The C++ language continually evolves through formal specifications established by its standards committee, proposing new features to maintain $\mathrm{C}++$ as a relevant programming language while improving usability, performance, and portability across platforms. With the addition of parallel Standard Template Library (STL) algorithms in C++17, programmers can now leverage parallel processing capabilities via vendor-neutral parallel execution policies. This study presents an adaptation of the NAS Parallel Benchmarks (NPB)—a well-established suite of applications for evaluating parallel architectures-by porting its sequential C-style code to use C++ STL abstractions and performance-portable parallelism features. Our goals are to (1) assess the suitability of C++ STL for scientific applications like the ones in the NPB and (2) provide a comparative performance and portability of STL algorithms’ parallel execution policies across different multicore architectures (x86 and AArch64). Results indicate that the performance of parallel STL algorithms is often close to that of optimized handwritten versions (OpenMP, Intel TBB, and FastFlow) on different architectures, with notable shortfalls. Across all NPB benchmarks, the STL algorithms’ geometric mean shows sequential execution times that are between 3.76% and $\mathrm{6. 9 \%}$ higher, while parallel executions may reach a geometric mean of up to $\mathrm{2 1. 2 1 \%}$ higher execution time.

ABSTRACT Given an undirected graph whose edge weights change over time slots, the sub‐tree scheduling for wireless sensor networks with partial coverage asks to partition the vertices of in non‐empty trees such that the total weight of the trees is minimized. In this article, we show that the problem is NP‐hard in both the cases where is part of the input and is a fixed instance parameter. In both our proofs we reduce the cardinality of the Steiner tree problem. Then, in order to provide easy‐to‐implement and effective computational tools to benchmark heuristics, we introduce new polynomial‐size integer linear programming formulations for the problem. Being defined by a polynomial number of variables and constraints, the formulations can be used to address instances of the problem by means of off‐the‐shelf mixed‐integer linear programming solvers with minimum implementation efforts. All proposed formulations share the property that the integrality requirement can be relaxed on subsets of variables. This enables several algorithmic choices to solve the models, including Benders' decomposition approaches and branch‐and‐bound with specific branching priorities. We experimentally identify the best resolution method for each formulation. Moreover, the experimental results obtained on benchmark instances of the problem, compared against those reported in the literature, support the effectiveness arising from using the new proposed formulations.

Many routing and scheduling problems are modeled through variables that represent paths (routes, schedules, etc.). For such extensive formulations, branch-price-and-cut (BPC) algorithms nowadays constitute the leading exact solution technique, and most of the time, the pricing problem is a shortest-path problem with resource constraints that can be solved by a dynamic-programming labeling algorithm. For this setting, variable fixing techniques based on the reduced costs of the paths have been proposed with the aim of eliminating arcs from the underlying network and speeding up the solution process of the pricing problem as well as of the overall BPC algorithm. For an efficient variable fixation, bidirectional labeling must be possible. We move one step forward and show how the reduced costs of paths can also be exploited to reduce the resource windows for many types of resources, including the time resource and a load-related resource. This can be achieved without modifying the pricing problem network and altering the structure of the pricing problem itself. Moreover, different resources can be considered simultaneously. A straightforward reduction of the resource windows associated with the vertices of the network can tighten them, but this reduction does not translate into savings in computation times. On the contrary, the reduction of the resource windows is effective when distinct forward and backward resource windows are defined for each arc and reduced independently based on the traversal direction of the arc itself. Moreover, an arc can be eliminated when one of its arc-specific resource windows becomes empty, and the explicit use of variable fixing techniques can be avoided. Computational results obtained for benchmark instances of the vehicle-routing problem with time windows show that the overall computation times of the BPC algorithm can be significantly reduced compared with a fully fledged BPC algorithm using variable fixing techniques. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This research was supported by the Deutsche Forschungsgemeinschaft (DFG) [Grants GS 83/1-1 and IR 122/10-1] of Project 418727865. This support is gratefully acknowledged.

Abstract Given a wireless sensor network, we consider the problem to minimize its total energy consumption over consecutive time slots with respect to communication activities. Nonempty and disjoint subsets of nodes are required to be active and connected under a tree topology configuration in the different time slots, and each network node must be active in a unique time slot. Moreover, the power required by the same pair of network nodes to communicate on the associated direct channel may vary in the different time slots. The problem has been recently introduced in the literature under the name Sub‐Tree Scheduling for Wireless Sensor Networks with Partial Coverage. We focus on the exact solution of the problem. We present a branch‐and‐cut (BC) algorithm based on a novel integer linear programming formulation which allows avoiding the introduction of symmetries in the solution space. In particular, the algorithm relies on an efficient and nontypical separation algorithm for known valid inequalities, and on an easy‐to‐implement primal bound heuristic. The effectiveness of the BC algorithm is empirically shown through an extensive experimental analysis involving 300 newly generated benchmark instances with up to 200 network nodes and 8 time slots. Additionally, the experimental results show that the BC algorithm represents a valid computational tool to benchmark the performance of heuristics addressing the problem, and can be used in practice, as an heuristic solver, to tackle problem instances that are not too large.

Abstract In this article, we study the capacitated team orienteering problem where split deliveries are allowed. A set of potential customers is given, each associated with a demand and a profit. The set of customers to be served by a fleet of capacitated vehicles has to be identified in such a way that the profit collected is maximized, while satisfying constraints on the maximum time duration of each route and the vehicle capacity constraints. When split deliveries are allowed, each customer may be served by more than one vehicle. We show that the profit collected by allowing split deliveries may be as large as twice the profit collected under the constraint that each customer has to be served by one vehicle at most. We then present a branch‐and‐price exact algorithm and a hybrid heuristic. We show the effectiveness of the proposed approaches on benchmark instances and on a new set of instances that allow us to computationally evaluate the impact of split deliveries. © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 63(1), 16–33 2014

Abstract In this article, we study a variant of the capacitated team orienteering problem, that is the problem where a fleet of vehicles, each with a constraint on the time available, is given to serve profitable customers with the objective of maximizing the collected profit. We study the variant where customers may be only partially served (incomplete service) and, if beneficial, also by more than one vehicle (split deliveries). We will analyze the maximum theoretical increase of the profit due to the incomplete service and to the split deliveries. We also computationally measure such increase on a set of instances, by means of an exact algorithm on small/medium size instances and of two heuristics on instances of larger size. © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 63(2), 135–145 2014

Abstract In this article we present a branch‐and‐price‐and‐cut method for the solution of the split delivery vehicle routing problem (SDVRP). The SDVRP is the problem to serve customers with a fleet of capacitated vehicles at minimum traveling cost. With respect to the classical vehicle routing problem, where each customer is visited exactly once, in the SDVRP a customer may be visited any number of times. The exact method we propose is based on a decomposition of the problem where the possible routes, with the delivery quantities, are generated in the subproblem. The generated routes are also used to find a heuristic solution to the problem. We consider both the case where the fleet of vehicles is unlimited and the case where the fleet is limited to the minimum possible number of vehicles. We solve to optimality instances with larger size with respect to previous approaches, find new best solutions to several benchmark instances and reduce the optimality gap on most of the benchmark instances. © 2011 Wiley Periodicals, Inc. NETWORKS, Vol. 58(4), 241–254 2011