Search NASA⌕ Search

SEARCH · Search NASA

Results for “NP-hard problems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

The Algorithm Selection Problem

Work on NP-hard problems has shown that many instances of these theoretically computationally difficult problems are quite easy. The field has also shown that choosing the right algorithm for the problem can have a profound effect on the time needed to find a solution. However, to date there has been little work showing how to select the right algorithm for solving any particular problem. The paper refers to this as the algorithm selection problem. It describes some of the aspects that make this problem difficult, as well as proposes a technique for addressing it.

Minton, Steve↗
NASA NTRS1990

Automated Spacelab Stowage Expert System for SLS missions

Issues related to the development of the Automated Spacelab Stowage Expert System (ASSESS) are examined including the problem domain, design, and status. The ASSESS concept is designed to configure stowage items into Spacelab lockers with an expert-system approach in which knowledge is available for every item and locker and for the complete heuristics. ASSESS employs the Knowledge Engineering Environment for development, and graphic displays present data on the items, lockers, and general system status. The automatic and manual modes are presented; the former provides the capability for an automatic solution to the stowage of a set of items into Spacelab lockers based on stowage heuristics defined and/or set by the user. The approach and heuristics algorithms are shown to permit the effective practical solution of NP-hard problems.

Kao, C. Y.↗
NASA NTRS1993

Learning Search Control Knowledge for Deep Space Network Scheduling

While the general class of most scheduling problems is NP-hard in worst-case complexity, in practice, for specific distributions of problems and constraints, domain-specific solutions have been shown to perform in much better than exponential time.

Deep Space Network Search Control↗
NASA NTRS1992

Generating effective project scheduling heuristics by abstraction and reconstitution

A project scheduling problem consists of a finite set of jobs, each with fixed integer duration, requiring one or more resources such as personnel or equipment, and each subject to a set of precedence relations, which specify allowable job orderings, and a set of mutual exclusion relations, which specify jobs that cannot overlap. No job can be interrupted once started. The objective is to minimize project duration. This objective arises in nearly every large construction project--from software to hardware to buildings. Because such project scheduling problems are NP-hard, they are typically solved by branch-and-bound algorithms. In these algorithms, lower-bound duration estimates (admissible heuristics) are used to improve efficiency. One way to obtain an admissible heuristic is to remove (abstract) all resources and mutual exclusion constraints and then obtain the minimal project duration for the abstracted problem; this minimal duration is the admissible heuristic. Although such abstracted problems can be solved efficiently, they yield inaccurate admissible heuristics precisely because those constraints that are central to solving the original problem are abstracted. This paper describes a method to reconstitute the abstracted constraints back into the solution to the abstracted problem while maintaining efficiency, thereby generating better admissible heuristics. Our results suggest that reconstitution can make good admissible heuristics even better.

Janakiraman, Bhaskar↗
DOE OSTI2026

T-FSM: A Scalable Distributed Task-Based System for Frequent Subgraph Pattern Mining from a Big Graph

Finding frequent subgraph patterns in a big graph is an important problem with many applications such as classifying chemical compounds and building indexes to speed up graph queries. Since this problem is NP-hard, some recent parallel and distributed systems have been developed to accelerate the mining. However, they often have a huge memory cost, very long running time, suboptimal load balancing, poor scale-out capability, and possibly inaccurate results. In this article, we propose an efficient system called T-FSM for parallel mining of frequent subgraph patterns in a big graph. T-FSM supports a new anti-monotonic frequentness measure called Fraction-Score, which is more accurate than the widely used MNI measure. The execution engine of T-FSM supports both intra-machine parallelism and inter-machine parallelism. For intra-machine parallelism, T-FSM adopts a novel task-based execution model to ensure high multithreading concurrency, bounded memory consumption, and effective load balancing. For inter-machine parallelism, T-FSM ensures good scale-out performance with a lightweight pattern rebalancing approach that reduces workload skewness of pattern evaluations among machines. To avoid recomputing the contexts for migrated patterns, we design a novel context cache table to support concurrent and asynchronous requesting and caching of remote context data, which can timely evict and garbage collect used pattern contexts that are no longer needed to keep memory consumption bounded. Extensive experiments show that T-FSM is orders of magnitude faster than existing state-of-the-art parallel systems (more than 10×, 51×, 131×, 55× speedup over ScaleMine, DistGraph, Pangolin and Peregrine, respectively) and distributed systems (more than 42× and 88× over ScaleMine and DistGraph, respectively) for frequent subgraph pattern mining, and it scales out satisfactorily to 512 CPU cores on the Polaris supercomputer at Argonne National Laboratory.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Inference in fuzzy rule bases with conflicting evidence

Inference based on fuzzy 'If ... then' rules has played a very important role since when Zadeh proposed the Compositional Rule of Inference and, especially, since the first successful application presented by Mamdani. From the mid-1980's when the 'fuzzy boom' started in Japan, numerous industrial applications appeared, all using simplified techniques because of the high levels of computational complexity. Another feature is that antecedents in the rules are distributed densely in the input space, so the conclusion can be calculated by some weighted combination of the consequents of the matching (fired) rules. The CRI works in the following way: If R is a rule and A* is an observation, the conclusion is computed by B* = R o A* (o stands for the max-min composition). Algorithms implementing this idea directly have an exponential time complexity (maybe the problem is NP-hard) as the rules are relations in X x Y, a k1 x k2 dimensional space, if X is k1, Y is k2 dimensional. The simplified techniques usually decompose the relation into k1 projections in X(sub i) and measure in some way the degree of similarity between observation and antecedent by some parameter of the overlapping. These parameters are aggregated to a single value in (0,1) which is applied as a resulting weight for the given rule. The projections of rules in dimensions Y(sub i) are weighted by these aggregated values and then they are combined in order to obtain a resulting conclusion separately in every dimension. This method is unapplicable with sparse bases as there is no guarantee that an arbitrary observation matches with any of the antecedents. Then, the degree of similarity is 0 and all consequents are weighted by 0. Some considerations for such a situation are summarized in the next sections.

Koczy, Laszlo T.↗
NASA NTRS1996

Site Partitioning for Redundant Arrays of Distributed Disks

Redundant arrays of distributed disks (RADD) can be used in a distributed computing system or database system to provide recovery in the presence of disk crashes and temporary and permanent failures of single sites. In this paper, we look at the problem of partitioning the sites of a distributed storage system into redundant arrays in such a way that the communication costs for maintaining the parity information are minimized. We show that the partitioning problem is NP-hard. We then propose and evaluate several heuristic algorithms for finding approximate solutions. Simulation results show that significant reduction in remote parity update costs can be achieved by optimizing the site partitioning scheme.

Mourad, Antoine N.↗
NASA NTRS2001

Temporal Constraint Reasoning With Preferences

A number of reasoning problems involving the manipulation of temporal information can naturally be viewed as implicitly inducing an ordering of potential local decisions involving time (specifically, associated with durations or orderings of events) on the basis of preferences. For example. a pair of events might be constrained to occur in a certain order, and, in addition. it might be preferable that the delay between them be as large, or as small, as possible. This paper explores problems in which a set of temporal constraints is specified, where each constraint is associated with preference criteria for making local decisions about the events involved in the constraint, and a reasoner must infer a complete solution to the problem such that, to the extent possible, these local preferences are met in the best way. A constraint framework for reasoning about time is generalized to allow for preferences over event distances and durations, and we study the complexity of solving problems in the resulting formalism. It is shown that while in general such problems are NP-hard, some restrictions on the shape of the preference functions, and on the structure of the preference set, can be enforced to achieve tractability. In these cases, a simple generalization of a single-source shortest path algorithm can be used to compute a globally preferred solution in polynomial time.

Khatib, Lina↗
DOE OSTI2024

Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. In conclusion, we numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs.

Derivative-free Optimization↗
DOE OSTI2025

Comparing three generations of D-Wave quantum annealers for minor embedded combinatorial optimization problems

Abstract Quantum annealing (QA) is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. QA in the transverse Ising model, implemented on D-Wave quantum processing units, are available as cloud computing resources. In this study we report concise benchmarks across three generations of D-Wave quantum annealers, consisting of four different devices, for the NP-hard discrete combinatorial optimization problems unweighted maximum clique and unweighted maximum cut on random graphs. The Ising, or equivalently quadratic unconstrained binary optimization, formulation of these problems do not require auxiliary variables for order reduction, and their overall structure and weights are not highly variable, which makes these problems simple test cases to understand the sampling capability of current D-Wave quantum annealers. All-to-all minor embeddings of size 52, with relatively uniform chain lengths, are used for a direct comparison across the Chimera, Pegasus, and Zephyr device topologies. A grid-search over annealing times and the minor embedding chain strengths is performed in order to determine the level of reasonable performance for each device and problem type. Experiment metrics that are reported are approximation ratios for non-broken chain samples, chain break proportions, and time-to-solution for the maximum clique problem instances. How fairly the quantum annealers sample optimal maximum cliques, for instances which contain multiple maximum cliques, is quantified using entropy of the measured ground state distributions. The newest generation of quantum annealing hardware, which has a Zephyr hardware connectivity, performed the best overall with respect to approximation ratios and chain break frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Enabling Real-Time Communication in Multi-Agent Systems: A Graph Neural Network Based Approach

Global connectivity enables effective coordination in Multi-Agent Systems (MAS). Solving these connection problems under hardware constraints is an NP-hard non-Euclidean Degree Constrained Minimum Spanning Tree (DCMST) problem. Prior MAS controllers coordinate team movement for task completion and collision avoidance; some considering Line-of-Sight (LOS) maintenance but prioritizing flexibility over guarantees. Evolutionary Algorithms (EA) have been shown to find good solutions for DCMST, but their performance degrades with larger populations required to support a large MAS. We present a method based on edge graph attention networks, trained offline to reduce online computation times. Empirical comparisons with greedy polynomial-time solvers and EA show that our method leverages latent graph information to consistently find constraint-satisfying solutions in less time.

connectivity maintenance↗
NASA NTRS1997

Sequential Testing Algorithms for Multiple Fault Diagnosis

In this paper, we consider the problem of constructing optimal and near-optimal test sequencing algorithms for multiple fault diagnosis. The computational complexity of solving the optimal multiple-fault isolation problem is super-exponential, that is, it is much more difficult than the single-fault isolation problem, which, by itself, is NP-hard. By employing concepts from information theory and AND/OR graph search, we present several test sequencing algorithms for the multiple fault isolation problem. These algorithms provide a trade-off between the degree of suboptimality and computational complexity. Furthermore, we present novel diagnostic strategies that generate a diagnostic directed graph (digraph), instead of a diagnostic tree, for multiple fault diagnosis. Using this approach, the storage complexity of the overall diagnostic strategy reduces substantially. The algorithms developed herein have been successfully applied to several real-world systems. Computational results indicate that the size of a multiple fault strategy is strictly related to the structure of the system.

Shakeri, Mojdeh↗
NASA NTRS1997

Sequential Test Strategies for Multiple Fault Isolation

In this paper, we consider the problem of constructing near optimal test sequencing algorithms for diagnosing multiple faults in redundant (fault-tolerant) systems. The computational complexity of solving the optimal multiple-fault isolation problem is super-exponential, that is, it is much more difficult than the single-fault isolation problem, which, by itself, is NP-hard. By employing concepts from information theory and Lagrangian relaxation, we present several static and dynamic (on-line or interactive) test sequencing algorithms for the multiple fault isolation problem that provide a trade-off between the degree of suboptimality and computational complexity. Furthermore, we present novel diagnostic strategies that generate a static diagnostic directed graph (digraph), instead of a static diagnostic tree, for multiple fault diagnosis. Using this approach, the storage complexity of the overall diagnostic strategy reduces substantially. Computational results based on real-world systems indicate that the size of a static multiple fault strategy is strictly related to the structure of the system, and that the use of an on-line multiple fault strategy can diagnose faults in systems with as many as 10,000 failure sources.

Shakeri, M.↗
NASA NTRS1992

Traffic routing for multicomputer networks with virtual cut-through capability

Consideration is given to the problem of selecting routes for interprocess communication in a network with virtual cut-through capability, while balancing the network load and minimizing the number of times that a message gets buffered. An approach is proposed that formulates the route selection problem as a minimization problem with a link cost function that depends upon the traffic through the link. The form of this cost function is derived using the probability of establishing a virtual cut-through route. The route selection problem is shown to be NP-hard, and an algorithm is developed to incrementally reduce the cost by rerouting the traffic. The performance of this algorithm is exemplified by two network topologies: the hypercube and the C-wrapped hexagonal mesh.

Kandlur, Dilip D.↗
NASA NTRS1997

Dynamic Flow Management Problems in Air Transportation

In 1995, over six hundred thousand licensed pilots flew nearly thirty-five million flights into over eighteen thousand U.S. airports, logging more than 519 billion passenger miles. Since demand for air travel has increased by more than 50% in the last decade while capacity has stagnated, congestion is a problem of undeniable practical significance. In this thesis, we will develop optimization techniques that reduce the impact of congestion on the national airspace. We start by determining the optimal release times for flights into the airspace and the optimal speed adjustment while airborne taking into account the capacitated airspace. This is called the Air Traffic Flow Management Problem (TFMP). We address the complexity, showing that it is NP-hard. We build an integer programming formulation that is quite strong as some of the proposed inequalities are facet defining for the convex hull of solutions. For practical problems, the solutions of the LP relaxation of the TFMP are very often integral. In essence, we reduce the problem to efficiently solving large scale linear programming problems. Thus, the computation times are reasonably small for large scale, practical problems involving thousands of flights. Next, we address the problem of determining how to reroute aircraft in the airspace system when faced with dynamically changing weather conditions. This is called the Air Traffic Flow Management Rerouting Problem (TFMRP) We present an integrated mathematical programming approach for the TFMRP, which utilizes several methodologies, in order to minimize delay costs. In order to address the high dimensionality, we present an aggregate model, in which we formulate the TFMRP as a multicommodity, integer, dynamic network flow problem with certain side constraints. Using Lagrangian relaxation, we generate aggregate flows that are decomposed into a collection of flight paths using a randomized rounding heuristic. This collection of paths is used in a packing integer programming formulation, the solution of which generates feasible and near-optimal routes for individual flights. The algorithm, termed the Lagrangian Generation Algorithm, is used to solve practical problems in the southwestern portion of United States in which the solutions are within 1% of the corresponding lower bounds.

Patterson, Sarah Stock↗
DOE OSTI2026

Computing an Optimal Entanglement Path with Throughput and Fidelity Considerations

Entanglement distribution is a core function of quantum networks essential for operations including teleportation, distributed quantum sensing, and multisite computation. Entanglement throughput and fidelity are two critical performance measures that depend on the quantum transmission along the links and swapping operations at the repeaters along the path. We study the problem of computing a end-to-end entanglement path that satisfies both fidelity and throughput requirements, leveraging qubit buffers at the nodes and considering the sequential swapping order. We show that the general problem of simultaneously satisfying both metrics to be NP-hard, and develop an algorithm to maximize throughput subject to a given fidelity threshold. We introduce the concepts of entanglement probability distribution and path domination and exploit them in the design of our algorithm. Extensive numerical results show that our algorithm can find optimal solutions in networks with thousands of nodes in less than a second. We also describe practical and possible implementation aspects of this algorithm in terms of devices and architecture support.

Xue, Guoliang [Arizona State University]↗
NASA NTRS2003

Scheduling in the Face of Uncertain Resource Consumption and Utility

We discuss the problem of scheduling tasks that consume a resource with known capacity and where the tasks have varying utility. We consider problems in which the resource consumption and utility of each activity is described by probability distributions. In these circumstances, we would like to find schedules that exceed a lower bound on the expected utility when executed. We first show that while some of these problems are NP-complete, others are only NP-Hard. We then describe various heuristic search algorithms to solve these problems and their drawbacks. Finally, we present empirical results that characterize the behavior of these heuristics over a variety of problem classes.

Koga, Dennis↗