scholarly journals Reflections on kernelizing and computing unrooted agreement forests

2021 ◽  
Author(s):  
Rim van Wersch ◽  
Steven Kelk ◽  
Simone Linz ◽  
Georgios Stamoulis
Keyword(s):  
Phylogenetic Trees ◽  
Added Value ◽  
Worst Case ◽  
Maximum Agreement Forest ◽  
Minimum Number ◽  
Np Hard Problem ◽  
Number Of Leaves ◽  
Labelled Trees ◽  
Practical Impact ◽  
Tbr Distance

AbstractPhylogenetic trees are leaf-labelled trees used to model the evolution of species. Here we explore the practical impact of kernelization (i.e. data reduction) on the NP-hard problem of computing the TBR distance between two unrooted binary phylogenetic trees. This problem is better-known in the literature as the maximum agreement forest problem, where the goal is to partition the two trees into a minimum number of common, non-overlapping subtrees. We have implemented two well-known reduction rules, the subtree and chain reduction, and five more recent, theoretically stronger reduction rules, and compare the reduction achieved with and without the stronger rules. We find that the new rules yield smaller reduced instances and thus have clear practical added value. In many cases they also cause the TBR distance to decrease in a controlled fashion, which can further facilitate solving the problem in practice. Next, we compare the achieved reduction to the known worst-case theoretical bounds of $$15k-9$$ 15 k - 9 and $$11k-9$$ 11 k - 9 respectively, on the number of leaves of the two reduced trees, where k is the TBR distance, observing in both cases a far larger reduction in practice. As a by-product of our experimental framework we obtain a number of new insights into the actual computation of TBR distance. We find, for example, that very strong lower bounds on TBR distance can be obtained efficiently by randomly sampling certain carefully constructed partitions of the leaf labels, and identify instances which seem particularly challenging to solve exactly. The reduction rules have been implemented within our new solver Tubro which combines kernelization with an Integer Linear Programming (ILP) approach. Tubro also incorporates a number of additional features, such as a cluster reduction and a practical upper-bounding heuristic, and it can leverage combinatorial insights emerging from the proofs of correctness of the reduction rules to simplify the ILP.

Enhancing the Steel Tube Manufacturing Process With a Zero Defects Approach

2020 ◽  
Author(s):  
João Sousa ◽  
José Ferreira ◽  
Carlos Lopes ◽  
João Sarraipa ◽  
João Silva
Keyword(s):  
Manufacturing Process ◽  
Manufacturing Industry ◽  
Service Oriented Architecture ◽  
Continuous Process ◽  
Management Strategies ◽  
Steel Tube ◽  
Added Value ◽  
Case Scenario ◽  
Worst Case ◽  
Inspection Systems

Abstract The continuous thrive for working safety, customer satisfaction and increasing profits for companies has led to numerous manufacturing and management strategies. One of the most promising strategies nowadays is Zero Defects that focuses on the elimination of defected parts in the manufacturing processes. The benefits of Zero Defect implementation in the manufacturing industry are mainly related to the reduction of scrap material, and everything that does not bring any added value to the product. The result is a reduction of the company’s expenditure for dealing with defective products. In spite the concept not being new, the practical application of such strategies were limited by technological constraints and high investment costs. With the Industry 4.0 evolution, some Zero Defects concepts are more accessible due to the availability of sensors and data related techniques such as Machine Learning and Big Data although a lot of work is still required for component integration to enhance the capability of the heterogeneous technologies. The quality of the steel tubes is evaluated by sampling and relies on the expertise of the operators for checking for nonconformities. When a defect is detected, the process parameters are adjusted based on prior experience. However, since this is a continuous process, the delay between the appearance of a defect in the process and its awareness leads to a considerable amount of produced scrap material. Worst-case scenario, the defective product can be delivered to the customer damaging the customers trust and leading to additional replacement costs. This paper addresses the application of the Zero Defects approach to the steel tube manufacturing industry. This approach is part of the Zero Defects Manufacturing Platform EU project that is based around a Service Oriented Architecture and microservices approach capable of building, running and managing specific use-case oriented software applications called zApps. The Zero Defects methodology to design a zApp based on key criteria for the steel tube industry is described. Additionally, the envisioned zApps to monitor all the produced steel tube during the manufacturing process are detailed. The inspection systems uses a scanning camera and a laser profile scanner to capture the steel tube defects during manufacturing and prior to packaging. Although the ultimate goal is to eliminate the cause of the defective products, the objective of the zApp is to increase the number of detections of defective products based on industry standards and reduce the amount of generated scrap material.

APPROXIMATION ALGORITHMS FOR A VARIANT OF DISCRETE PIERCING SET PROBLEM FOR UNIT DISKS

2013 ◽  
Vol 23 (06) ◽  
pp. 461-477 ◽  
Author(s):  
MINATI DE ◽  
GAUTAM K. DAS ◽  
PAZ CARMI ◽  
SUBHAS C. NANDY
Keyword(s):  
Approximation Algorithms ◽  
Simple Algorithm ◽  
Constant Factor ◽  
Performance Ratio ◽  
Approximation Result ◽  
Worst Case ◽  
Approximation Factor ◽  
Minimum Number ◽  
Unit Disks ◽  
Set Of Points

In this paper, we consider constant factor approximation algorithms for a variant of the discrete piercing set problem for unit disks. Here a set of points P is given; the objective is to choose minimum number of points in P to pierce the unit disks centered at all the points in P. We first propose a very simple algorithm that produces 12-approximation result in O(n log n) time. Next, we improve the approximation factor to 4 and then to 3. The worst case running time of these algorithms are O(n8 log n) and O(n15 log n) respectively. Apart from the space required for storing the input, the extra work-space requirement for each of these algorithms is O(1). Finally, we propose a PTAS for the same problem. Given a positive integer k, it can produce a solution with performance ratio [Formula: see text] in nO(k) time.

A Design-and-Build Project to Introduce Concepts Relating to Dimensional Variation

1998 ◽  
Vol 26 (4) ◽  
pp. 259-272
Author(s):  
S. M. Panton ◽  
P. R. Milner
Keyword(s):  
Classroom Environment ◽  
Tolerance Analysis ◽  
Cylinder Block ◽  
Worst Case ◽  
Good Design ◽  
Minimum Number ◽  
Dimensional Variation ◽  
Assembly Problem ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis

A design-and-build project which has been used to introduce Year 2 students of Mechanical Engineering to the concepts of dimensional variation and the influence of dimensional variation on function and assembly. The project simulates the cylinder head cylinder block assembly problem and specifies requirements in terms of a tolerance on concentricity of the cylinders in the head and block, and the interchangeable assembly of the head and block. Materials which are easily and cheaply sourced and tools which are easily manufactured and safe to use in a classroom environment are used throughout. During the project the students are exposed to concepts such as worst-case and statistical tolerance analysis, sensitivity analysis, geometric moment effects, minimum constraint design, co-variance and gauging. The exercise also emphasizes that good design means components that function and assemble with the minimum number of tight tolerances.

CONSTANT LEAF-SIZE HIERARCHY OF TWO-DIMENSIONAL ALTERNATING TURING MACHINES

1994 ◽  
Vol 08 (02) ◽  
pp. 509-524
Author(s):  
AKIRA ITO ◽  
KATSUSHI INOUE ◽  
ITSUO TAKANAMI ◽  
YASUYOSHI INAGAKI
Keyword(s):  
Finite Automata ◽  
Leaf Size ◽  
Two Dimensional ◽  
Turing Machines ◽  
Size Hierarchy ◽  
Minimum Number ◽  
Space Function ◽  
Number Of Leaves ◽  
Alternating Turing Machines ◽  
Necessary And Sufficient

“Leaf-size” (or “branching”) is the minimum number of leaves of some accepting computation trees of alternating devices. For example, one leaf corresponds to nondeterministic computation. In this paper, we investigate the effect of constant leaves of two-dimensional alternating Turing machines, and show the following facts: (1) For any function L(m, n), k leaf- and L(m, n) space-bounded two-dimensional alternating Turing machines which have only universal states are equivalent to the same space bounded deterministic Turing machines for any integer k≥1, where m (n) is the number of rows (columns) of the rectangular input tapes. (2) For square input tapes, k+1 leaf- and o(log m) space-bounded two-dimensional alternating Turing machines are more powerful than k leaf-bounded ones for each k≥1. (3) The necessary and sufficient space for three-way deterministic Turing machines to simulate k leaf-bounded two-dimensional alternating finite automata is nk+1, where we restrict the space function of three-way deterministic Turing machines to depend only on the number of columns of the given input tapes.

scholarly journals Intruder capture algorithms considering visible intruders

2019 ◽  
Vol 16 (3) ◽  
pp. 172988141984673
Author(s):  
Jonghoek Kim
Keyword(s):  
Real Time ◽  
Weighted Graph ◽  
Search Algorithms ◽  
Tree Graph ◽  
Multiple Robots ◽  
Weighted Tree ◽  
Topological Map ◽  
Worst Case ◽  
Minimum Number ◽  
Full Knowledge

In this article, we consider the problem of using multiple robots (searchers) to capture intruders in an environment. Assume that a robot can access the position of an intruder in real time, that is, an intruder is visible by a robot. We simplify the environment so that robots and worst-case intruders move along a weighted graph, which is a topological map of the environment. In such settings, a worst-case intruder is characterized by unbounded speed, complete awareness of searcher location and intent, and full knowledge of the search environment. The weight of an edge or a vertex in a weighted graph is a cost describing the clearing requirement of the edge or the vertex. This article provides non-monotone search algorithms to capture every visible intruder. Our algorithms are easy to implement, thus are suitable for practical robot applications. Based on the non-monotone search algorithms, we derive the minimum number of robots required to clear a weighted tree graph. Considering a general weighted graph, we derive bounds for the number of robots required. Finally, we present switching algorithms to improve the time efficiency of capturing intruders while not increasing the number of robots. We verify the effectiveness of our approach using MATLAB simulations.

scholarly journals On Compact Encoding of Pagenumber $k$ Graphs

2008 ◽  
Vol Vol. 10 no. 3 ◽  
Author(s):  
Cyril Gavoille ◽  
Nicolas Hanusse
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Constant Time ◽  
Worst Case ◽  
Encoding Scheme ◽  
Information Theoretic ◽  
Auxiliary Table ◽  
Minimum Number ◽  
International Audience

International audience In this paper we show an information-theoretic lower bound of kn - o(kn) on the minimum number of bits to represent an unlabeled simple connected n-node graph of pagenumber k. This has to be compared with the efficient encoding scheme of Munro and Raman of 2kn + 2m + o(kn+m) bits (m the number of edges), that is 4kn + 2n + o(kn) bits in the worst-case. For m-edge graphs of pagenumber k (with multi-edges and loops), we propose a 2mlog2k + O(m) bits encoding improving the best previous upper bound of Munro and Raman whenever m ≤ 1 / 2kn/log2 k. Actually our scheme applies to k-page embedding containing multi-edge and loops. Moreover, with an auxiliary table of o(m log k) bits, our coding supports (1) the computation of the degree of a node in constant time, (2) adjacency queries with O(logk) queries of type rank, select and match, that is in O(logk *minlogk / loglogm, loglogk) time and (3) the access to δ neighbors in O(δ) runs of select, rank or match;.

scholarly journals An Executive Approach to Achieve Mutual Exclusion in Distributed Data using Topology and Association Rule.

2014 ◽  
Vol 13 (6) ◽  
pp. 4537-4542
Author(s):  
Mr. Anurag Singh ◽  
Dr. Amod Tiwari
Keyword(s):  
Distributed System ◽  
Association Rule ◽  
Message Passing ◽  
Computer Network ◽  
Mutual Exclusion ◽  
Distributed Data ◽  
Worst Case ◽  
New Approach ◽  
And Topology ◽  
Minimum Number

In this paper, a new approach is being proposed to achieve mutual exclusion in distributed system using computer network and topology of nth nodes. In this executive approach nodes communicate among themselves using message passing technique. In this executive approach, distributed system with n nodes is logically partitioned into number of sub distributed system having only m½ nodes, where m is obtained by adding a minimum number in n to make it next perfect square number only if n is not a perfect square. Proposed algorithm is a Token based approach and achieves token optimally in 2 messages only for the best case and in worst case a node achieves token in n messages only.

scholarly journals A note on bipartite graphs whose [1,k]-domination number equal to their number of vertices

2020 ◽  
Vol 40 (3) ◽  
pp. 375-382
Author(s):  
Narges Ghareghani ◽  
Iztok Peterin ◽  
Pouyeh Sharifani
Keyword(s):  
Decision Problem ◽  
Dominating Set ◽  
Domination Number ◽  
Short Note ◽  
Bipartite Graphs ◽  
Hard Problem ◽  
Simple Construction ◽  
Minimum Number ◽  
Vertex Set ◽  
Np Hard Problem

A subset \(D\) of the vertex set \(V\) of a graph \(G\) is called an \([1,k]\)-dominating set if every vertex from \(V-D\) is adjacent to at least one vertex and at most \(k\) vertices of \(D\). A \([1,k]\)-dominating set with the minimum number of vertices is called a \(\gamma_{[1,k]}\)-set and the number of its vertices is the \([1,k]\)-domination number \(\gamma_{[1,k]}(G)\) of \(G\). In this short note we show that the decision problem whether \(\gamma_{[1,k]}(G)=n\) is an \(NP\)-hard problem, even for bipartite graphs. Also, a simple construction of a bipartite graph \(G\) of order \(n\) satisfying \(\gamma_{[1,k]}(G)=n\) is given for every integer \(n \geq (k+1)(2k+3)\).

scholarly journals Markov Katana: a Novel Method for Bayesian Resampling of Parameter Space Applied to Phylogenetic Trees

2018 ◽  
Author(s):  
Stephen T. Pollard ◽  
Kenji Fukushima ◽  
Zhengyuan O. Wang ◽  
Todd A. Castoe ◽  
David D. Pollock
Keyword(s):  
Phylogenetic Tree ◽  
Phylogenetic Trees ◽  
Statistical Approach ◽  
Evolutionary Model ◽  
Complex Model ◽  
Tree Topology ◽  
Added Value ◽  
General Idea ◽  
Branch Lengths ◽  
Tree Space

ABSTRACTPhylogenetic inference requires a means to search phylogenetic tree space. This is usually achieved using progressive algorithms that propose and test small alterations in the current tree topology and branch lengths. Current programs search tree topology space using branch-swapping algorithms, but proposals do not discriminate well between swaps likely to succeed or fail. When applied to datasets with many taxa, the huge number of possible topologies slows these programs dramatically. To overcome this, we developed a statistical approach for proposal generation in Bayesian analysis, and evaluated its applicability for the problem of searching phylogenetic tree space. The general idea of the approach, which we call ‘Markov katana’, is to make proposals based on a heuristic algorithm using bootstrapped subsets of the data. Such proposals induce an unintended sampling distribution that must be determined and removed to generate posterior estimates, but the cost of this extra step can in principle be small compared to the added value of more efficient parameter exploration in Markov chain Monte Carlo analyses. Our prototype application uses the simple neighbor-joining distance heuristic on data subsets to propose new reasonably likely phylogenetic trees (including topologies and branch lengths). The evolutionary model used to generate distances in our prototype was far simpler than the more complex model used to evaluate the likelihood of phylogenies based on the full dataset. This prototype implementation indicates that the Markov katana approach could be easily incorporated into existing phylogenetic search programs and may prove a useful alternative in conjunction with existing methods. The general features of this statistical approach may also prove useful in disciplines other than phylogenetics. We demonstrate that this method can be used to efficiently estimate a Bayesian posterior.

CONVEX DRAWINGS OF PLANE GRAPHS OF MINIMUM OUTER APICES

2006 ◽  
Vol 17 (05) ◽  
pp. 1115-1127 ◽  
Author(s):  
KAZUYUKI MIURA ◽  
MACHIKO AZUMA ◽  
TAKAO NISHIZEKI
Keyword(s):  
Convex Polygon ◽  
Linear Time ◽  
Plane Graph ◽  
Decomposition Tree ◽  
Necessary And Sufficient Condition ◽  
Component Decomposition ◽  
Minimum Number ◽  
Convex Drawing ◽  
Number Of Leaves ◽  
Necessary And Sufficient

In a convex drawing of a plane graph G, every facial cycle of G is drawn as a convex polygon. A polygon for the outer facial cycle is called an outer convex polygon. A necessary and sufficient condition for a plane graph G to have a convex drawing is known. However, it has not been known how many apices of an outer convex polygon are necessary for G to have a convex drawing. In this paper, we show that the minimum number of apices of an outer convex polygon necessary for G to have a convex drawing is, in effect, equal to the number of leaves in a triconnected component decomposition tree of a new graph constructed from G, and that a convex drawing of G having the minimum number of apices can be found in linear time.

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