In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using estab...
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In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from multiobjective optimization. Our strategy consists of deriving a parametric family of multiobjective optimization problems whose optimal solution sets approximate, in a specific sense, that of the set-valued problem with arbitrary accuracy. We also examine particular classes of set-valued mappings for which the corresponding set optimization problem is equivalent to a multiobjective optimization problem in the generated family. Surprisingly, this includes set-valued mappings with a convex graph.
Given an edge-weighted graph G, the minimum maximal matching problem asks to find a minimum weight maximal matching. The problem is known to be NP-hard even if the graph is planar and unweighted. In this paper, we con...
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Given an edge-weighted graph G, the minimum maximal matching problem asks to find a minimum weight maximal matching. The problem is known to be NP-hard even if the graph is planar and unweighted. In this paper, we consider the problem in planar graphs. First, we prove a strong inapproximability for the problem in weighted planar graphs. Second, in contrast with the first result, we show that a polynomial time approximation scheme (PTAS) for the problem in unweighted planar graphs can be obtained by a divide-and-conquer method based on the planar separator theorem. For a given epsilon > 0, our scheme delivers in O(n log n + alphaepsilon(1/2) epsilon(-1)n) time a solution with size at most (1 + epsilon) times the optimal value, where n is the number of vertices in G and a is a constant number.
Given a graph G with vertex set V, a secure connected (resp. total) dominating set of G is a connected (resp. total) dominating set S c V with the property that for each u e V \ S, there exists v e S adjacent to u suc...
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Given a graph G with vertex set V, a secure connected (resp. total) dominating set of G is a connected (resp. total) dominating set S c V with the property that for each u e V \ S, there exists v e S adjacent to u such that (S U {u}) \ {v} is a connected (resp. total) dominating set of G. The minimum secure connected dominating set (or, for short, MSCDS) (resp. minimum secure total dominating set (or, for short, MSTDS)) problem is to find an MSCDS (resp. MSTDS) in a given graph. In this paper, we initiate to consider complexity and algorithmic aspects of the MSCDS problem and the MSTDS problem in unit disk graphs and rectangle graphs. Firstly, we show that the decision version of the MSCDS problem is NP-complete in unit square graphs and unit disk graphs. Then we show that the decision version of the MSTDS problem is NP-complete even in grid graphs (a subclass of unit square graphs and unit disk graphs). Secondly, we give linear-time constant-approximation algorithms for the two problems in unit square graphs, unit disk graphs and unit-height rectangle graphs. Thirdly, we propose a PTAS for the MSTDS problem in unit square graphs and unit disk graphs. Finally, we show that the two problems in proper rectangle graphs are APX-hard. Further we give an explicit lower bound 1.00147 on efficient approximability for the two problems in proper rectangle graphs unless P=NP.& COPY;2023 Elsevier B.V. All rights reserved.
Ride-pooling, which accommodates multiple passenger requests in a single trip, has the potential to substantially enhance the throughput of mobility-on-demand (MoD) systems. This paper investigates MoD systems that op...
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Ride-pooling, which accommodates multiple passenger requests in a single trip, has the potential to substantially enhance the throughput of mobility-on-demand (MoD) systems. This paper investigates MoD systems that operate mixed fleets composed of "basic supply" and "augmented supply" vehicles. When the basic supply is insufficient to satisfy demand, augmented supply vehicles can be repositioned to serve rides at a higher operational cost. We formulate the joint vehicle repositioning and ride-pooling assignment problem as a two-stage stochastic integer program, where repositioning augmented supply vehicles precedes the realization of ride requests. Sequential ride-pooling assignments aim to maximize total utility or profit on a shareability graph: a hypergraph representing the matching compatibility between available vehicles and pending requests. Two approximation algorithms for midcapacity and high-capacity vehicles are proposed in this paper;the respective approximation ratios are 1/p2 and (e � 1)/(2e + o(1))plnp, where p is the maximum vehicle capacity plus one. Our study evaluates the performance of these approximation algorithms using an MoD simulator, demonstrating that these algorithms can parallelize computations and achieve solutions with small optimality gaps (typically within 1%). These efficient algorithms pave the way for various multimodal and multiclass MoD applications.
For a property pi on graphs, the edge-contraction problem with respect to pi is defined as a problem of finding a set of edges of minimum cardinality whose contraction results in a graph satisfying the property pi. Th...
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For a property pi on graphs, the edge-contraction problem with respect to pi is defined as a problem of finding a set of edges of minimum cardinality whose contraction results in a graph satisfying the property pi. This paper gives a lower bound for the approximation ratio for the problem for any property pi that is hereditary on contractions and determined by biconnected components.
Model-based design methodologies based on the synchrony assumption are widely used in many safety-critical application domains. The synchrony assumption asserts that actions (such as the execution of code) occur insta...
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Model-based design methodologies based on the synchrony assumption are widely used in many safety-critical application domains. The synchrony assumption asserts that actions (such as the execution of code) occur instantaneously;however, physical platforms obviously do not possess this property. This paper considers a scheduling problem that arises when one seeks to implement programs that are written under the synchrony assumption upon actual multiprocessor platforms, and proposes algorithms for solving this problem exactly and approximately.
Partitioning a network into k pieces is a fundamental problem in network science. A simple measure of partitioning a network is provided by the Max k-Uncut problem. Given an nvertex undirected graph G with nonnegative...
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Partitioning a network into k pieces is a fundamental problem in network science. A simple measure of partitioning a network is provided by the Max k-Uncut problem. Given an nvertex undirected graph G with nonnegative weights defined on edges, and a positive integer k, the Max k-Uncut problem asks to find a k-partition of the vertices of G to maximize the total weight of edges that are not in the cut. This problem is the complement of the classic Min k-Cut problem, and has close relation to many combinatorial optimization problems, including the famous Densest k-Subgraph problem. In this paper, we propose a greedy approximation algorithm for the Max k-Uncut problem with performance ratio 1 - 2(k-1) n . The algorithm is very simple, which consists of only k -1 min cut computations. The algorithm has fast running time O(kn2) and is hence implementable. The experimental results show that the algorithm has excellent practical performance. (c) 2023 Elsevier B.V. All rights reserved.
Emerging IoT applications impose line barrier coverage (LBC) tasks with min-max movement objective due to requirements of energy balance, fairness, etc. In LBC, we are given a line barrier and a set of n sensors distr...
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Emerging IoT applications impose line barrier coverage (LBC) tasks with min-max movement objective due to requirements of energy balance, fairness, etc. In LBC, we are given a line barrier and a set of n sensors distributed on the plane. The aim is to move the sensors to fully cover the given barrier, such that the maximum movement of the mobile sensors is minimized and hence the energy consumption of the sensors are balanced. This paper proposes an exact algorithm to optimally solve LBC, which deserves a runtime O (n2) compared favorably to the previous state-of-art runtime O (n2 log n). The key idea of the improvement is acceleration -via-approximation: devise a novel approximation algorithm and then use it to accelerate the calculation of optimum solutions. Extensive numerical experiments were carried out to evaluate the practical performance of our algorithm against other baselines, demonstrating its performance gain over the previous state-of-art algorithms.
In this paper, we consider the multitasking scheduling with alternate odd-period and even-period. For the minimization of makespan on one single machine, we present a 2-approximation algorithm for the general case and...
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In this paper, we consider the multitasking scheduling with alternate odd-period and even-period. For the minimization of makespan on one single machine, we present a 2-approximation algorithm for the general case and a 4/3-approximation algorithm for a special case when jobs have identical release dates. And we prove that the problem is strongly NP-hard when jobs have different release dates. For the minimization of makespan on identical parallel machines, we present a (5/2 - 1/m)-approximation algorithm for the general case and a pseudo-polynomial time algorithm when the number of machines is constant. Furthermore, we prove that the single-machine scheduling of minimizing the lateness is strongly NP-hard.
Realizing autonomic management control loops is pivotal for achieving self-driving networks. Some studies have recently evidence the feasibility of using Automated Planning (AP) to carry out these loops. However, in p...
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Realizing autonomic management control loops is pivotal for achieving self-driving networks. Some studies have recently evidence the feasibility of using Automated Planning (AP) to carry out these loops. However, in practice, the use of AP is complicated since network administrators, who are non-experts in Artificial Intelligence, need to define network management policies as AP-goals and combine them with the network status and network management tasks to obtain AP-problems. AP planners use these problems to build up autonomic solutions formed by primitive tasks that modify the initial network state to achieve management goals. Although recent approaches have investigated transforming network management policies expressed in specific languages into low-level configuration rules, transforming these policies expressed in natural language into AP-goals and, subsequently, build up AP-based autonomic management loops remains unexplored. This paper introduces a novel approach, called NORA, to automatically generate AP-problems by translating Goal Policies expressed in natural language into AP-goals and combining them with both the network status and the network management tasks. NORA uses Natural Language Processing as the translation technique and templates as the combination technique to avoid network administrators to learn policy languages or AP-notations. We used a dataset containing Goal Policies to evaluate the NORA's prototype. The results show that NORA achieves high precision and spends a short-time on generating AP-problems, which evinces NORA aids to overcome barriers to using AP in autonomic network management scenarios.
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