Multiple facility location on a network with linear reliability order of edges

We study the problem of locating facilities on the nodes of a network to maximize the expected demand serviced. The edges of the input graph are subject to random failure due to a disruptive event. We consider a special type of failure correlation. The edge dependency model assumes that the failure of a more reliable edge implies the failure of all less reliable ones. Under this dependency model called Linear Reliability Order (LRO) we give two polynomial time exact algorithms. When two distinct LRO’s exist, we prove the total unimodularity of a linear programming formulation. In addition, we show that minimizing the sum of facility opening costs and expected cost of unserviced demand under two orderings reduces to a matching problem. We prove NP-hardness of the three orderings case and show that the problem with an arbitrary number of orderings generalizes the deterministic maximum coverage problem. When a demand point can be covered only if a facility exists within a distance limit, we show that the problem is NP-hard even for a single ordering.     

Minimizing the total cost of barrier coverage in a linear domain

Barrier coverage, as one of the most important applications of wireless sensor network (WSNs), is to provide coverage for the boundary of a target region. We study the barrier coverage problem by using a set of n sensors with adjustable coverage radii deployed along a line interval or circle. Our goal is to determine a range assignment \(\mathbf {R}=({r_{1}},{r_{2}}, \ldots , {r_{n}})\) of sensors such that the line interval or circle is fully covered and its total cost \(C(\mathbf {R})=\sum _{i=1}^n {r_{i}}^\alpha \) is minimized. For the line interval case, we formulate the barrier coverage problem of line-based offsets deployment, and present two approximation algorithms to solve it. One is an approximation algorithm of ratio 4 / 3 runs in \(O(n^{2})\) time, while the other is a fully polynomial time approximation scheme (FPTAS) of computational complexity \(O(\frac{n^{2}}{\epsilon })\). For the circle case, we optimally solve it when \(\alpha = 1\) and present a \(2(\frac{\pi }{2})^\alpha \)-approximation algorithm when \(\alpha > 1\). Besides, we propose an integer linear programming (ILP) to minimize the total cost of the barrier coverage problem such that each point of the line interval is covered by at least k sensors.     

Coverage by directional sensors in randomly deployed wireless sensor networks

We study a novel “coverage by directional sensors” problem with tunable orientations on a set of discrete targets. We propose a Maximum Coverage with Minimum Sensors (MCMS) problem in which coverage in terms of the number of targets to be covered is maximized whereas the number of sensors to be activated is minimized. We present its exact Integer Linear Programming (ILP) formulation and an approximate (but computationally efficient) centralized greedy algorithm (CGA) solution. These centralized solutions are used as baselines for comparison. Then we provide a distributed greedy algorithm (DGA) solution. By incorporating a measure of the sensors residual energy into DGA, we further develop a Sensing Neighborhood Cooperative Sleeping (SNCS) protocol which performs adaptive scheduling on a larger time scale. Finally, we evaluate the properties of the proposed solutions and protocols in terms of providing coverage and maximizing network lifetime through extensive simulations. Moreover, for the case of circular coverage, we compare against the best known existing coverage algorithm.     

Balancing Revenues and Repair Costs under Partial Information about Product Reliability

We consider the problem faced by a company selling a product with warranty and under partial information about the product reliability. The product can fail from multiple failure types, each of which is associated with an inherently different repair cost. If the product fails within the warranty duration, then the company is required to pay the repair cost. The company does not know the probabilities associated with different failure types, but it learns the failure probabilities as sales occur and failure information is accumulated. If the failure probabilities turn out to be too high and it becomes costly to fulfill the warranty coverage, then the company may decide to stop selling the product, possibly replacing it with a more reliable alternative. The objective is to decide if and when to stop. By formulating the problem as a dynamic program with Bayesian learning, we establish structural properties of the optimal policy. Since computing the optimal policy is intractable due to the high dimensional state space, we propose two approximation methods. The first method is based on decomposing the problem by failure types and it provides upper bounds on the value functions. The second method provides lower bounds on the value functions and it is based on a deterministic approximation. Computational experiments indicate that the policy from the first method provides noticeable benefits, especially when it is difficult to form good estimates of the failure probabilities quickly.     

On the minimum routing cost clustered tree problem

For an edge-weighted graph \(G=(V,E,w)\), in which the vertices are partitioned into k clusters \(\mathcal {R}=\{R_1,R_2,\ldots ,R_k\}\), a spanning tree T of G is a clustered spanning tree if T can be cut into k subtrees by removing \(k-1\) edges such that each subtree is a spanning tree for one cluster. In this paper, we show the inapproximability of finding a clustered spanning tree with minimum routing cost, where the routing cost is the total distance summed over all pairs of vertices. We present a 2-approximation for the case that the input is a complete weighted graph whose edge weights obey the triangle inequality. We also study a variant in which the objective function is the total distance summed over all pairs of vertices of different clusters. We show that the problem is polynomial-time solvable when the number of clusters k is 2 and NP-hard for \(k=3\). Finally, we propose a polynomial-time 2-approximation algorithm for the case of three clusters.     

Online set multicover algorithms for dynamic D2D communications

Motivated by the dynamic resource allocation problem for device-to-device (D2D) communications, we study the online set multicover problem (OSMC). In the online set multicover, the set X of elements to be covered is unknown in advance; furthermore, the coverage requirement of each element \(x \in X\) is initially unknown. Elements of X together with coverage requirements are presented one at a time in an online fashion; and a feasible solution must be maintained at all times. We provide the first deterministic, online algorithms for OSMC with competitive ratios. We consider two versions of OSMC; in the first, each set may be picked only once, while the second version allows each set to be picked multiple times. For both versions, we present the first deterministic, online algorithms, with competitive ratios \(O( \log n \log m )\) and \(O( \log n (\log m + \log k) )\), repectively, where n is the number of elements, m is the number of sets, and k is the maximum coverage requirement. By simulation, we show the efficacy of these algorithms for resource allocation in the D2D setting by analyzing network throughput and other metrics, obtaining a large improvement in running time over offline methods.     

Facility Dispersion Problems Under Capacity and Cost Constraints

The MAX-MIN dispersion problem, which arises in the placement of undesirable facilities, involves selecting a specified number of sites among a set of potential sites so as to maximize the minimum distance between any pair of selected sites. We consider different versions of this dispersion problem where each potential site has an associated storage capacity and a storage cost. A typical problem in this context is to choose a subset of potential sites so that the total capacity of the chosen sites is at least a given value, the total storage cost is within the specified budget and the minimum distance between any pair of chosen sites is maximized. Since these constrained optimization problems are NP-hard in general, we consider whether there are efficient approximation algorithms for them with good performance guarantees. Our results include approximation algorithms for some versions, approximation schemes for some geometric versions and polynomial algorithms for special cases. We also present results that bring out the intrinsic difficulty of obtaining near-optimal solutions to some versions.     

A Bicriterion Maximal Covering Location Formulation Which Considers the Satisfaction of Uncovered Demand

There have been many applications of the maximal covering location problem (MCLP). An underlying assumption of the MCLP is that demand not covered (i.e., not within a prespecified maximal distance of a facility) is not served. This may be an unrealistic assumption in many location planning scenarios, especially in the public sector. For example, in cases such as fire protection or ambulance service, calls not technically covered will still be serviced. The MCLP, however, does not consider the distances or travel times necessary to service such demand. This paper presents a bicriterion locational covering model which explicitly considers the travel distance or time necessary to service demand not within the maximal covering distance of a facility. The model may be used to generate noninferior (Pareto optimal) siting configurations which demonstrate the inherent trade-offs between a siting scheme designed to maximize total coverage and one designed to minimize total travel time for uncovered demand to reach its nearest facility. In addition, it is shown that for any particular weighting scheme on the two objectives, the problem can be solved as a p-median problem; a problem for which several efficient solution methods exist.     

Cost sharing and strategyproof mechanisms for set cover games

We develop for set cover games several general cost-sharing methods that are approximately budget-balanced, in the core, and/or group-strategyproof. We first study the cost sharing for a single set cover game, which does not have a budget-balanced mechanism in the core. We show that there is no cost allocation method that can always recover more than $\frac{1}{\ln n}$ of the total cost and in the core. Here n is the number of all players to be served. We give a cost allocation method that always recovers $\frac{1}{\ln d_{\mathit{max}}}$ of the total cost, where d _max is the maximum size of all sets. We then study the cost allocation scheme for all induced subgames. It is known that no cost sharing scheme can always recover more than $\frac{1}{n}$ of the total cost for every subset of players. We give an efficient cost sharing scheme that always recovers at least $\frac{1}{2n}$ of the total cost for every subset of players and furthermore, our scheme is cross-monotone. When the elements to be covered are selfish agents with privately known valuations, we present a strategyproof charging mechanism, under the assumption that all sets are simple sets; further, the total cost of the set cover is no more than ln?d _max times that of an optimal solution. When the sets are selfish agents with privately known costs, we present a strategyproof payment mechanism to them. We also show how to fairly share the payments to all sets among the elements.     

制造企业服务化路径选择研究

服务化已经成为制造企业获取和保持竞争优势的重要途径，其本质是企业价值链的延伸，既包括投入服务化，又包括产出服务化。在实施服务化战略时，制造企业可以选择将投入、产出服务功能内部化或外部化，即自营或外包。从产品层面构建理论模型，比较研究制造企业的四种服务化路径：（1）外包投入服务和产出服务；（2）外包投入服务，自营产出服务；（3）自营投入服务，外包产出服务；（4）自营投入服务和产出服务。首先，通过分析需求质量弹性和质量成本系数、制造企业产品及服务的质量和价格、生产性服务企业服务的质量和价格以及制造企业与生产性服务企业的市场基础等模型变量，得到制造企业在每种服务化路径下的最大化利润。其次，通过比较每种路径下的最大化利润，得到路径选择的临界条件。最后，通过数值实验和算例分析，验证了模型的有效性和实用性。研究结果表明，何种路径成为更优的选择取决于制造企业的自身条件和所面临的市场环境。总体而言，在质量成本系数足够大于需求质量弹性的前提下，生产性服务企业所提供投入服务或产出服务的市场基础越大，将该种服务外部化的预期利润越高。研究结果将为制造企业的服务化路径选择提供理论依据和解决方案。     

The density maximization problem in graphs

We consider a framework for bi-objective network construction problems where one objective is to be maximized while the other is to be minimized. Given a host graph G=(V,E) with edge weights w _e ∈? and edge lengths ? _e ∈? for e∈E we define the density of a pattern subgraph H=(V′,E′)?G as the ratio ?(H)=∑ _e∈E′ w _e /∑ _e∈E′ ? _e . We consider the problem of computing a maximum density pattern H under various additional constraints. In doing so, we compute a single Pareto-optimal solution with the best weight per cost ratio subject to additional constraints further narrowing down feasible solutions for the underlying bi-objective network construction problem. First, we consider the problem of computing a maximum density pattern with weight at least W and length at most L in a host G. We call this problem the biconstrained density maximization problem. This problem can be interpreted in terms of maximizing the return on investment for network construction problems in the presence of a limited budget and a target profit. We consider this problem for different classes of hosts and patterns. We show that it is NP-hard, even if the host has treewidth 2 and the pattern is a path. However, it can be solved in pseudo-polynomial linear time if the host has bounded treewidth and the pattern is a graph from a given minor-closed family of graphs. Finally, we present an FPTAS for a relaxation of the density maximization problem, in which we are allowed to violate the upper bound on the length at the cost of some penalty. Second, we consider the maximum density subgraph problem under structural constraints on the vertex set that is used by the patterns. While a maximum density perfect matching can be computed efficiently in general graphs, the maximum density Steiner-subgraph problem, which requires a subset of the vertices in any feasible solution, is NP-hard and unlikely to admit a constant-factor approximation. When parameterized by the number of vertices of the pattern, this problem is W[1]-hard in general graphs. On the other hand, it is FPT on planar graphs if there is no constraint on the pattern and on general graphs if the pattern is a path.     

On nonlinear multi-covering problems

In this paper we define the exact k-coverage problem, and study it for the special cases of intervals and circular-arcs. Given a set system consisting of a ground set of n points with integer demands \(\{d_0,\dots ,d_{n-1}\}\) and integer rewards, subsets of points, and an integer k, select up to k subsets such that the sum of rewards of the covered points is maximized, where point i is covered if exactly \(d_i\) subsets containing it are selected. Here we study this problem and some related optimization problems. We prove that the exact k-coverage problem with unbounded demands is NP-hard even for intervals on the real line and unit rewards. Our NP-hardness proof uses instances where some of the natural parameters of the problem are unbounded (each of these parameters is linear in the number of points). We show that this property is essential, as if we restrict (at least) one of these parameters to be a constant, then the problem is polynomial time solvable. Our polynomial time algorithms are given for various generalizations of the problem (in the setting where one of the parameters is a constant).     

协同运输的路线整合问题研究

本文研究协同运输的路线整合问题(CTRIP):允许所有的O-D流(运输任务)在规定的路线长度内任意采取直通运输、单点中转、两点中转的整合运输路线,整合运输的中枢路段在支付固定成本后可产生运费折扣,如何选择O-D流的整合路线使得总成本最小? CTRIP广泛应用于航空、物流、快递等领域的整合运输实践。论文构造了CTRIP的混合整数规划模型和Benders分解算法,实验显示,算法表现出非常好的计算绩效。最后,我们利用一个具体实例对CTRIP与已有研究展开了比较,结论显示CTRIP更能保证中枢路段的规模优势 。     

Information Diffusion among Agents: Implications for Humanitarian Operations

The basis for this article is an information‐processing view of the UN's cluster approach. We use agent‐based modeling and simulations to show that clusters, if properly utilized, encourage better information flow and thus facilitate effective response to disasters. The article intends to turn the attention of the humanitarian community to the importance of sharing information and the role of cluster leads in facilitating humanitarian aid. Our results indicate that if cluster leads act as information hubs, information reaches its target faster, enabling a prompt humanitarian response. In addition, we show that information quality is critical for effective resource utilization—if cluster leads filter information, it moves faster. We also found evidence that the willingness to exchange information plays a larger role in transmitting information than that of an information hub, particularly during later stages of response operations.     

Relay node placement in two-tiered wireless sensor networks with base stations

This paper addresses the relay node placement problem in two-tiered wireless sensor networks with base stations, which aims to deploy a minimum number of relay nodes to achieve certain coverage and connectivity requirement. Under the assumption that the communication range of the sensor nodes is no more than that of the relay node, we present a polynomial time (5+?)-approximation algorithm for the 1-coverage 1-connected problem. Furthermore, we consider the fault tolerant problem in the network, we present a polynomial time (20+?)-approximation algorithm for the 2-coverage 2-connected problem, where ? is any given positive constant. For the k-coverage 2-connected situation, we present a polynomial time (15k?10+?)-approximation algorithm.     

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.     

Change-making problems revisited: a parameterized point of view

The change-making problem is the problem of representing a given amount of money with the fewest number of coins possible from a given set of coin denominations. In the general version of the problem, an upper bound for the availability of every coin value is given. Even the special case, where for each value an unlimited number of coins is available, is NP-hard. Since in the original problem some amounts can not be represented, especially if no coin of value one exists, we introduce generalized problems that look for approximations of the given amount such that a cost function is minimized. We recall algorithms for the change-making problem and present new algorithms for the generalized version of the problem. Motivated by the NP-hardness we study fixed-parameter tractability of all these problems. We show that some of these problems are fixed-parameter tractable and that some are \(\hbox {W}[1]\)-hard. In order to show the existence of polynomial and constant-size kernels we prove some general results and apply them to several parameterizations of the change-making problems.     

Maximizing target-temporal coverage of mission-driven camera sensor networks

In camera sensor networks (CSNs), the target coverage problem is of special importance since a sensor with different viewing directions captures distinct views for the same target. Furthermore, mission-driven monitoring applications in CSNs usually have special network lifetime requirements in which the limited battery lifetime of sensors probably can not sustain for full coverage. In this paper, based on effective-sensing model, we address three new coverage problems in mission-driven camera sensor networks, namely the target-temporal effective-sensing coverage with non-adjustable cameras (TEC-NC) problem, the target-temporal effective-sensing coverage with adjustable cameras (TEC-AC) problem, and the target-temporal effective-sensing coverage with fully-adjustable cameras (TEC-FAC) problem. Given a mission period, the common objective of the problems is to find a sleep-wakeup schedule such that the overall target-temporal coverage is maximized. For TEC-NC, we propose a 2-approximation algorithm and two new heuristics. We also design two greedy strategies, each of which can be combined with our solutions for TEC-NC to deal with TEC-AC and TEC-FAC, respectively. We finally conduct extensive experiments to evaluate the performance of the proposed algorithms, whose results indicate the proposed algorithms outperform the existing alternatives as well as are close to the theoretical optimum on average under certain conditions.     

Efficient point coverage in wireless sensor networks

We study minimum-cost sensor placement on a bounded 3D sensing field, R, which comprises a number of discrete points that may or may not be grid points. Suppose we have ℓ types of sensors available with different sensing ranges and different costs. We want to find, given an integer σ ≥ 1, a selection of sensors and a subset of points to place these sensors such that every point in R is covered by at least σ sensors and the total cost of the sensors is minimum. This problem is known to be NP-hard. Let k_i denote the maximum number of points that can be covered by a sensor of the ith type. We present in this paper a polynomial-time approximation algorithm for this problem with a proven approximation ratio . In applications where the distance of any two points has a fixed positive lower bound, each k_i is a constant, and so we have a polynomial-time approximation algorithms with a constant guarantee. While γ may be large, we note that it is only a worst-case upper bound. In practice the actual approximation ratio is small, even on randomly generated points that do not have a fixed positive minimum distance between them. We provide a number of numerical results for comparing approximation solutions and optimal solutions, and show that the actual approximation ratios in these examples are all less than 3, even though γ is substantially larger. This research was supported in part by NSF under grant CCF-04080261 and by NSF of China under grant 60273062.     

Optimization problems with color-induced budget constraints

In 1984, Gabow and Tarjan provided a very elegant and fast algorithm for the following problem: given a matroid defined on a red and blue colored ground set, determine a basis of minimum cost among those with k red elements, or decide that no such basis exists. In this paper, we investigate extensions of this problem from ordinary matroids to the more general notion of poset matroids which take precedence constraints on the ground set into account. We show that the problem on general poset matroids becomes -hard, already if the underlying partially ordered set (poset) consists of binary trees of height two. On the positive side, we present two algorithms: a pseudopolynomial one for integer polymatroids, i.e., the case where the poset consists of disjoint chains, and a polynomial algorithm for the problem to determine a minimum cost ideal of size l with k red elements, i.e., the uniform rank-l poset matroid, on series-parallel posets.