杂度。     

一种可重构阵列的最小瑕点覆盖算法

关于可重构阵列的瑕点覆盖问题受到了很多文献的关注，特别地，关于可重构阵列的最小瑕点覆盖问题等价于二分图的受约束最小点覆盖问题，并被证明是NP-完全问题。针对本问题提出的算法运行时间为O(1．19^k kn)，这里k为可替换行与列的数目，改进了原有的最好结果，其运行时间为0(1．266k kn)，较好地组合并扩展了研究参数计算的最新技术与经典匹配理论，且具有较好的实用价值。这是关于可重构阵列的最小瑕点覆盖问题算法又一较大的改进，也是目前最小点覆盖问题相关参数算法的较有意义的改进。     

测试集问题的集合覆盖贪心算法的深入近似

测试集问题是一个有着广泛应用的NP难问题.集合覆盖贪心算法是测试集问题的一个常用近似算法,其由集合覆盖问题得到的近似比21nn+1能否改进是一个公开的问题.集合覆盖贪心算法的推广被用来求解生物信息学中出现的冗余测试集问题.通过分析条目对被区分次数的分布情况,用去随机方法证明了集合覆盖贪心算法对测试集问题的近似比可以为1.51nn+0.5lnlnn+2,从而缩小了这种算法近似比分析的间隙.另外,给出了集合覆盖贪心算法对冗余度为n-1的加权冗余测试集问题的近似比的紧密下界(2-o(1))lnn-Θ 1).     

Multicut问题参数算法的改进

Multicut问题即在一个图上删除最少个数的顶点,使得预先给定的一组顶点对均不连通.该问题是NP难的.在深入分析问题结构特点的基础上,运用集合划分策略和相关问题的最新研究结果,对它提出了一种时间复杂度为O*的参数化算法,其中,l为给定的顶点对数目,k为需删除的顶点个数.该算法明显改进了当前时间复杂度为O*的最好算法.     

Multicut问题参数算法的改进

Multicut问题即在一个图上删除最少个数的顶点,使得预先给定的一组顶点对均不连通.该问题是NP难的.在深入分析问题结构特点的基础上,运用集合划分策略和相关问题的最新研究结果,对它提出了一种时间复杂度为O*的参数化算法,其中,l为给定的顶点对数目,k为需删除的顶点个数.该算法明显改进了当前时间复杂度为O*的最好算法.     

高维空间球集覆盖问题的改进1+ε近似算法

高维空间球集的覆盖问题是指对高维空间中多个球构成的集合S,构造一个直径最小的球来覆盖S中所有已知球。本文提出了球集直径的概念,给出求解球集直径的1/3~(1/2)近似算法。基于此算法求解球集实例集合S的初始核心集,进而给出高维空间球集覆盖问题的1+ε近似算法,算法时间复杂度为O(nd/ε+d2/ε3/2(1/ε+d)lg1/ε)。算法保证核心集中球的个数为O(1/ε),与S中球的个数和空间维数无关。     

一个基于着色和动态规划的3-维匹配问题算法

3-维匹配问题是六个经典的NP完全问题之一,在调度、分配、交通和网络流等问题方面有很强的应用.参数计算理论是近年来发展起来的研究和解决NP-难问题的新方法.针对3-维匹配问题,目前确定式参数算法的最好结果是O*(163k).本文结合着色和动态规划技术,提出了一个算法运行时间为O*(3.423k)的确定式参数算法,大大提高了算法的运行效率.     

Using Nondeterminism to Design Efficient Deterministic Algorithms

In this paper we illustrate how nondeterminism can be used conveniently and effectively in designing efficient deterministic algorithms. In particular, our method gives a parameterized algorithm of running time O((5.7 k)^k n) for the 3-D matching problem, which significantly improves the previous algorithm by Downey et al. The algorithm can be generalized to yield an improved algorithm for the r-D matching problem for any positive integer r. The method can also be employed in designing deterministic algorithms for other optimization problems as well.     

An Improved Approximation Algorithm for the Most Points Covering Problem

In this paper we present a polynomial time approximation scheme for the most points covering problem. In the most points covering problem, n points in R ², r>0, and an integer m>0 are given and the goal is to cover the maximum number of points with m disks with radius r. The dual of the most points covering problem is the partial covering problem in which n points in R ² are given, and we try to cover at least p≤n points of these n points with the minimum number of disks. Both these problems are NP-hard. To solve the most points covering problem, we use the solution of the partial covering problem to obtain an upper bound for the problem and then we generate a valid solution for the most points covering problem by a careful modification of the partial covering solution. We first present an improved approximation algorithm for the partial covering problem which has a better running time than the previous algorithm for this problem. Using this algorithm, we attain a \((1 - \frac{{2\varepsilon }}{{1 +\varepsilon }})\)-approximation algorithm for the most points covering problem. The running time of our algorithm is \(O((1+\varepsilon )mn+\epsilon^{-1}n^{4\sqrt{2}\epsilon^{-1}+2}) \) which is polynomial with respect to both m and n, whereas the previously known algorithm for this problem runs in \(O(n \log n +n\epsilon^{-6m+6} \log (\frac{1}{\epsilon}))\) which is exponential regarding m.     

An O(2<Superscript>O(k)</Superscript>n<Superscript>3</Superscript>) FPT Algorithm for the Undirected Feedback Vertex Set Problem

We describe an algorithm for the Feedback Vertex Set problem on undirected graphs, parameterized by the size k of the feedback vertex set, that runs in time O(c^kn³) where c = 10.567 and n is the number of vertices in the graph. The best previous algorithms were based on the method of bounded search trees, branching on short cycles. The best previous running time of an FPT algorithm for this problem, due to Raman, Saurabh and Subramanian, has a parameter function of the form 2^{O(k log k /log log k)}. Whether an exponentially linear in k FPT algorithm for this problem is possible has been previously noted as a significant challenge. Our algorithm is based on the new FPT technique of iterative compression. Our result holds for a more general form of the problem, where a subset of the vertices may be marked as forbidden to belong to the feedback set. We also establish "exponential optimality" for our algorithm by proving that no FPT algorithm with a parameter function of the form O(2^o(k)) is possible, unless there is an unlikely collapse of parameterized complexity classes, namely FPT = M[1].     

RUSPACE(log n) \subseteq DSPACE(log2 n/log log n)

We present a deterministic algorithm running in space O(log² n /log log n ) solving the connectivity problem on strongly unambiguous graphs. In addition, we present an O(log n ) time-bounded algorithm for this problem running on a parallel pointer machine. Received February 1997, and in revised form August 1997, and in final form February 1998.     

A modified genetic algorithm with fuzzy roulette wheel selection for job-shop scheduling problems

The job-shop scheduling problem is one of the most difficult production planning problems. Since it is in the NP-hard class, a recent trend in solving the job-shop scheduling problem is shifting towards the use of heuristic and metaheuristic algorithms. This paper proposes a novel metaheuristic algorithm, which is a modification of the genetic algorithm. This proposed algorithm introduces two new concepts to the standard genetic algorithm: (1) fuzzy roulette wheel selection and (2) the mutation operation with tabu list. The proposed algorithm has been evaluated and compared with several state-of-the-art algorithms in the literature. The experimental results on 53 JSSPs show that the proposed algorithm is very effective in solving the combinatorial optimization problems. It outperforms all state-of-the-art algorithms on all benchmark problems in terms of the ability to achieve the optimal solution and the computational time.