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SOLVING NP-HARD PROBLEMS ON GRAPHS THAT ARE ALMOST TREES AND AN APPLICATION TO FACILITY LOCATION-PROBLEMS

JOURNAL OF THE ACM 1984年第3期31卷 459-473页

作者： GUREVICH, Y STOCKMEYER, L VISHKIN, U IBM CORP THOMAS J WATSON RES CTRYORKTOWN HTSNY 10598

A general technique is described for solving certain NP-hard graph problems in time that is exponential in a parameter k defined as the maximum, over all nonseparable components C of the graph, of the number of edges that must be added to a tree to produce C;for a connected graph, k is no more than the number of edges of the graph minus the number of vertices plus one. The technique is illustrated in detail for the following facility location problem: Given a connected graph G(V,E) such that each edge has an associated positive integer length and given a positive integer r, place the minimum number of centers on points of the graph such that every point of the graph is within distance r from some center (a 'point' is either a vertex or a point on some edge). An algorithm is given. A parallel implementation of the algorithm, with optimal speedup over the sequential version for a fairly wide range for the number of processors, is presented.

关键词： location problems NP-complete problems parallel algorithms polynomial time algorithms

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Data Collection for time-Critical Applications in the Low-Duty-Cycle Wireless Sensor Networks

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INTERNATIONAL JOURNAL OF DISTRIBUTED SENSOR NETWORKS 2015年第8期11卷 1-15页

作者： Luo, Shuyun Sun, Yongmei Ji, Yuefeng Beijing Univ Posts & Telecommun State Key Lab Informat Photon & Opt Commun Beijing 100876 Peoples R China

In low-duty-cycle wireless sensor networks, wireless nodes usually have two states: active state and dormant state. The necessary condition for a successful wireless transmission is that both the sender and the receiver are awake. In this paper, we study the problem: How fast can raw data be collected from all source nodes to a sink in low-duty-cycle WSNs with general topology? Both the lower and upper tight bounds are given for this problem. We use TDMA scheduling on the same frequency channel and present centralized and distributed fast data collection algorithms to find an optimal solution in polynomial time when no interfering links happen. If interfering links happen, multichannel scheduling is introduced to eliminate them. We next propose a novel Receiver-based Channel and time Scheduling (RCTS) algorithm to obtain the optimal solution. Based on real trace, extensive simulations are conducted and the results show that the proposed RCTS algorithm is significantly more efficient than the link schedule on one channel and achieves the lower bound. We also evaluate the proposed data collection algorithms and find that RCTS is time-efficient and suffices to eliminate most of the interference in both indoor and outdoor environment for moderate size networks.

关键词： WIRELESS sensor networks TOPOLOGY polynomial time algorithms MULTICHANNEL communication ACQUISITION of data SIMULATION methods & models

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Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

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JOURNAL OF PHYSICAL CHEMISTRY B 2016年第33期120卷 8354-8360页

作者： Purvine, Emilie Monson, Kyle Jurrus, Elizabeth Star, Keith Baker, Nathan A. Pacific Northwest Natl Lab Computat & Stat Analyt Div Richland WA 99354 USA Pacific Northwest Natl Lab Adv Comp Math & Data Div Richland WA 99354 USA Brown Univ Div Appl Math Providence RI 02912 USA

There are several applications in computational biophysics that require the optimization of discrete interacting states, for example, amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of "maximum flow-minimum cut" graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.

关键词： VOLUMETRIC analysis GRAPH theory polynomial time algorithms BIOPHYSICS PROTEIN analysis AMINO acids

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Numerical Investigation of the Role of Volumetric Transformation Strain on the Relaxation Stress and the Corresponding Hydrogen Interstitial Concentration in Niobium Matrix

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ADVANCES IN MATERIALS SCIENCE AND ENGINEERING 2017年第1期2017卷 1-7页

作者： Bal, Burak Abdullah Gul Univ Dept Mech Engn TR-38080 Kayseri Turkey Univ Calif Los Angeles Dept Mech & Aerosp Engn Los Angeles CA 90095 USA

The effects of relaxation stress on the hydrogen concentration in Niobium-(Nb-) H media were investigated by iterative numerical modeling approach. To calculate the transformation strain, relaxation stress, and corresponding relaxed hydrogen concentration around an edge dislocation, a new third-order polynomial formulation was utilized in the model. With the aid of this polynomial, hydrogen induced relaxation stress never exceeds the dislocation stress, which indicates that the total stress field never turns to compressive state and diverges the results. The current model calculates the hydrogen concentration not only in the vicinity of an edge dislocation but also far away from the dislocation. Furthermore, the effect of relaxation stress on the interaction energy was also captured in the model. Overall, the current findings shed light on the complicated hydrogen embrittlement mechanisms of metallic materials by demonstrating that hydrogen induced relaxation has a significant effect on the hydrogen atom concentration and the interaction energy between the existing internal stress field and the solute hydrogen atom.

关键词： STRAINS & stresses (Mechanics) HYDROGEN polynomial time algorithms HYDROGEN-deuterium exchange DISLOCATION interactions

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Phase transition for cutting-plane approach to vertex-cover problem

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Physical Review E 2012年第4期86卷 041128-041128页

作者： Timo Dewenter Alexander K. Hartmann []Institut für Physik Universit?t Oldenburg D-26111 Oldenburg Germany

We study the vertex-cover problem, which is a nondeterministic polynomial-time hard optimization problem and a prototypical model exhibiting phase transitions on random graphs, such as Erdős-Rényi (ER) random graphs. These phase transitions coincide with changes of the solution space structure, e.g., for the ER ensemble at connectivity c=e≈2.7183 from replica symmetric to replica-symmetry broken. For the vertex-cover problem, the typical complexity of exact branch-and-bound algorithms, which proceed by exploring the landscape of feasible configurations, also changes close to this phase transition from “easy” to “hard.” In this work, we consider an algorithm which has a completely different strategy: The problem is mapped onto a linear programming problem augmented by a cutting-plane approach; hence the algorithm operates in a space outside the space of feasible configurations until the final step, where a solution is found. Here we show that this type of algorithm also exhibits an easy-hard transition around c=e, which strongly indicates that the typical hardness of a problem is fundamental to the problem and not due to a specific representation of the problem.

关键词： PHASE transformations (Physics) RANDOM graphs MATHEMATICAL optimization polynomial time algorithms BROKEN symmetry (Physics) LINEAR programming

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Information-theoretic approach to ground-state phase transitions for two- and three-dimensional frustrated spin systems

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Physical Review E 2013年第2期87卷 022107-022107页

作者： O. Melchert A. K. Hartmann []Institut für Physik Universit?t Oldenburg Carl-von-Ossietzky Strasse 26111 Oldenburg Germany

The information-theoretic observables entropy (a measure of disorder), excess entropy (a measure of complexity), and multi-information are used to analyze ground-state spin configurations for disordered and frustrated model systems in two and three dimensions. For both model systems, ground-state spin configurations can be obtained in polynomial time via exact combinatorial optimization algorithms, which allowed us to study large systems with high numerical accuracy. Both model systems exhibit a continuous transition from an ordered to a disordered ground state as a model parameter is varied. By using the above information-theoretic observables it is possible to detect changes in the spatial structure of the ground states as the critical point is approached. It is further possible to quantify the scaling behavior of the information-theoretic observables in the vicinity of the critical point. For both model systems considered, the estimates of critical properties for the ground-state phase transitions are in good agreement with existing results reported in the literature.

关键词： ENTROPY NUCLEAR spin GROUND state (Quantum mechanics) polynomial time algorithms COMBINATORIAL optimization CRITICAL point

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Amortized Fairness for Drive-Thru Internet

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INTERNATIONAL JOURNAL OF DISTRIBUTED SENSOR NETWORKS 2013年第unknown期2013卷 1-12页

作者： Li, Zhi Sun, Limin Zhou, Xinyun Chinese Acad Sci State Key Lab Informat Secur Inst Informat Engn Beijing 100093 Peoples R China Chinese Acad Sci Grad Univ Beijing 100049 Peoples R China

The drive-thru Internet is an effective mean to provide Internet access service for wireless sensor networks deployed on vehicles. In these networks, vehicles often experience different link qualities due to different relative positions to the access point. This makes fair and efficient system design a very challenging task. In traditional approaches, the network efficiency has to be greatly sacrificed to provide the fair share for vehicles with low link quality. To address this issue, we propose a novel amortized fairness MAC protocol. The basic idea is that vehicles with lower link quality can defer their fairness requests and let the lost fairness be "amortized" in the future when their links become the high quality. The amortized fairness MAC requires predictions of future link quality. For this, we fully exploit the inner and inter-AP correlations revealed from our extensive field studies and design a link quality prediction algorithm. Based on the predicted link quality, we formulate the optimal amortized fairness MAC as a convex programming problem, which can be solved with the desired precision in polynomial time. Extensive simulation on real traces shows that the amortized fairness MAC scheme is more efficient than the existing fairness schemes in terms of efficiency and fairness.

关键词： INTERNET access WIRELESS sensor networks VEHICLES EQUIPMENT & supplies COMPUTER algorithms FIELD work (Research) polynomial time algorithms COMPUTER simulation

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Star covers and star partitions of double-split graphs

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2024年第3期47卷 17-17页

作者： Mondal, Joyashree Vijayakumar, S. Indian Inst Informat Technol Design & Mfg IIITDM Chennai 600127 India

A graph that is isomorphic to the complete bipartite graph K1,r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{1,r}$$\end{document} for some r >= 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r\ge 0$$\end{document} is called a star. A collection C={V1, horizontal ellipsis ,Vk}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C} = \{V_1, \ldots , V_k\}$$\end{document} of subsets of the vertex set of a graph G=(V,E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G = (V, E)$$\end{document} is called a star cover of G if each set in the collection induces a star and has V1 boolean OR horizontal ellipsis boolean OR Vk=V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_1\cup \ldots \cup V_k = V$$\end{document}. A star cover C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C}$$\end{document} of a graph G=(V,E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym

关键词： Star cover Star partition Double-split graphs polynomial time algorithms

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TAXONOMIC SYNTAX FOR 1ST-ORDER INFERENCE

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JOURNAL OF THE ACM 1993年第2期40卷 246-283页

作者： MCALLESTER, D GIVAN, R Massachusetts Institute of Technology Cambridge Massachusetts Institute of Technology Cambridge

A new polynomial time decidable fragment of first order logic is identified, and a general method for using polynomial time inference procedures in knowledge representation systems is presented. The results shown in this paper indicate that a nonstandard ''taxonomic'' syntax is essential in constructing natural and powerful polynomial time inference procedures. The central role of taxonomic syntax in the polynomial time inference procedures provides technical support for the often-expressed intuition that knowledge is better represented in terms of taxonomic relationships than classical first order formulas. To use the procedures in a knowledge representation system, a ''Socratic proof system'' is defined, which is complete for first order inference and which can be used as a semi-automated interface to a first order knowledge base.

关键词： algorithms DEDUCTION AUTOMATED REASONING INFERENCE RULES MACHINE INFERENCE MECHANICAL VERIFICATION polynomial time algorithms PROOF SYSTEMS PROOF THEORY THEOREM PROVING

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(m,k)-firm pattern spinning to improve the GTS allocation of periodic messages in IEEE 802.15.4 networks

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EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND NETWORKING 2013年第1期2013卷 1页

作者： Semprebom, Tiago Montez, Carlos Vasques, Francisco Fed Inst Santa Catarina IFSC P-88130310 Sao Jose Portugal Univ Fed Santa Catarina Automat & Syst Dept BR-88040900 Florianopolis SC Brazil Univ Porto IDMEC FEUP Fac Engn P-4200465 Oporto Portugal

The IEEE 802.15.4 standard provides a flexible communication support for low-rate wireless personal area networks) applications. When active, the beacon-enabled mode provides a real-time communication to the supported application by adopting a guaranteed time slot (GTS) mechanism. However, this mechanism permits only up to seven real-time communicating devices. One way to deal with this limitation is to share the communication opportunities among the periodic tasks, by skipping some of the task activations in a controlled way. One of the widely accepted periodic task models that allows skips in periodic activations is the (m,k)-firm model. Motivated by this problem, this paper proposes the use of a dynamic GTS scheduling approach based on the (m,k)-firm task model, to deal with the GTS starvation problem. The proposed scheduling approach is based on pre-defined spins of the originally defined (m,k)-firm pattern. The use of an exact schedulability analysis test ensures that for each admitted message stream, at least m messages will be transmitted within each window of k consecutive deadlines. The schedulability analysis may be executed in polynomial time and therefore can be used as an online admission test for GTS requests. The effectiveness of the approach has been assessed both by a set of simulations and an experimental evaluation.

关键词： ZIGBEE (Standard) RESEARCH QUALITY of service SCHEDULING polynomial time algorithms WIRELESS communication systems -- Testing WIRELESS communication systems -- Research

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