An effective local search for the maximum clique problem

We propose a variable depth search based algorithm, called k-opt local search (KLS), for the maximum clique problem. KLS efficiently explores the k-opt neighborhood defined as the set of neighbors that can be obtained by a sequence of several add and drop moves that are adaptively changed in the feasible search space. Computational results on DIMACS benchmark graphs indicate that KLS is capable of finding considerably satisfactory cliques with reasonable running times in comparison with those of state-of-the-art metaheuristics.     

A simple simulated annealing algorithm for the maximum clique problem

Simulated annealing technique has mostly been used to solve various optimization and learning problems, and it is well known that the maximum clique problem is one of the most studied NP-hard optimization problems owing to its numerous applications. In this note, a simple simulated annealing algorithm for the maximum clique problem is proposed and tested on all 80 DIMACS maximum clique instances. Although it is simple, the proposed simulated annealing algorithm is efficient on most of the DIMACS maximum clique instances. The simulation results show that the proposed simulated annealing algorithm outperforms a recent efficient simulated annealing algorithm proposed by Xu and Ma, and the solutions obtained by the proposed simulated annealing algorithm have the equal quality with those obtained by a recent trust region heuristic algorithm of Stanislav Busygin.     

An exact bit-parallel algorithm for the maximum clique problem

This paper presents a new exact maximum clique algorithm which improves the bounds obtained in state of the art approximate coloring by reordering the vertices at each step. Moreover, the algorithm can make full use of bit strings to sort vertices in constant time as well as to compute graph transitions and bounds efficiently, exploiting the ability of CPUs to process bitwise operations in blocks of size the ALU register word. As a result it significantly outperforms a current leading algorithm.     

Weighted and unweighted maximum clique algorithms with upper bounds from fractional coloring

The linear programming relaxation of the minimum vertex coloring problem, called the fractional coloring problem, is NP-hard. We describe efficient approximation procedures for both the weighted and unweighted versions of the problem. These fractional coloring procedures are then used for generating upper bounds for the (weighted or unweighted) maximum clique problem in the framework of a branch-and-bound procedure. Extensive computational testing shows that replacing the standard upper bounding procedures based on various integer coloring heuristics with the somewhat more expensive fractional coloring procedure results in improvements of the bound by up to one-fourth in the unweighted and up to one-fifth in the weighted case, accompanied by a decrease in the size of the search tree by a factor of almost two.This research was supported by the National Science Foundation under Grant No. DDM-9201340 and the Office of Naval Research through Contract N00014-85-K-0198.     

On the maximum acyclic subgraph problem under disjunctive constraints

Disjunctively constrained versions of classic problems in graph theory such as shortest paths, minimum spanning trees and maximum matchings were recently studied. In this article we introduce disjunctive constrained versions of the Maximum Acyclic Subgraph problem. Negative disjunctive constraints state that a certain pair of edges cannot be contained simultaneously in a feasible solution. Positive disjunctive constraints enforces that at least one arc for the underlying pair is in a feasible solution. It is convenient to represent these disjunctive constraints in terms of an undirected graph, called constraint graph, whose vertices correspond to the arcs of the original graph, and whose edges encode the disjunctive constraints. For the Maximum Acyclic Subgraph problem under Negative Disjunctive Constraints we develop 1/2-approximative algorithms that are polynomial for certain classes of constraint graphs. We also show that determining if a feasible solution exists for an instance of the Maximum Acyclic Subgraph problem under Positive Disjunctive Constraints is an NP-Complete problem.     

An improved algorithm for the maximum agreement subtree problem

In this paper, we solve the maximum agreement subtree problem for a set T of k rooted leaf-labeled evolutionary trees on n leaves where T contains a binary tree. We show that the O(kn³)-time dynamic-programming algorithm proposed by Bryant [Building trees, hunting for trees, and comparing trees: theory and methods in phylogenetic analysis, Ph.D. thesis, Dept. Math., University of Canterbury, 1997, pp. 174-182] can be implemented in O(kn²+n²logk−2nloglogn) and O(kn3−1/(k−1)) time by using multidimensional range search related data structures proposed by Gabow et al. [Scaling and related techniques for geometry problems, in: Proc. 16th Annual ACM Symp. on Theory of Computing, 1984, pp. 135-143] and Bentley [Multidimensional binary search trees in database applications, IEEE Trans. Softw. Eng. SE-5 (4) (1979) 333-340], respectively. When k<2+(logn−logloglogn)/(loglogn), the first implementation will be significantly faster than Bryant's algorithm. For k=3, it yields the best known algorithm which runs in O(n²lognloglogn)-time.     

Physical mapping of chromosomes: A combinatorial problem in molecular biology

This paper is concerned wth the physical mapping of DNA molecules using data about the hybridization of oligonucleotide probes to a library of clones. In mathematical terms, the DNA molecule corresponds to an interval on the real line, each clone to a subinterval, and each probe occurs at a finite set of points within the interval. A stochastic model for the occurrences of the probes and the locations of the clones is assumed. Given a matrix of incidences between probes and clones, the task is to reconstruct the most likely interleaving of the clones. Combinatorial algorithms are presented for solving approximations to this problem, and computational results are presented.Research supported in part by NSF Grant No. CDA-9211106.Research supported in part by NSF Grant No. CCR-9005448.     

On single-walk parallelization of the job shop problem solving algorithms

New parallel objective function determination methods for the job shop scheduling problem are proposed in this paper, considering makespan and the sum of jobs execution times criteria, however, the methods proposed can be applied also to another popular objective functions such as jobs tardiness or flow time. Parallel Random Access Machine (PRAM) model is applied for the theoretical analysis of algorithm efficiency. The methods need a fine-grained parallelization, therefore the approach proposed is especially devoted to parallel computing systems with fast shared memory (e.g. GPGPU, General-Purpose computing on Graphics Processing Units).     

A tissue P system and a DNA microfluidic device for solving the shortest common superstring problem

This paper describes a tissue P system for solving the Shortest Common Superstring Problem in linear time. This tissue P system is well suited for parallel and distributed implementation using a microfluidic device working with DNA strands. The approach is not based on the usual brute force generate/test technique applied in DNA computing, but it builds the space solution gradually. The possible solutions/superstrings are build step by step through the parallel distributed combination of strings using the overlapping concatenation operation. Moreover, the DNA microfluidic device solves the problem autonomously, without the need of external control or manipulation.An erratum to this article can be found at     

通过八数码问题比较搜索算法的性能

搜索算法的核心在于搜索策略的制定.一般的搜索算法采用无信息指导的搜索策略,如深度优先搜索(DFS)和宽度优先搜索(BFS),还有一些搜索算法采用了启发式信息指导的搜索策略,如A*算法.不同的搜索策略会使得搜索算法的性能有很大的差异.使用以上3种搜索算法实现八教码问题的求解,分析和比较三者所表现出来的性能,同时指出3种搜索算法的特点和应用范围,最后给出分析结论以指导开发和使用更加高效的搜索策略.     

A greedy search for the three-dimensional bin packing problem: the packing static stability case

We suggest a greedy search heuristic for solving the three-dimensional bin packing problem (3D-BPP) where in addition to the usual requirement of minimum amount of bins being used, the resulting packing of items into the bins must be physically stable. The problem is NP-hard in the strong sense and imposes severe computational strain for solving it in practice. Computational experiments are also presented and the results are compared with those obtained by the Martello, Pisinger and Vigo (2000) heuristic.     

DNA计算的原理及研究进展

阐述了DNA计算的机理及其数学原理,介绍了Adleman实验,指出了DNA计算目前的应用领域和存在的问题,并对DNA计算的发展前景进行了展望。     

On the implication problem for cardinality constraints and functional dependencies

In database design, integrity constraints are used to express database semantics. They specify the way by that the elements of a database are associated to each other. The implication problem asks whether a given set of constraints entails further constraints. In this paper, we study the finite implication problem for cardinality constraints. Our main result is a complete characterization of closed sets of cardinality constraints. Similar results are obtained for constraint sets containing cardinality constraints, but also key and functional dependencies. Moreover, we construct Armstrong databases for these constraint sets, which are of special interest for example-based deduction in database design.     

The parallel complexity of approximation algorithms for the maximum acyclic subgraph problem

Several classes of sequential algorithms to approximate themaximum acyclic subgraph problem are examined. The equivalentfeedback arc set problem isNP-complete and there are only a few classes of graphs for which it is known to be inP. Thus, approximation algorithms are very important for this problem. Our goal is to determine how effectively the various sequential algorithms parallelize. Of the sequential algorithms we study, natural decision problems based on several of them are provedP-complete. Parallel implementations usingO(log ¦V¦) time and ¦E¦ processors on an EREW PRAM exist for the other algorithms. Interestingly, the parallelizable algorithms appear very similar to some of theinherently sequential algorithms. Thus, for approximating the maximum acyclic subgraph problem small algorithmic changes drastically alter parallel complexity, unlessNC equalsP.     

基于闭环DNA模型的八皇后问题算法

给出了闭环DNA计算模型及其基本生化实验,提出了基于闭环DNA的求解八皇后问题全部可行解的DNA算法,分析了算法的实现步骤及其实现方式并得到了全部的可行解。最后讨论了算法的复杂性。     

最大流有效算法的实用化设计与动态实现

对一个O（｜V｜^3）的最大流有效组合算法进行了研究,提出了用广度优先搜索的方法实现该算法的实用化设计方法。给出了该实用化方法具有的性质,利用该性质,采取正逆双向广度优先搜索的方式,按路径长度递增的次序依次形成各辅助网L,从而计算各辅助网L的最大流,最终组合成最大流。设计了十字双向链表存储结构,该结构采用了独特的动态双向邻接表存储辅助网L,这样即保留有用信息并删除无用信息,又保证最大流有效算法的时间复杂虚仍为O（｜P｜^3）从而实现了动态存储。     

Antibody-based computing: an application to the stable marriage problem

Antibodies, among other things, are important components of the immune system. This paper proposes using the specific recognition capability exhibited by antibodies for computation, in particular, for solving the stable marriage problem, which has been studied as a combinatorial computational problem. Antibody-based computation is proposed by integrating the recognition capabilities of antibodies. The computation is carried out on an array form that is suitable not only for expressing stable marriage problems, but also for further integration to antibody microarrays. This work was presented in part at the 12th International Symposium on Artificial Life and Robotics, Oita, Japan, January 25–27, 2007     

Variations of the maximum leaf spanning tree problem for bipartite graphs

The maximum leaf spanning tree problem is known to be NP-complete. In [M.S. Rahman, M. Kaykobad, Complexities of some interesting problems on spanning trees, Inform. Process. Lett. 94 (2005) 93-97], a variation on this problem was posed. This variation restricts the problem to bipartite graphs and asks, for a fixed integer K, whether or not the graph contains a spanning tree with at least K leaves in one of the partite sets. We show not only that this problem is NP-complete, but that it remains NP-complete for planar bipartite graphs of maximum degree 4. We also consider a generalization of a related decision problem, which is known to be polynomial-time solvable. We show the problem is still polynomial-time solvable when generalized to weighted graphs.     

On the universality of peptide computing

We present a simulation of Turing machines by peptide–antibody interactions. In contrast to an earlier simulation, this new technique simulates the computation steps automatically by the interaction between peptides and antibodies and does not rely on a “look-and-do” approach, in which the Turing machine program would be interpreted by an extraneous computing agent. We determine the resource requirements of the simulation. Towards a precise definition for peptide computing we construct a new theoretical model. We examine how the simulations presented in this paper fits this model. We also give conditions on the peptide computing model so that it can be simulated by a Turing machine.