New algorithms for pattern matching with wildcards and length constraints

2015 ◽  
Vol 07 (03) ◽  
pp. 1550032 ◽  
Author(s):  
Abdullah N. Arslan ◽  
Betsy George ◽  
Kirsten Stor
Keyword(s):  
Pattern Matching ◽  
Polynomial Time ◽  
Original Problem ◽  
Heuristic Algorithms ◽  
Optimal Solution ◽  
Exact Algorithm ◽  
Exact Algorithms ◽  
Worst Case ◽  
Special Cases ◽  
New Algorithms

The pattern matching with wildcards and length constraints problem is an interesting problem in the literature whose computational complexity is still open. There are polynomial time exact algorithms for its special cases. There are heuristic algorithms, and online algorithms that do not guarantee an optimal solution to the original problem. We consider two special cases of the problem for which we develop offline solutions. We give an algorithm for one case with provably better worst case time complexity compared to existing algorithms. We present the first exact algorithm for the second case. This algorithm uses integer linear programming (ILP) and it takes polynomial time under certain conditions.

scholarly journals Defending with Shared Resources on a Network

2020 ◽  
Vol 34 (02) ◽  
pp. 2111-2118
Author(s):  
Minming Li ◽  
Long Tran-Thanh ◽  
Xiaowei Wu
Keyword(s):  
Lower Bound ◽  
Approximation Algorithm ◽  
Polynomial Time ◽  
General Problem ◽  
Exact Algorithm ◽  
Exact Algorithms ◽  
Np Hard ◽  
Shared Resources ◽  
Target Node ◽  
Special Cases

In this paper we consider a defending problem on a network. In the model, the defender holds a total defending resource of R, which can be distributed to the nodes of the network. The defending resource allocated to a node can be shared by its neighbors. There is a weight associated with every edge that represents the efficiency defending resources are shared between neighboring nodes. We consider the setting when each attack can affect not only the target node, but its neighbors as well. Assuming that nodes in the network have different treasures to defend and different defending requirements, the defender aims at allocating the defending resource to the nodes to minimize the loss due to attack. We give polynomial time exact algorithms for two important special cases of the network defending problem. For the case when an attack can only affect the target node, we present an LP-based exact algorithm. For the case when defending resources cannot be shared, we present a max-flow-based exact algorithm. We show that the general problem is NP-hard, and we give a 2-approximation algorithm based on LP-rounding. Moreover, by giving a matching lower bound of 2 on the integrality gap on the LP relaxation, we show that our rounding is tight.

scholarly journals The Complexity Landscape of Resource-Constrained Scheduling

2020 ◽  
Author(s):  
Robert Ganian ◽  
Thekla Hamm ◽  
Guillaume Mescoff
Keyword(s):  
Artificial Intelligence ◽  
Polynomial Time ◽  
Project Scheduling ◽  
Scheduling Problem ◽  
Comprehensive Understanding ◽  
Resource Constrained ◽  
Special Cases ◽  
Project Scheduling Problem ◽  
Np Complete ◽  
New Algorithms

The Resource-Constrained Project Scheduling Problem (RCPSP) and its extension via activity modes (MRCPSP) are well-established scheduling frameworks that have found numerous applications in a broad range of settings related to artificial intelligence. Unsurprisingly, the problem of finding a suitable schedule in these frameworks is known to be NP-complete; however, aside from a few results for special cases, we have lacked an in-depth and comprehensive understanding of the complexity of the problems from the viewpoint of natural restrictions of the considered instances. In the first part of our paper, we develop new algorithms and give hardness-proofs in order to obtain a detailed complexity map of (M)RCPSP that settles the complexity of all 1024 considered variants of the problem defined in terms of explicit restrictions of natural parameters of instances. In the second part, we turn to implicit structural restrictions defined in terms of the complexity of interactions between individual activities. In particular, we show that if the treewidth of a graph which captures such interactions is bounded by a constant, then we can solve MRCPSP in polynomial time.

Fast Filtering of Search Results Sorted by Attribute

2022 ◽  
Vol 40 (2) ◽  
pp. 1-24
Author(s):  
Franco Maria Nardini ◽  
Roberto Trani ◽  
Rossano Venturini
Keyword(s):  
Heuristic Algorithms ◽  
State Of The Art ◽  
Optimal Algorithm ◽  
Computational Cost ◽  
Approximation Error ◽  
Optimal Solution ◽  
Exact Algorithm ◽  
Performance Bounds ◽  
Search Results ◽  
Filtering Problem

Modern search services often provide multiple options to rank the search results, e.g., sort “by relevance”, “by price” or “by discount” in e-commerce. While the traditional rank by relevance effectively places the relevant results in the top positions of the results list, the rank by attribute could place many marginally relevant results in the head of the results list leading to poor user experience. In the past, this issue has been addressed by investigating the relevance-aware filtering problem, which asks to select the subset of results maximizing the relevance of the attribute-sorted list. Recently, an exact algorithm has been proposed to solve this problem optimally. However, the high computational cost of the algorithm makes it impractical for the Web search scenario, which is characterized by huge lists of results and strict time constraints. For this reason, the problem is often solved using efficient yet inaccurate heuristic algorithms. In this article, we first prove the performance bounds of the existing heuristics. We then propose two efficient and effective algorithms to solve the relevance-aware filtering problem. First, we propose OPT-Filtering, a novel exact algorithm that is faster than the existing state-of-the-art optimal algorithm. Second, we propose an approximate and even more efficient algorithm, ϵ-Filtering, which, given an allowed approximation error ϵ, finds a (1-ϵ)–optimal filtering, i.e., the relevance of its solution is at least (1-ϵ) times the optimum. We conduct a comprehensive evaluation of the two proposed algorithms against state-of-the-art competitors on two real-world public datasets. Experimental results show that OPT-Filtering achieves a significant speedup of up to two orders of magnitude with respect to the existing optimal solution, while ϵ-Filtering further improves this result by trading effectiveness for efficiency. In particular, experiments show that ϵ-Filtering can achieve quasi-optimal solutions while being faster than all state-of-the-art competitors in most of the tested configurations.

scholarly journals An Exact Algorithm for Bilevel 0-1 Knapsack Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Raid Mansi ◽  
Cláudio Alves ◽  
J. M. Valério de Carvalho ◽  
Saïd Hanafi
Keyword(s):  
Optimization Problem ◽  
Original Problem ◽  
Parametric Optimization ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Exact Algorithm ◽  
Decision Makers ◽  
Knapsack Problems ◽  
Hierarchical Decision ◽  
Parametric Optimization Problem

We propose a new exact method for solving bilevel 0-1 knapsack problems. A bilevel problem models a hierarchical decision process that involves two decision makers called the leader and the follower. In these processes, the leader takes his decision by considering explicitly the reaction of the follower. From an optimization standpoint, these are problems in which a subset of the variables must be the optimal solution of another (parametric) optimization problem. These problems have various applications in the field of transportation and revenue management, for example. Our approach relies on different components. We describe a polynomial time procedure to solve the linear relaxation of the bilevel 0-1 knapsack problem. Using the information provided by the solutions generated by this procedure, we compute a feasible solution (and hence a lower bound) for the problem. This bound is used together with an upper bound to reduce the size of the original problem. The optimal integer solution of the original problem is computed using dynamic programming. We report on computational experiments which are compared with the results achieved with other state-of-the-art approaches. The results attest the performance of our approach.

Robust Tolerance Synthesis With the Design of Experiments Approach

1999 ◽  
Vol 122 (3) ◽  
pp. 520-528 ◽  
Author(s):  
Chang-Xue (Jack) Feng ◽  
Andrew Kusiak
Keyword(s):  
Design Of Experiments ◽  
Heuristic Algorithms ◽  
Exact Algorithms ◽  
Manufacturing Processes ◽  
Manufacturing Cost ◽  
Simulation Approach ◽  
Worst Case ◽  
Quality Cost ◽  
Tolerance Synthesis ◽  
Selection Of

Design of tolerances impacts quality, cost, and cycle time of a product. Most literature on deterministic tolerance design has focused on developing exact and heuristic algorithms to minimize manufacturing cost. Some research has been published on probabilistic tolerance synthesis and optimization. This paper presents the design of experiments (DOE) approach for concurrent selection of component tolerances and the corresponding manufacturing processes. The objective is to minimize the variation of tolerance stackups. Numerical examples illustrate the methodology. The Monte Carlo simulation approach is used to obtain component tolerances and tolerance stackups. Process shift, the worst case and root sum square tolerance stackup constraints, and setup reduction constraints have been incorporated into the proposed methodology. Benefits of the proposed DOE approach over exact algorithms are discussed. [S1087-1357(00)00202-1]

scholarly journals Heuristic and Exact Algorithms for the Two-Machine Just in Time Job Shop Scheduling Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Mohammed Al-Salem ◽  
Leonardo Bedoya-Valencia ◽  
Ghaith Rabadi
Keyword(s):  
Job Shop ◽  
Heuristic Algorithms ◽  
Job Shop Scheduling ◽  
Optimal Solution ◽  
Approximate Solutions ◽  
Exact Algorithms ◽  
Just In Time ◽  
Scheduling Problem ◽  
Job Shop Scheduling Problem ◽  
Shop Scheduling

The problem addressed in this paper is the two-machine job shop scheduling problem when the objective is to minimize the total earliness and tardiness from a common due date (CDD) for a set of jobs when their weights equal 1 (unweighted problem). This objective became very significant after the introduction of the Just in Time manufacturing approach. A procedure to determine whether the CDD is restricted or unrestricted is developed and a semirestricted CDD is defined. Algorithms are introduced to find the optimal solution when the CDD is unrestricted and semirestricted. When the CDD is restricted, which is a much harder problem, a heuristic algorithm is proposed to find approximate solutions. Through computational experiments, the heuristic algorithms’ performance is evaluated with problems up to 500 jobs.

Solution of “Hard” Knapsack Instances Using Quantum Inspired Evolutionary Algorithm

2014 ◽  
Vol 5 (1) ◽  
pp. 52-68 ◽  
Author(s):  
C. Patvardhan ◽  
Sulabh Bansal ◽  
Anand Srivastav
Keyword(s):  
Evolutionary Algorithm ◽  
Exact Algorithm ◽  
Population Based ◽  
Exact Algorithms ◽  
Programming Technique ◽  
Worst Case ◽  
Problem Instances ◽  
Population Based Search ◽  
Made In

Knapsack Problem (KP) is a popular combinatorial optimization problem having application in many technical and economic areas. Several attempts have been made in past to solve the problem. Various exact and non-exact approaches exist to solve KP. Exact algorithms for KP are based on either branch and bound or dynamic programming technique. Heuristics exist which solve KP non-exactly in lesser time. Heuristic approaches do not provide any guarantee regarding the quality of solution whereas exact approaches have high worst case complexities. Quantum-inspired Evolutionary Algorithm (QEA) is a subclass of Evolutionary Algorithm, a naturally inspired population based search technique. QEA uses concepts of quantum computing. An engineered Quantum-inspired Evolutionary Algorithm (QEA-E), an improved version of QEA, is presented which quickly solves extremely large spanner problem instances (e.g. 290,000 items) that are very difficult for the state of the art exact algorithm as well as the original QEA.

Linear pattern matching of compressed terms and polynomial rewriting

2018 ◽  
Vol 28 (8) ◽  
pp. 1415-1450 ◽  
Author(s):  
MANFRED SCHMIDT-SCHAUß
Keyword(s):  
Pattern Matching ◽  
Polynomial Time ◽  
Directed Acyclic Graph ◽  
Term Rewriting ◽  
Single Step ◽  
Worst Case ◽  
Linear Pattern ◽  
Input Size ◽  
Straight Line ◽  
Rewrite System

We consider term rewriting under sharing in the form of compression by singleton tree grammars (STG), which is more general than the term dags. Algorithms for the subtasks of rewriting are analysed: finding a redex for rewriting by locating a position for a match, performing a rewrite step by constructing the compressed result and executing a sequence of rewrite steps. The first main result is that locating a match of a linear termsin another termtcan be performed in polynomial time ifs,tare both STG-compressed. This generalizes results on matching of STG-compressed terms, matching of straight-line-program-compressed strings with character-variables, where every variable occurs at most once, and on fully compressed matching of strings. Also, for the case wheresis directed-acyclic-graph (DAG)-compressed, it is shown that submatching can be performed in polynomial time. The general case of compressed submatching can be computed in non-deterministic polynomial time, and an algorithm is described that may be exponential in the worst case, its complexity isnO(k), wherekis the number of variables with double occurrences insandnis the size of the input. The second main result is that in case there is an oracle for the redex position, a sequence ofmparallel or single-step rewriting steps under STG-compression can be performed in polynomial time. This generalizes results on DAG-compressed rewriting sequences. Combining these results implies that for an STG-compressed term rewrite system with left-linear rules,mparallel or single-step term rewrite steps can be performed in polynomial time in the input sizenandm.

scholarly journals Exact and Heuristic Algorithms for Routing AGV on Path with Precedence Constraints

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Liang Xu ◽  
Yao Wang ◽  
Lin Liu ◽  
Jiaxing Wang
Keyword(s):  
Dynamic Programming ◽  
Traveling Salesman Problem ◽  
Polynomial Time ◽  
Heuristic Algorithms ◽  
Exact Algorithm ◽  
Precedence Constraints ◽  
Traveling Salesman ◽  
Automated Guided Vehicle ◽  
Np Complete

A new problem arises when an automated guided vehicle (AGV) is dispatched to visit a set of customers, which are usually located along a fixed wire transmitting signal to navigate the AGV. An optimal visiting sequence is desired with the objective of minimizing the total travelling distance (or time). When precedence constraints are restricted on customers, the problem is referred to as traveling salesman problem on path with precedence constraints (TSPP-PC). Whether or not it is NP-complete has no answer in the literature. In this paper, we design dynamic programming for the TSPP-PC, which is the first polynomial-time exact algorithm when the number of precedence constraints is a constant. For the problem with number of precedence constraints, part of the input can be arbitrarily large, so we provide an efficient heuristic based on the exact algorithm.

scholarly journals The Static Bike Sharing Rebalancing Problem with Forbidden Temporary Operations

2019 ◽  
Vol 53 (3) ◽  
pp. 882-896 ◽  
Author(s):  
Bruno P. Bruck ◽  
Fábio Cruz ◽  
Manuel Iori ◽  
Anand Subramanian
Keyword(s):  
Minimum Cost ◽  
Exact Algorithm ◽  
Exact Algorithms ◽  
Worst Case Analysis ◽  
Worst Case ◽  
Online Appendix ◽  
Bike Sharing ◽  
Courier Service ◽  
Demand And Capacity ◽  
Theoretical Results

This paper introduces and solves the static bike rebalancing problem with forbidden temporary operations. In this problem, one aims at finding a minimum cost route in which a vehicle performs a series of pickup and delivery operations while satisfying demand and capacity constraints. In addition, a vehicle can visit stations multiple times but cannot use them to temporarily store or provide bikes. Apart from bike rebalancing, the problem also models courier service transportation and repositioning of inventory between retail stores, where temporary operations are frequently disliked because they require additional manual work and service time. We present some theoretical results concerning problem complexity and worst-case analysis, and then propose three exact algorithms based on different mathematical formulations. Extensive computational results on instances involving up to 80 stations show that an exact algorithm based on a minimal extended network produces the best average results. The online appendix is available at https://doi.org/10.1287/trsc.2018.0859 .

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