scholarly journals On Guaranteeing Polynomially Bounded Search Tree Size

Author(s):  
David A. Cohen ◽  
Martin C. Cooper ◽  
Martin J. Green ◽  
Dániel Marx
Keyword(s):  
2014 ◽  
Vol 50 ◽  
pp. 697-722 ◽  
Author(s):  
D. Bergman ◽  
A. A. Cire ◽  
W. Van Hoeve

We study propagation for the Sequence constraint in the context of constraint programming based on limited-width MDDs. Our first contribution is proving that establishing MDD-consistency for Sequence is NP-hard. Yet, we also show that this task is fixed parameter tractable with respect to the length of the sub-sequences. In addition, we propose a partial filtering algorithm that relies on a specific decomposition of the constraint and a novel extension of MDD filtering to node domains. We experimentally evaluate the performance of our proposed filtering algorithm, and demonstrate that the strength of the MDD propagation increases as the maximum width is increased. In particular, MDD propagation can outperform conventional domain propagation for Sequence by reducing the search tree size and solving time by several orders of magnitude. Similar improvements are observed with respect to the current best MDD approach that applies the decomposition of Sequence into Among constraints.


2020 ◽  
Vol 34 (03) ◽  
pp. 2392-2399
Author(s):  
Yanli Liu ◽  
Chu-Min Li ◽  
Hua Jiang ◽  
Kun He

The performance of a branch-and-bound (BnB) algorithm for maximum common subgraph (MCS) problem and its related problems, like maximum common connected subgraph (MCCS) and induced Subgraph Isomorphism (SI), crucially depends on the branching heuristic. We propose a branching heuristic inspired from reinforcement learning with a goal of reaching a tree leaf as early as possible to greatly reduce the search tree size. Experimental results show that the proposed heuristic consistently and significantly improves the current best BnB algorithm for the MCS, MCCS and SI problems. An analysis is carried out to give insight on why and how reinforcement learning is useful in the new branching heuristic.


Author(s):  
Daniel Anderson ◽  
Gregor Hendel ◽  
Pierre Le Bodic ◽  
Merlin Viernickel

We propose a simple and general online method to measure the search progress within the Branch-and-Bound algorithm, from which we estimate the size of the remaining search tree. We then show how this information can help solvers algorithmically at runtime by designing a restart strategy for MixedInteger Programming (MIP) solvers that decides whether to restart the search based on the current estimate of the number of remaining nodes in the tree. We refer to this type of algorithm as clairvoyant. Our clairvoyant restart strategy outperforms a state-of-the-art solver on a large set of publicly available MIP benchmark instances. It is implemented in the MIP solver SCIP and will be available in future releases.


HortScience ◽  
1998 ◽  
Vol 33 (3) ◽  
pp. 553d-553
Author(s):  
C.R. Unrath

Historically, most airblast chemical applications to apple orchards used a single “average” water volume, resulting in variability of coverage with tree size and also the greatest variable in chemical thinning. This coverage variability can be eliminated by properly quantifying the tree canopy, as tree row volume (TRV), and relating that volume to airblast water rate for adequate coverge. Maximum typical tree height, cross-row limb spread, and between-row spacing are used to quantify the TRV. Further refinement is achieved by adjusting the water volume for tree canopy density. The North Carolina TRV model allows a density adjustment from 0.7 gal/1000 ft3 of TRV for young, very open tree canopies to 1.0 gal/1000 ft3 of TRV for large, thick tree canopies to deliver a full dilute application for maximum water application (to the point of run-off). Most dilute pesticide applications use 70% of full dilute to approach the point of drip (pesticide dilute) to not waste chemicals and reduce non-target environmental exposure. From the “chemical load” (i.e., lb/acre) calculated for the pesticide dilute application, the proper chemical load for lower (concentrate) water volumes can be accurately determined. Another significant source of variability is thinner application response is spray distribution to various areas of the tree. This variability is related to tree configuration, light, levels, fruit set, and natural thinning vs. the need for chemical thinning. Required water delivery patterns are a function of tree size, form, spacing, and density, as well as sprayer design (no. of nozzles and fan size). The TRV model, density adjustments, and nozzle patterns to effectively hit the target for uniform crop load will be addressed.


Author(s):  
Samina Saghir ◽  
Tasleem Mustafa

<p>Increase in globalization of the industry of software requires an exploration of requirements engineering (RE) in software development institutes at multiple locations. Requirements engineering task is very complicated when it is performed at single site, but it becomes too much complex when stakeholder groups define well-designed requirements under language, time zone and cultural limits. Requirements prioritization (RP) is considered as an imperative part of software requirements engineering in which requirements are ranked to develop best-quality software. In this research, a comparative study of the requirements prioritization techniques was done to overcome the challenges initiated by the corporal distribution of stakeholders within the organization at multiple locations. The objective of this study was to make a comparison between five techniques for prioritizing software requirements and to discuss the results for global software engineering. The selected techniques were Analytic Hierarchy Process (AHP), Cumulative Voting (CV), Value Oriented Prioritization (VOP), Binary Search Tree (BST), and Numerical Assignment Technique (NAT). At the end of the research a framework for Global Software Engineering (GSE) was proposed to prioritize the requirements for stakeholders at distributed locations.<strong></strong></p>


2009 ◽  
Vol 25 (2) ◽  
pp. 107-121 ◽  
Author(s):  
Jan H. D. Wolf ◽  
S. Robbert Gradstein ◽  
Nalini M. Nadkarni

Abstract:The sampling of epiphytes is fraught with methodological difficulties. We present a protocol to sample and analyse vascular epiphyte richness and abundance in forests of different structure (SVERA). Epiphyte abundance is estimated as biomass by recording the number of plant components in a range of size cohorts. Epiphyte species biomass is estimated on 35 sample-trees, evenly distributed over six trunk diameter-size cohorts (10 trees with dbh > 30 cm). Tree height, dbh and number of forks (diameter > 5 cm) yield a dimensionless estimate of the size of the tree. Epiphyte dry weight and species richness between forests is compared with ANCOVA that controls for tree size. SChao1 is used as an estimate of the total number of species at the sites. The relative dependence of the distribution of the epiphyte communities on environmental and spatial variables may be assessed using multivariate analysis and Mantel test. In a case study, we compared epiphyte vegetation of six Mexican oak forests and one Colombian oak forest at similar elevation. We found a strongly significant positive correlation between tree size and epiphyte richness or biomass at all sites. In forests with a higher diversity of host trees, more trees must be sampled. Epiphyte biomass at the Colombian site was lower than in any of the Mexican sites; without correction for tree size no significant differences in terms of epiphyte biomass could be detected. The occurrence of spatial dependence, at both the landscape level and at the tree level, shows that the inclusion of spatial descriptors in SVERA is justified.


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