Tree Search Problem Research Articles

Keyword-Driven Service Recommendation Via Deep Reinforced Steiner Tree Search

Developers need to reuse web services and create mashups suitable for various scenarios. Currently, it relies on the developer’s adequate domain knowledge to be able to find services and verify their compatibility. Although service recommendation systems already exist to assist them, inexperienced developers may not be able to adequately express their requirements, resulting in inappropriate and incompatible recommendations. To tackle this problem, we define a service-keyword correlation graph (SKCG) to capture the relationship between services and keywords, and the compatibility among services. Then, we propose keyword-based deep reinforced Steiner tree search (K-DRSTS) to recommend services for mashup creation. K-DRSTS models the task of service discovery as a Steiner tree search problem against SKCG. Leveraging deep reinforcement learning, K-DRSTS provides an efficient solution for solving the NP-hard search problem of the Steiner tree. Extensive experiments on real-world data sets have shown the effectiveness of K-DRSTS.

Diversified and compatible web APIs recommendation based on game theory in IoT

With the ever-increasing popularity of Internet of Things (IoT), massive enterprises are attempting to encapsulate their developed outcomes into various lightweight Web Application Programming Interfaces (APIs) that can be accessible remotely. In this context, finding and writing a list of existing Web APIs that can collectively meet the functional needs of software developers has become a promising approach to economically and easily develop successful mobile applications. However, the number and diversity of candidate IoT Web APIs places an additional burden on application developers’ Web API selection decisions, as it is often a challenging task to simultaneously ensure the diversity and compatibility of the final set of Web APIs selected. Considering this challenge and latest successful applications of game theory in IoT, a Diversified and Compatible Web APIs Recommendation approach, namely DivCAR, is put forward in this paper. First of all, to achieve API diversity, DivCAR employs random walk sampling technique on a pre-built “API-API” correlation graph to generate diverse “API-API” correlation subgraphs. Afterwards, with the diverse “API-API” correlation subgraphs, the compatible Web APIs recommendation problem is modeled as a minimum group Steiner tree search problem. A sorted set of multiple compatible and diverse Web APIs are returned to the application developer by solving the minimum group Steiner tree search problem. At last, a set of experiments are designed and implemented on a real dataset crawled from www.programmableweb.com. Experimental results validate the effectiveness and efficiency of our proposed DivCAR approach in balancing the Web APIs recommendation diversity and compatibility.

A Parallel Tempering Approach for Efficient Exploration of the Verification Tradespace in Engineered Systems

Verification is a critical process in the development of engineered systems. Through verification, engineers gain confidence in the correct functionality of the system before it is deployed into operation. Traditionally, verification strategies are fixed at the beginning of the system’s development and verification activities (VAs) are executed as the development progresses. Such an approach appears to give inferior results as the selection of the VAs does not leverage information gained through the system’s development process. In contrast, a set-based design (SBD) approach to verification, where VAs are dynamically selected as the system’s development progresses, has been shown to provide superior results. However, its application under realistic engineering scenarios remains unproven due to the large size of the verification tradespace. In this work, we propose a parallel tempering approach (PTA) to efficiently explore the verification tradespace. First, we formulate an exploration of the verification tradespace as a tree search problem. Second, we design a parallel tempering (PT) algorithm by simulating several replicas of the verification process at different temperatures to obtain a near-optimal result. Third, We apply the PT algorithm to all possible verification states to dynamically identify near-optimal results. The effectiveness of the proposed PTA is evaluated on a partial model of a notional satellite optical instrument.

A Generalized Information-Theoretic Framework for the Emergence of Hierarchical Abstractions in Resource-Limited Systems.

In this paper, a generalized information-theoretic framework for the emergence of multi-resolution hierarchical tree abstractions is developed. By leveraging ideas from information-theoretic signal encoding with side information, this paper develops a tree search problem which considers the generation of multi-resolution tree abstractions when there are multiple sources of relevant and irrelevant, or possibly confidential, information. We rigorously formulate an information-theoretic driven tree abstraction problem and discuss its connections with information-theoretic privacy and resource-limited systems. The problem structure is investigated and a novel algorithm, called G-tree search, is proposed. The proposed algorithm is analyzed and a number of theoretical results are established, including the optimally of the G-tree search algorithm. To demonstrate the utility of the proposed framework, we apply our method to a real-world example and provide a discussion of the results from the viewpoint of designing hierarchical abstractions for autonomous systems.

An Optimal Computing Budget Allocation Tree Policy for Monte Carlo Tree Search

We analyze a tree search problem with an underlying Markov decision process, in which the goal is to identify the best action at the root that achieves the highest cumulative reward. We present a new tree policy that optimally allocates a limited computing budget to maximize a lower bound on the probability of correctly selecting the best action at each node. Compared to widely used upper confidence bound (UCB) tree policies, the new tree policy presents a more balanced approach to manage the exploration and exploitation tradeoff when the sampling budget is limited. Furthermore, UCB assumes that the support of reward distribution is known, whereas our algorithm relaxes this assumption. Numerical experiments demonstrate the efficiency of our algorithm in selecting the best action at the root.

Dynamic VNF Forwarding Graph Extension Algorithms

This paper proposes a set of algorithms to extend initially deployed Virtualized Network Functions Forwarding Graphs (VNF-FG or Service Function Chains - SFCs) previously requested and acquired by tenants. The latter are likely to request extension of their already acquired, deployed, and running dedicated slices to embed additional networking functions to handle for instance new application flows requiring additional classification, authentication, authorization, processing, traffic steering, etc. The tenants (or end-user service providers) are also likely to introduce gradually their services as needs arise and as their consumer base and profiles evolve. Increasing traffic load often will also require extension of the service graphs and chaining such as introducing additional load balancers and servers, new security functions, and simply new VNFs related to new tenant services. The related service graph extension problem is addressed first through an ILP algorithm that serves as a reference for performance comparisons with a set of proposed heuristic algorithms. A heuristic directly inspired by and based on the ILP and the proposed alternative approaches are shown to scale much better than the ILP while providing good solutions. The solutions include an adaptation of an eigendecomposition approach that provides very good performance for highly connected graphs. The problem is also cast into the well know Steiner Tree search problem whose complexity and performance are formally characterized in the literature. The Steiner based algorithm is shown to provide the best overall tradeoff (in rejection rate, complexity, and quality) with performance closest to optimal.

Generating 2D Lego Compatible Puzzles Using Reinforcement Learning

We present a framework that generates a 2D Lego-compatible puzzle layout of greater than thousands pieces of bricks using a reinforcement learning technique. Many existing 2D legorization strategies have limitations in producing a Lego layout, which is composed of more than thousands of pieces. We attack this problem by employing a reinforcement learning technique, which accelerates the progress of various game strategies. We represent the legorization process as a game tree search problem, where each leaf node of the tree corresponds to a Lego layout. The goal of legorization is to find an optimal Lego layout that achieves maximum reward. To efficiently find a leaf node for the maximum reward layout, we reduce the search space using a dueling deep Q-Network (DQN), which is a widely used reinforcement learning model. Our framework is composed of a learning stage and a legorization stage. In the learning stage, we design a dueling DQN model and train this model using three heuristics for legorization strategies. In the legorization stage, we efficiently generate a large-scaled 2D Lego-compatible puzzle layout by reducing the search space using the trained dueling DQN. This approach enables us to produce a puzzle layout of more than a thousand of pieces, which has not been feasible for existing legorization schemes.

Accurate Content Push for Content-Centric Social Networks: A Big Data Support Online Learning Approach

With the rapid growth of the social network, information overload becomes a critical issue. Service providers push a lot of redundant contents and advertisements to users every day. Thus, users’ interests and the probability of reading them have dropped considerably and the network load is wasted. To address this issue, accurate content push is needed, where the main challenges are proving precise descriptions of users and supporting the big data nature of users and contents. Content-centric networking (CCN) has emerged as a new network architecture to meet today's requirement for content access and delivery. By using the named content, CCN makes it possible to track users’ real-time interests and motivates us studying a novel content accurate push (or called content recommendation) system. In this paper, we model this issue as a novel contextual multiarmed bandit based Monte Carlo tree search problem and propose a big data support online learning algorithm to meet the demand of content push with low cost. To avoid destroying CCN's energy efficient feature, the energy consumption is considered into our module. Then, we theoretically prove that our online learning algorithm achieves sublinear regret bound and sublinear storage, which is very efficient in the big data context and do not increase the network burden. Experiments in an offline collected dataset show that our approach significantly increases the accuracy and convergence speed against other state-of-the-art bandit algorithms and can overcome the cold start problem as well.

MP-LAMP: parallel detection of statistically significant multi-loci markers on cloud platforms.

SummaryExhaustive detection of multi-loci markers from genome-wide association study datasets is a computationally challenging problem. This paper presents a massively parallel algorithm for finding all significant combinations of alleles and introduces a software tool termed MP-LAMP that can be easily deployed in a cloud platform, such as Amazon Web Service, as well as in an in-house computer cluster. Multi-loci marker detection is an unbalanced tree search problem that cannot be parallelized by simple tree-splitting using generic parallel programming frameworks, such as Map-Reduce. We employ work stealing and periodic reduce-broadcast to decrease the running time almost linearly to the number of cores.Availability and implementationMP-LAMP is available at https://github.com/tsudalab/mp-lamp.Supplementary information Supplementary data are available at Bioinformatics online.

Efficient Globally Optimal Consensus Maximisation with Tree Search.

Maximum consensus is one of the most popular criteria for robust estimation in computer vision. Despite its widespread use, optimising the criterion is still customarily done by randomised sample-and-test techniques, which do not guarantee optimality of the result. Several globally optimal algorithms exist, but they are too slow to challenge the dominance of randomised methods. Our work aims to change this state of affairs by proposing an efficient algorithm for global maximisation of consensus. Under the framework of LP-type methods, we show how consensus maximisation for a wide variety of vision tasks can be posed as a tree search problem. This insight leads to a novel algorithm based on A* search. We propose efficient heuristic and support set updating routines that enable A* search to efficiently find globally optimal results. On common estimation problems, our algorithm is much faster than previous exact methods. Our work identifies a promising direction for globally optimal consensus maximisation.

On the tree search problem with non-uniform costs

Searching in partially ordered structures has been considered in the context of information retrieval and efficient tree-like indices, as well as in hierarchy based knowledge representation. In this paper we focus on tree-like partial orders and consider the problem of identifying an initially unknown vertex in a tree by asking edge queries: an edge query e returns the component of T−e containing the vertex sought for, while incurring some known cost c(e). The Tree Search Problem with Non-Uniform Cost is the following: given a tree T on n vertices, each edge having an associated cost, construct a strategy that minimizes the total cost of the identification in the worst case.Finding the strategy guaranteeing the minimum possible cost is an NP-complete problem already for input trees of degree 3 or diameter 6. The best known approximation guarantee was an O(log⁡n/log⁡log⁡log⁡n)-approximation algorithm of Cicalese et al. (2012) [4].We improve upon the above results both from the algorithmic and the computational complexity point of view: We provide a novel algorithm that provides an O(log⁡nlog⁡log⁡n)-approximation of the cost of the optimal strategy. In addition, we show that finding an optimal strategy is NP-hard even when the input tree is a spider of diameter 6, i.e., at most one vertex has degree larger than 2.

Multipath Matching Pursuit

In this paper, we propose an algorithm referred to as multipath matching pursuit (MMP) that investigates multiple promising candidates to recover sparse signals from compressed measurements. Our method is inspired by the fact that the problem to find the candidate that minimizes the residual is readily modeled as a combinatoric tree search problem and the greedy search strategy is a good fit for solving this problem. In the empirical results as well as the restricted isometry property-based performance guarantee, we show that the proposed MMP algorithm is effective in reconstructing original sparse signals for both noiseless and noisy scenarios.

Improved Approximation Algorithms for the Average-Case Tree Searching Problem

We study the following tree search problem: in a given tree T=(V,E) a vertex has been marked and we want to identify it. In order to locate the marked vertex, we can use edge queries. An edge query e asks in which of the two connected components of T∖e the marked vertex lies. The worst-case scenario where one is interested in minimizing the maximum number of queries is well understood, and linear time algorithms are known for finding an optimal search strategy. Here we study the more involved average-case analysis: A function w:V→ℝ+ is given which measures the likelihood for a vertex to be the one marked, and we seek to determine the strategy (decision tree) that minimizes the weighted average number of queries.

On the complexity of searching in trees and partially ordered structures

We study the problem of minimizing the weighted average number of queries to identify an initially unknown object in a poset. We show that for general posets, there cannot be any o ( log n ) -approximation algorithm unless NP ⊆ TIME ( n O ( log log n ) ) . When the Hasse diagram of the partially ordered set has the structure of a tree, the problem is equivalent to the following tree search problem: in a given rooted tree T = ( V , E ) a node has been marked and we want to identify it. In order to locate the marked node, we can perform node queries. A node query u asks whether the marked node lies in the subtree rooted at u . A function w : V → Z + is given which defines the likelihood for a node to be the one marked, and we want the strategy that minimizes the expected number of queries. Prior to this paper the complexity of this problem had remained open. We prove that the above tree search problem is NP -complete even for the class of trees with diameter at most 4. This results in a complete characterization of the complexity of the problem with respect to the diameter size. In fact, for diameter not larger than 3 we show that the problem is polynomially solvable using a dynamic programming approach. In addition we prove that the problem is NP -complete even for the class of trees of maximum degree at most 16. To the best of our knowledge, the only known result in this direction is that the tree search problem is solvable in O ( | V | log | V | ) time for trees with degree at most 2 (paths). Our results sharply contrast with those for the variant of the problem where one is interested in minimizing the maximum number of queries. In fact, for the worst case scenario, linear time algorithms are known for finding an optimal search strategy [K. Onak, P. Parys, Generalization of binary search: searching in trees and forest-like partial orders, in: FOCS’06: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Washington, DC, USA, 2006, pp. 379–388; S. Mozes, K. Onak, O. Weimann, Finding an optimal tree searching strategy in linear time, in: SODA’08: Proceedings of the Nineteenth Annual ACM–SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2008, pp. 1096–1105].

An A*-Based Algorithm for Constructing Reversible Variable Length Codes with Minimum Average Codeword Length

Variable length codes (VLCs) are widely adopted in many compression standards due to their good coding efficiency on average codeword length. However, an inherent problem with a VLC is that an error of even one bit can cause serious error propagation and thus loss of synchronization at the receiver, which would lead to a series of non-correctly decoded symbols. Reversible variable length codes (RVLCs) were introduced to significantly mitigate this phenomenon. In this work, a method to find an optimal RVLC in terms of the minimum average codeword length is first formulated as a tree-searching problem, and then, instead of performing an exhaustive search, an A*-based construction algorithm is proposed to find an optimal RVLC. The proposed algorithm has been applied to several benchmarks for sources and has found respective optimal symmetric and asymmetric RVLCs.

Accounting Information Systems Genetic Algorithms for All-Optical Shared Fiber-Delay-Line Packet Switches

All-optical shared fiber-delay-line (FDL) packet switches have been studied intensively in the literature and with theliterature, many scheduling genetic algorithms have been proposed. However, these genetic algorithms suffer from notbeing able to provide a delay bound, or require complex timing methods to compute scheduling assignments. In thispaper, we propose two fast scheduling algorithms for all-optical shared-FDL packet switches. In the first algorithm,packet scheduling is formulated as a tree-searching problem. This is accomplished by breaking down the search tree intomultiple smaller subsets and assigning each subset to a parallel processor. By using this method, scheduling solutions canbe obtained in a shorter time. Although this approach is superior to other algorithms, its overall complexity and processingoverheads are still too high to warrant its day to day use. In the second algorithm, the search tree is carefully trimmeddown in order to reduce complexity and overheads. The conclusion will consider a 32 × 32 switch with 32 FDLs, andassume a processor clock rate of 200MHz for schedulers. With this new and second algorithm, a scheduling assignmentcan be calculated for a given packet in 30ns if 8 parallel processors are employed and we show by simulation that bothalgorithms can achieve a loss rate of ? 10?7 even at load 0.9, where the average delay is 11.5 timeslots.

An efficient algorithm for the generation of two-electron repulsion integrals over gaussian basis functions

A synthesis of certain of the features of the recently developed HGP method of Head-Gordon and Pople with some of the constructs of the well-established McMurchie-Davidson (MD) scheme has led to the development of a new algorithm for the computation of the two-electron repulsion integrals which arise in conventional ab initio quantum chemical calculations using Gaussian basis sets. As in the MD scheme, derivatives of the two-electron integrals with respect to the nuclear coordinates are obtained very efficiently by the new algorithm. Moreover, in the spirit of the HGP approach, as much of the computational effort as possible is performed outside the contraction loops. This is achieved through the intermediacy of scaled, partially contracted integral sets and through the use of a near-optimal solution to the central tree-search problem. Explicit FLOP (floating point operation) counts suggest that the new algorithm is typically a factor of 2 cheaper than the HGP method for contracted basis sets.

Nested Quantum Search and NP-Hard Problems

A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order \(\), where d is the dimension of the search space, whereas any classical algorithm necessarily scales as O(d). It is shown here that an improved quantum search algorithm can be devised that exploits the structure of a tree search problem by nesting this standard search algorithm. The number of iterations required to find the solution of an average instance of a constraint satisfaction problem scales as \(\), with a constant α < 1 depending on the nesting depth and the problem considered. When applying a single nesting level to a problem with constraints of size 2 such as the graph coloring problem, this constant α is estimated to be around 0.62 for average instances of maximum difficulty. This corresponds to a square-root speedup over a classical nested search algorithm, of which our presented algorithm is the quantum counterpart.

Nested quantum search and structured problems

A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order $\sqrt{d}$, where $d$ is the dimension of the search space, whereas any classical algorithm necessarily scales as $O(d)$. It is shown here that an improved quantum search algorithm can be devised that exploits the structure of a tree search problem by nesting this standard search algorithm. The number of iterations required to find the solution of an average instance of a constraint satisfaction problem scales as $\sqrt{d^\alpha}$, with a constant $\alpha<1$ depending on the nesting depth and the problem considered. When applying a single nesting level to a problem with constraints of size 2 such as the graph coloring problem, this constant $\alpha$ is estimated to be around 0.62 for average instances of maximum difficulty. This corresponds to a square-root speedup over a classical nested search algorithm, of which our presented algorithm is the quantum counterpart.

Searching Game Trees under a Partial Order

Abstract The problem of partial order game tree search arises from game playing situations where multiple, conflicting and non-commensurate criteria dictate the merit of a position of the game. In partial order game trees, the outcomes evaluated at the tip nodes are vectors, where each dimension of the vector represents a distinct criterion of merit. This leads to an interesting variant of the game tree searching problem where corresponding to every game playing strategy of a player, several outcomes are possible depending on the individual priorities of the opponent. In this paper, we identify the necessary and sufficient conditions for a set of outcomes to be inferior to another set of outcomes for every strategy. Using an algebra called Dominance Algebra on sets of outcomes, we describe a bottom-up approach to find the non-inferior sets of outcomes at the root node. We also identify shallow and deep pruning conditions for partial order game trees and present a partial order search algorithm on lines similar to the α-β pruning algorithm for conventional game trees.