震后初期应急物资配送的模糊多目标选址-多式联运问题

针对震后初期应急物资配送系统优化问题,考虑应急物资需求模糊情况下应急物资配送中心选址和应急物资多式联运安排的集成决策,以应急物资配送总时间最短和受灾点应急物资未满足的总损失最小为目标,建立了一个震后应急物资配送的多目标选址-多式联运问题优化模型,设计了一种采用二维编码的非支配排序多目标遗传算法,并对该算法进行了复杂性分析。算例分析结果表明:该算法可以在得到Pareto前沿的同时,根据决策者偏好在Pareto前沿面上给出各种优化决策方案。     

On the complexity of path problems in properly colored directed graphs

We address the complexity class of several problems related to finding a path in a properly colored directed graph. A properly colored graph is defined as a graph G whose vertex set is partitioned into $\mathcal{X}(G)$ stable subsets, where $\mathcal{X}(G)$ denotes the chromatic number of G. We show that to find a simple path that meets all the colors in a properly colored directed graph is NP-complete, and so are the problems of finding a shortest and longest of such paths between two specific nodes.     

时变随机网络下有时间窗的有害物品运输路径选择研究

研究了时变随机网络下有害物品运输路径选择问题。首先定义了可行路径的具有随机性和时变性的选择向量,以期望值为目标,建立了多目标时变随机网络下有软、硬时间窗限制的有害物品运输路径选择模型。给出了时变随机网络下的有效路径的定义,并设计了多维时变随机动态标号,利用此标号设计了求解模型的多项式算法,通过此算法可以得到时变随机网络下有害物品运输路径的所有有效解。最后给出了一个应用算例。     

基于改进蚁群算法的低碳车辆路径问题研究

全球气候恶化危及人类生存环境,物流运输过程中产生的大量温室气体则是祸源之一。本文考虑带有碳排放约束的车辆路径问题（VRP）,以车辆行驶里程最短和碳排放量最小为目标,构建了多目标的VRP非线性规划模型。提出了一种改进的蚁群系统算法对该模型进行求解,算法在更新路径上的蚂蚁信息素时引入了混沌扰动机制,此举能降低算法运行时陷入局部最优解的概率并有效提高算法的适应性。同时,对启发因子、状态转移概率、信息素更新等环节进行了优化设计,提高了最优路径的搜索效率。最后,数值仿真实验证明了该算法的求解表现优于同类研究常用的遗传算法和禁忌搜索算法,具有较强的全局寻优能力。在灵敏性和有效性的保证下,本研究所设计的改进蚁群算法能够较好地处理低碳车辆路径问题（LCVRP）。     

The maximum flow problem with disjunctive constraints

We study the maximum flow problem subject to binary disjunctive constraints in a directed graph: A negative disjunctive constraint states that a certain pair of arcs in a digraph cannot be simultaneously used for sending flow in a feasible solution. In contrast to this, positive disjunctive constraints force that for certain pairs of arcs at least one arc has to carry flow in a feasible solution. It is convenient to represent the negative disjunctive constraints in terms of a so-called conflict graph whose vertices correspond to the arcs of the underlying graph, and whose edges encode the constraints. Analogously we represent the positive disjunctive constraints by a so-called forcing graph. For conflict graphs we prove that the maximum flow problem is strongly $\mathcal{NP}$ -hard, even if the conflict graph consists only of unconnected edges. This result still holds if the network consists only of disjoint paths of length three. For forcing graphs we also provide a sharp line between polynomially solvable and strongly $\mathcal{NP}$ -hard instances for the case where the flow values are required to be integral. Moreover, our hardness results imply that no polynomial time approximation algorithm can exist for both problems. In contrast to this we show that the maximum flow problem with a forcing graph can be solved efficiently if fractional flow values are allowed.     

Improving robustness of next-hop routing

A weakness of next-hop routing is that following a link or router failure there may be no routes between some source-destination pairs, or packets may get stuck in a routing loop as the protocol operates to establish new routes. In this article, we address these weaknesses by describing mechanisms to choose alternate next hops. Our first contribution is to model the scenario as the following tree augmentation problem. Consider a mixed graph where some edges are directed and some undirected. The directed edges form a spanning tree pointing towards the common destination node. Each directed edge represents the unique next hop in the routing protocol. Our goal is to direct the undirected edges so that the resulting graph remains acyclic and the number of nodes with outdegree two or more is maximized. These nodes represent those with alternative next hops in their routing paths. We show that tree augmentation is NP-hard in general and present a simple \(\frac{1}{2}\)-approximation algorithm. We also study 3 special cases. We give exact polynomial-time algorithms for when the input spanning tree consists of exactly 2 directed paths or when the input graph has bounded treewidth. For planar graphs, we present a polynomial-time approximation scheme when the input tree is a breadth-first search tree. To the best of our knowledge, tree augmentation has not been previously studied.     

Approximation algorithm for uniform bounded facility location problem

The uniform bounded facility location problem (UBFLP) seeks for the optimal way of locating facilities to minimize total costs (opening costs plus routing costs), while the maximal routing costs of all clients are at most a given bound M. After building a mixed 0–1 integer programming model for UBFLP, we present the first constant-factor approximation algorithm with an approximation guarantee of 6.853+? for UBFLP on plane, which is composed of the algorithm by Dai and Yu (Theor. Comp. Sci. 410:756–765, 2009) and the schema of Xu and Xu (J. Comb. Optim. 17:424–436, 2008). We also provide a heuristic algorithm based on Benders decomposition to solve UBFLP on general graphes, and the computational experience shows that the heuristic works well.     

On the generalized multiway cut in trees problem

Given a tree $T = (V, E)$ with $n$ vertices and a collection of terminal sets $D = \{S_1, S_2, \ldots , S_c\}$ , where each $S_i$ is a subset of $V$ and $c$ is a constant, the generalized multiway cut in trees problem (GMWC(T)) asks to find a minimum size edge subset $E^{\prime } \subseteq E$ such that its removal from the tree separates all terminals in $S_i$ from each other for each terminal set $S_i$ . The GMWC(T) problem is a natural generalization of the classical multiway cut in trees problem, and has an implicit relation to the Densest $k$ -Subgraph problem. In this paper, we show that the GMWC(T) problem is fixed-parameter tractable by giving an $O(n^2 + 2^k)$ time algorithm, where $k$ is the size of an optimal solution, and the GMWC(T) problem is polynomial time solvable when the problem is restricted in paths.We also discuss some heuristics for the GMWC(T) problem     

Spanning 3-connected index of graphs

For an integer $s>0$ and for $u,v\in V(G)$ with $u\ne v$ , an $(s;u,v)$ -path-system of G is a subgraph H of G consisting of s internally disjoint (u, v)-paths, and such an H is called a spanning $(s;u,v)$ -path system if $V(H)=V(G)$ . The spanning connectivity $\kappa ^{*}(G)$ of graph G is the largest integer s such that for any integer k with $1\le k \le s$ and for any $u,v\in V(G)$ with $u\ne v$ , G has a spanning ( $k;u,v$ )-path-system. Let G be a simple connected graph that is not a path, a cycle or a $K_{1,3}$ . The spanning k-connected index of G, written $s_{k}(G)$ , is the smallest nonnegative integer m such that $L^m(G)$ is spanning k-connected. Let $l(G)=\max \{m:\,G$ has a divalent path of length m that is not both of length 2 and in a $K_{3}$ }, where a divalent path in G is a path whose interval vertices have degree two in G. In this paper, we prove that $s_{3}(G)\le l(G)+6$ . The key proof to this result is that every connected 3-triangular graph is 2-collapsible.     

多模式交通条件下合理制定旅客票价的优化模型及算法

在本文中,充分考虑了旅客和交通管理部门两方面的利益,提出了一个双层规划模型来描述城市间多种交通方式竞争条件下合理制定旅客票价问题。在此模型中,既保障了旅客使自己的广义出行费用最小,又使得交通管理部门在客运市场的竞争中取得最大的经济效益。然后给出了求解该模型的基于灵敏度分析的启发式算法 (SAB)。最后用一个实际算例说明了该模型及算法的应用。     

Finding paths with minimum shared edges

Motivated by a security problem in geographic information systems, we study the following graph theoretical problem: given a graph G, two special nodes s and t in G, and a number k, find k paths from s to t in G so as to minimize the number of edges shared among the paths. This is a generalization of the well-known disjoint paths problem. While disjoint paths can be computed efficiently, we show that finding paths with minimum shared edges is NP-hard. Moreover, we show that it is even hard to approximate the minimum number of shared edges within a factor of $2^{\log^{1-\varepsilon}n}$ , for any constant ε>0. On the positive side, we show that there exists a (k?1)-approximation algorithm for the problem, using an adaption of a network flow algorithm. We design some heuristics to improve the quality of the output, and provide empirical results.     

Efficient polynomial-time algorithms for the constrained LCS problem with strings exclusion

In this paper, we revisit a recent variant of the longest common subsequence (LCS) problem, the string-excluding constrained LCS (STR-EC-LCS) problem, which was first addressed by Chen and Chao (J Comb Optim 21(3):383–392, 2011). Given two sequences \(X\) and \(Y\) of lengths \(m\) and \(n,\) respectively, and a constraint string \(P\) of length \(r,\) we are to find a common subsequence \(Z\) of \(X\) and \(Y\) which excludes \(P\) as a substring and the length of \(Z\) is maximized. In fact, this problem cannot be correctly solved by the previously proposed algorithm. Thus, we give a correct algorithm with \(O(mnr)\) time to solve it. Then, we revisit the STR-EC-LCS problem with multiple constraints \(\{ P_1, P_2, \ldots , P_k \}.\) We propose a polynomial-time algorithm which runs in \(O(mnR)\) time, where \(R = \sum _{i=1}^{k} |P_i|,\) and thus it overthrows the previous claim of NP-hardness.     

Radiation hybrid map construction problem parameterized

In this paper, we study the Radiation hybrid map construction ( $\mathsf{{RHMC} }$ ) problem which is about reconstructing a genome from a set of gene clusters. The problem is known to be $\mathsf{{NP} }$ -complete even when all gene clusters are of size two and the corresponding problem ( $\mathsf{{RHMC}_2 }$ ) admits efficient constant-factor approximation algorithms. In this paper, for the first time, we consider the more general case when the gene clusters can have size either two or three ( $\mathsf{{RHMC}_3 }$ ). Let ${p\text{- }\mathsf {RHMC} }$ be a parameterized version of $\mathsf{{RHMC} }$ where the parameter is the size of solution. We present a linear kernel for ${p\text{- }\mathsf {RHMC}_3 }$ of size $22k$ that when combined with a bounded search-tree algorithm, gives an FPT algorithm running in $O(6^kk+n)$ time. For ${p\text{- }\mathsf {RHMC}_3 }$ we present a bounded search tree algorithm which runs in $O^*(2.45^k)$ time, greatly improving the previous bound using weak kernels.     

Recognition of overlap graphs

Overlap graphs occur in computational biology and computer science, and have applications in genome sequencing, string compression, and machine scheduling. Given two strings \(s_{i}\) and \(s_{j}\) , their overlap string is defined as the longest string \(v\) such that \(s_{i} = uv\) and \(s_{j} = vw\) , for some non empty strings \(u,w\) , and its length is called the overlap between these two strings. A weighted directed graph is an overlap graph if there exists a set of strings with one-to-one correspondence to the vertices of the graph, such that each arc weight in the graph equals the overlap between the corresponding strings. In this paper, we characterize the class of overlap graphs, and we present a polynomial time recognition algorithm as a direct consequence. Given a weighted directed graph \(G\) , the algorithm constructs a set of strings that has \(G\) as its overlap graph, or decides that this is not possible.     

Computing an effective decision making group of a society using social network analysis

Recent years have witnessed how much a decision making group can be dysfunctional due to the extreme hyperpartisanship. While partisanship is crucial for the representatives to pursue the wishes of those whom they represent for, such an extremism results in a severe gridlock in the decision making progress, and makes themselves highly inefficient. It is known that such a problem can be mitigated by having negotiators in the group. This paper investigates the potential of social network analysis techniques to choose an effective leadership group of a society such that it suffers less from the extreme hyperpartisanship. We establish three essential requirements for an effective representative group, namely Influenceability, Partisanship, and Bipartisanship. Then, we formulate the problem of finding a minimum size representative group satisfying the three requirements as the minimum connected \(k\) -core dominating set problem (MC \(k\) CDSP), and show its NP-hardness. We introduce an extension of MC \(k\) CDSP, namely MC \(k\) CDSP-C, which assumes the society has a number of sub-communities and requires at least one representative from each sub-community should be in the leadership. We also propose an approximation algorithm for a subclass of MC \(k\) CDSP with \(k=2\) , and show an \(\alpha \) -approximation algorithm of MC \(k\) CDSP can be used to obtain an \(\alpha \) -approximation algorithm of MC \(k\) CDSP-SC.     

Online maximum directed cut

We investigate a natural online version of the well-known Maximum Directed Cut problem on DAGs. We propose a deterministic algorithm and show that it achieves a competitive ratio of $\frac{3\sqrt{3}}{2}\approx 2.5981$ . We then give a lower bound argument to show that no deterministic algorithm can achieve a ratio of $\frac{3\sqrt{3}}{2}-\epsilon$ for any ??>0 thus showing that our algorithm is essentially optimal. Then, we extend our technique to improve upon the analysis of an old result: we show that greedily derandomizing the trivial randomized algorithm for MaxDiCut in general graphs improves the competitive ratio from 4 to 3, and also provide a tight example.     

Online bottleneck matching

We consider the online bottleneck matching problem, where $k$ server-vertices lie in a metric space and $k$ request-vertices that arrive over time each must immediately be permanently assigned to a server-vertex. The goal is to minimize the maximum distance between any request and its server. Because no algorithm can have a competitive ratio better than $O(k)$ for this problem, we use resource augmentation analysis to examine the performance of three algorithms: the naive Greedy algorithm, Permutation, and Balance. We show that while the competitive ratio of Greedy improves from exponential (when each server-vertex has one server) to linear (when each server-vertex has two servers), the competitive ratio of Permutation remains linear when an extra server is introduced at each server-vertex. The competitive ratio of Balance is also linear with an extra server at each server-vertex, even though it has been shown that an extra server makes it constant-competitive for the min-weight matching problem.     

A heuristic approach to long-haul freight transportation with multiple objective functions

This paper studies a long-haul freight transportation problem stimulated by a real-life application, whose underlying vehicle routing problem is a multi-objective one, where travel time and route cost are to be minimized together with the maximization of a transportation mean sharing index, related to the capability of the transportation system of generating economy scale solutions. In terms of constraints, besides vehicle capacity and time windows, transportation jobs have to obey additional constraints related to mandatory nodes (e.g., logistic platform nearest to the origin or the destination) and forbidden nodes (e.g., logistic platforms not compatible with the operations required). Based on the network definition, routes can be multimodal. To solve this problem, we propose a heuristic algorithm that can be applied in the tactical and the operational planning phase, and present the results of an extensive experimentation.     

Algorithms for the minimum diameter terminal Steiner tree problem

Given an undirected connected graph \(G=(V(G),E(G),d)\) with a function \(d(\cdot )\ge 0\) on edges and a subset \(S\subseteq V(G)\) of terminals, the minimum diameter terminal Steiner tree problem (MDTSTP) asks for a terminal Steiner tree in \(G\) of a minimum diameter. In the paper, the diameter of a tree refers to the longest of all the distances between two different leaves of the tree. When \(G\) is a complete graph and \(d(\cdot )\) is a metric function, we demonstrate that an optimal solution of MDTSTP is monopolar or dipolar and give an \(O(|S|\cdot |V(G)\setminus S|^2)\) -time exact algorithm. For the nonmetric version of MDTSTP, we present a simple 2-approximation algorithm with a time complexity of \(O(|V(G)\setminus S|\log |S|)\) , as well as two exact algorithms with a time complexity of \(O(|S|^3|V(G)|^2)\) and \(O(|S|\cdot |V(G)\setminus S|^2+|S|^2\cdot |V(G)\setminus S|)\) , respectively.     

The minimum vulnerability problem on specific graph classes

Suppose that each edge e of an undirected graph G is associated with three nonnegative integers \(\mathsf{cost}(e)\), \(\mathsf{vul}(e)\) and \(\mathsf{cap}(e)\), called the cost, vulnerability and capacity of e, respectively. Then, we consider the problem of finding \(k\) paths in G between two prescribed vertices with the minimum total cost; each edge e can be shared without any cost by at most \(\mathsf{vul}(e)\) paths, and can be shared by more than \(\mathsf{vul}(e)\) paths if we pay \(\mathsf{cost}(e)\), but cannot be shared by more than \(\mathsf{cap}(e)\) paths even if we pay the cost for e. This problem generalizes the disjoint path problem, the minimum shared edges problem and the minimum edge cost flow problem for undirected graphs, and it is known to be NP-hard. In this paper, we study the problem from the viewpoint of specific graph classes, and give three results. We first show that the problem is NP-hard even for bipartite outerplanar graphs, 2-trees, graphs with pathwidth two, complete bipartite graphs, and complete graphs. We then give a pseudo-polynomial-time algorithm for bounded treewidth graphs. Finally, we give a fixed-parameter algorithm for chordal graphs when parameterized by the number \(k\) of required paths.