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Polynomial algorithms for p-dispersion problems in a 2d Pareto Front [article]

Nicolas Dupin
2020 arXiv   pre-print
The Max-Min p-dispersion problem is proven solvable in O(pnlog n) time and O(n) memory space. The Max-Sum-Min p-dispersion problem is proven solvable in O(pn^3) time and O(pn^2) space.  ...  Firstly, it is proven that 2-dispersion and 3-dispersion problems are solvable in O(n) time in a 2d PF.  ...  Max-Min p-dispersion is NP hard in the planar case, it is thus also the case for three dimensional PF, there is no hope to extend the results of this paper in dimension 3.  ... 
arXiv:2002.11830v1 fatcat:h4cosho3mjefzg2f3mx62oz3oy

Approximation Guarantees for Max Sum and Max Min Facility Dispersion with Parameterised Triangle Inequality and Applications in Result Diversification

Marcin Sydow
2015 Mathematica Applicanda  
We present generalised 2/α approximation guarantees for the Facility Dispersion Problem in its two most common variants: Max Sum and Max Min, when the underlying dissimilarity measure satisfies parameterised  ...  Facility Dispersion Problem, originally studied in Operations Research, has recently found important new applications in Result Diversification approach in information sciences.  ...  Max Min Dispersion Problem In the Max Min Dispersion Problem the objective function to be maximised is defined as follows: f M IN (P ) = min u,v∈P,u =v d(u, v). (3) Similarly to Max Sum, even if the distance  ... 
doi:10.14708/ma.v42i2.547 fatcat:mbgkwud44rfm7kuobw6h6zrp5e

An Efficient Proximal Point Algorithm for Unweighted Max-Min Dispersion Problem*

Siqi Tao
2018 Advances in Pure Mathematics  
In this paper, we first reformulate the max-min dispersion problem as a saddle-point problem.  ...  Specifically, we introduce an auxiliary problem whose optimum value gives an upper bound on that of the original problem.  ...  In this paper, we focus on the equal weight max-min dispersion problem, which is called by "max-min dispersion problem" for simplicity.  ... 
doi:10.4236/apm.2018.84022 fatcat:b6g4ukzlanhy7fo2bqslaaztp4

Max-Margin Ratio Machine

Suicheng Gu, Yuhong Guo
2012 Journal of machine learning research  
We first present a unified general framework for the existing min-max machine methods in terms of within-class dispersions and between-class dispersions.  ...  By defining a new within-class dispersion measure, we then propose a novel max-margin ratio machine (MMRM) method that can be formulated as a linear programming problem with scalability for large data  ...  One can easily verify that this problem is equivalent to a min-max machine problem with the between-class dispersion d c b (w) defined in (3) and the within-class dispersion defined as the sum of the standard  ... 
dblp:journals/jmlr/GuG12 fatcat:nawboqdqyjbvheknegfvupxp3q

Max-Min k-Dispersion on a Convex Polygon [article]

Vishwanath R. Singireddy, Manjanna Basappa
2022 arXiv   pre-print
In this paper, we consider the following k-dispersion problem.  ...  We then present an O(logn)-time 1/2√(2)-approximation algorithm for the problem when k=3 if the points are given in convex position order.  ...  1 /approximation algorithm for the max-min 3-dispersion problem on a convex polygon. ) Since r max ≤ |α 1 α 3 | 2 and |ad| ≥ |α 3 α 4 | 2 where r 1 = |ad| 2 ,Figure 5 : 1 case 2 : 2 and |ae| ≥ |α 3  ... 
arXiv:2205.02021v1 fatcat:lsjsjfmqmndnflbfzpeikk6uuu

The equitable dispersion problem

Oleg A. Prokopyev, Nan Kong, Dayna L. Martinez-Torres
2009 European Journal of Operational Research  
We propose the equitable dispersion problem that maximizes the equity among elements based on the introduced measures in a system defined by inter-element distances.  ...  Most optimization problems focus on efficiency-based objectives.  ...  Maximum minsum dispersion problem (Max-Minsum DP) The mathematical programming problem corresponding to the minsum dispersion measure is formulated as: max x2f0;1g n min i:x i ¼1 X j:j-i d ij x j ( ) s  ... 
doi:10.1016/j.ejor.2008.06.005 fatcat:dod6wupo7redxgafqqwzw2h76a

A maximum dispersion approach for rate feasibility problems in SINR model

Shashi Prabh
2017 2017 15th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)  
In this paper, we propose a maximum dispersion based approach for the problem of determining the feasibility of a set of single-hop rates in SINR model.  ...  The results confirm that maximum dispersion-based approach is well suited for the problem and that such an approach performs significantly better than the existing work.  ...  : find l ∈ L\(S ∪ S) that maximizes k∈S d(s l , r k ) if l ⊥ S £ Explained in the text min := Min k δ k 11: do for each k ∈ S 12: Figure 3 Fig. 2 : 32 Figure 3 shows the performance of MAX-RATE-GREEDY-DISPERSION  ... 
doi:10.23919/wiopt.2017.7959908 dblp:conf/wiopt/Prabh17 fatcat:mnbipdkshbcezihokhyi4cogo4

A Novel TOPSIS Method Based on Improved Grey Relational Analysis for Multiattribute Decision-Making Problem

Wenguang Yang, Yunjie Wu
2019 Mathematical Problems in Engineering  
Finally, the comprehensive grey TOPSIS is utilized to analyze the ranking of weapon selection problem.  ...  Based on the understanding of data dispersion degree, a new grey TOPSIS method for MADM is studied.  ...  multiattribute decision data [27] . max max max max max min 0 min X 1 6 750 6 24 100 8 0.75 20 0.3 1000 3 X 2 5.5 2300 5 27 90 8 0.8 15 0.025 1000 5 X 3 4.4 1200 5  ... 
doi:10.1155/2019/8761681 fatcat:tzihoy6wmvgjnaz5rhkz6hlwv4

A dispersion theorem for communication networks based on term sets

Soren Riis, Maximilien Gadouleau
2011 2011 IEEE International Symposium on Information Theory Proceedings  
To any choice of coding functions we associate a measure of performance, referred to as the dispersion. Many communication problems can be recast as dispersion problems in this setup.  ...  The dispersion theorem resembles the max-flow mincut theorem for commodity networks and states that the minimal cut value can be asymptotically achieved by the use of coding functions based on a routing  ...  Section III then proves the max-flow min-cut theorems for the dispersion and the one-to-one dispersion. Section V then concludes and offers some problems for future research. II.  ... 
doi:10.1109/isit.2011.6034198 dblp:conf/isit/RiisG11 fatcat:7b73c4ud65c5nltf24hfwjabfm

Increasing the range of ultra wideband radars based on antenna arrays

Boris Lagovsky, Alexander Samokhin, Malay Tripathy, P. Yermolov
2019 ITM Web of Conferences  
Solutions of variational problems of searching for the optimal shape of probing UWB pulses are investigated.  ...  Optimization of the form allows to obtain good results when using even approximate data on the dispersion dependences of the radar cross-section.  ...  Using (3) , we represent the second additional condition of the problem in the form:   ) ) exp( ) ( ) , ( ) ( ( max ) ) exp( ) ( ) , 0 ( ) ( ( max 2 2 max min 2 max min 2                ... 
doi:10.1051/itmconf/20193005017 fatcat:tdiv3fmtwjgnlc6mbfbusqj3bm

Efficient Dispersion of Mobile Agents without Global Knowledge [article]

Takahiro Shintaku, Yuichi Sudo, Hirotsugu Kakugawa, Toshimitsu Masuzawa
2020 arXiv   pre-print
We consider the dispersion problem for mobile agents. Initially, k agents are located at arbitrary nodes in an undirected graph.  ...  In this paper, we present a dispersion algorithm that does not require such global knowledge but keeps the asymptotically same running time and slightly smaller memory space.  ...  In Section 3, we briefly explain the existing techniques used for the dispersion problem in the literature.  ... 
arXiv:2008.09379v1 fatcat:oytgourmfvhrpbwf7dgogm2dei

Max-Flow Min-Cut Theorems for Multi-User Communication Networks [article]

Soren Riis, Maximilien Gadouleau
2014 arXiv   pre-print
One technical result is a max-flow min-cut theorem for the Rényi entropy with order less than one, given that the sources are equiprobably distributed; conversely, we show that the max-flow min-cut theorem  ...  We state and prove variants of a theorem concerning the dispersion of information in single-receiver communications. 4) We show that the solvability of an abstract multi-user communication problem is  ...  MAX-FLOW MIN-CUT THEOREM FOR THE DISPERSION OF TERM SETS The main purpose of this section is to prove the following max-flow min-cut theorem for the dispersion and the one-to-one dispersion of term sets  ... 
arXiv:1012.5224v3 fatcat:jq5xp6onojakpidp22izclcbnq

Mixed Platoon Flow Dispersion Model Based on Speed-Truncated Gaussian Mixture Distribution

Weitiao Wu, Wenzhou Jin, Luou Shen
2013 Journal of Applied Mathematics  
Based on field data, a macroscopic mixed platoon flow dispersion model (MPFDM) was proposed to simulate the platoon dispersion process along the road section between two adjacent intersections from the  ...  { { { { { { { { { { { { { { { { { { { 0, < V max ∪ > V min + ∫ V max / (V) V, V max ≤ < V max + ∫ /( − ) / (V) V, V max + ≤ ≤ V min ∫ /( − ) V min (V) V, V min < ≤ V min + . (6) Let = (V− )/ and the dispersion  ...  The investigation of the mixed platoon dispersion problem will provide theoretical support for signal coordination and bus priority control.  ... 
doi:10.1155/2013/480965 fatcat:ktr4es4pifco3g2jr7o2g5vwsa

Exploration of Multi-objective Tradeoff during High Level Synthesis Using Bacterial Chemotaxis and Dispersal

Anirban Sengupta, Saumya Bhadauria
2014 Procedia Computer Science  
key sub-contributions of the proposed approach can be classified as follows: i) Exploration drift using a novel chemotaxis algorithm ii) Diversity introduction in resource configuration using a novel dispersal  ...  (N(R D )) (4) The bacterium's are uniformly distributed over the design space and is initialized as: x 1 = (min(R 1 ), min(R 2 ),.. min(R D )) (5) x 2 = (max(R 1 ), max(R 2 ),.. max(R D )) (6) x 3 =((min  ...  ,((min(R D )+max(R D ))/2 (7) While rests of the bacterium's (x 4 ...x n ) are initialized by: ( ) (min( ) max( ))/ 2 d d d N R R R (8) The approach is explained with the demonstration of a MESA Horner  ... 
doi:10.1016/j.procs.2014.08.085 fatcat:uxorgnkyyne2pjqapigfeuj3zu

An O(n2)-Time Algorithm for Computing a Max-Min 3-Dispersion on a Point Set in Convex Position

Yasuaki KOBAYASHI, Shin-ichi NAKANO, Kei UCHIZAWA, Takeaki UNO, Yutaro YAMAGUCHI, Katsuhisa YAMANAKA
2022 IEICE transactions on information and systems  
Thus, the k-dispersion problem is a natural generalization of the diameter problem. In this paper, we consider the case of k = 3, which is the 3-dispersion problem, when P is in convex position.  ...  We present an O(n 2 )-time algorithm to compute a 3-dispersion of P.  ...  Now, we define the max-min k-dispersion problem.  ... 
doi:10.1587/transinf.2021fcp0013 fatcat:ikatgpzgpjgadaqp43utkexojy
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