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

2020
*
arXiv
*
pre-print

The

arXiv:2002.11830v1
fatcat:h4cosho3mjefzg2f3mx62oz3oy
*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*. ...##
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Approximation Guarantees for Max Sum and Max Min Facility Dispersion with Parameterised Triangle Inequality and Applications in Result Diversification

2015
*
Mathematica Applicanda
*

We present generalised 2/α approximation guarantees for the Facility

doi:10.14708/ma.v42i2.547
fatcat:mbgkwud44rfm7kuobw6h6zrp5e
*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 ...##
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An Efficient Proximal Point Algorithm for Unweighted Max-Min Dispersion Problem*

2018
*
Advances in Pure Mathematics
*

In this paper, we first reformulate the

doi:10.4236/apm.2018.84022
fatcat:b6g4ukzlanhy7fo2bqslaaztp4
*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. ...##
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Max-Margin Ratio Machine

2012
*
Journal of machine learning research
*

We first present a unified general framework for the existing

dblp:journals/jmlr/GuG12
fatcat:nawboqdqyjbvheknegfvupxp3q
*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 ...##
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Max-Min k-Dispersion on a Convex Polygon
[article]

2022
*
arXiv
*
pre-print

In this paper, we consider the following k-

arXiv:2205.02021v1
fatcat:lsjsjfmqmndnflbfzpeikk6uuu
*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*...##
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The equitable dispersion problem

2009
*
European Journal of Operational Research
*

We propose the equitable

doi:10.1016/j.ejor.2008.06.005
fatcat:dod6wupo7redxgafqqwzw2h76a
*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 ...##
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A maximum dispersion approach for rate feasibility problems in SINR model

2017
*
2017 15th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)
*

In this paper, we propose a maximum

doi:10.23919/wiopt.2017.7959908
dblp:conf/wiopt/Prabh17
fatcat:mnbipdkshbcezihokhyi4cogo4
*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*...##
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A Novel TOPSIS Method Based on Improved Grey Relational Analysis for Multiattribute Decision-Making Problem

2019
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Mathematical Problems in Engineering
*

Finally, the comprehensive grey TOPSIS is utilized to analyze the ranking of weapon selection

doi:10.1155/2019/8761681
fatcat:tzihoy6wmvgjnaz5rhkz6hlwv4
*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 ...##
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A dispersion theorem for communication networks based on term sets

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

doi:10.1109/isit.2011.6034198
dblp:conf/isit/RiisG11
fatcat:7b73c4ud65c5nltf24hfwjabfm
*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. ...##
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Increasing the range of ultra wideband radars based on antenna arrays

2019
*
ITM Web of Conferences
*

Solutions of variational

doi:10.1051/itmconf/20193005017
fatcat:tdiv3fmtwjgnlc6mbfbusqj3bm
*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 ...##
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Efficient Dispersion of Mobile Agents without Global Knowledge
[article]

2020
*
arXiv
*
pre-print

We consider the

arXiv:2008.09379v1
fatcat:oytgourmfvhrpbwf7dgogm2dei
*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. ...##
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Max-Flow Min-Cut Theorems for Multi-User Communication Networks
[article]

2014
*
arXiv
*
pre-print

One technical result is a

arXiv:1012.5224v3
fatcat:jq5xp6onojakpidp22izclcbnq
*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 ...##
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Mixed Platoon Flow Dispersion Model Based on Speed-Truncated Gaussian Mixture Distribution

2013
*
Journal of Applied Mathematics
*

Based on field data, a macroscopic mixed platoon flow

doi:10.1155/2013/480965
fatcat:ktr4es4pifco3g2jr7o2g5vwsa
*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. ...##
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Exploration of Multi-objective Tradeoff during High Level Synthesis Using Bacterial Chemotaxis and Dispersal

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

doi:10.1016/j.procs.2014.08.085
fatcat:uxorgnkyyne2pjqapigfeuj3zu
*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 ...##
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An O(n2)-Time Algorithm for Computing a Max-Min 3-Dispersion on a Point Set in Convex Position

2022
*
IEICE transactions on information and systems
*

Thus, the k-

doi:10.1587/transinf.2021fcp0013
fatcat:ikatgpzgpjgadaqp43utkexojy
*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*. ...
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