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Solving a multicoloring problem with overlaps using integer programming

Isabel Méndez-Díaz, Paula Zabala
2010 Discrete Applied Mathematics  
This paper presents a new generalization of the graph multicoloring problem. We propose a Branch-and-Cut algorithm based on a new integer programming formulation.  ...  The cuts used are valid inequalities that we could identify to the polytope associated with the model.  ...  We refer to this problem as a multicoloring problem with overlaps.  ... 
doi:10.1016/j.dam.2009.05.007 fatcat:a3lzf56hhjhlpc2dss4zsbmlay

Page 10289 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
-r) time algorithm to solve this problem using a dynamic programming technique, where n, m and r are the lengths of X, Y and P, respectively.  ...  As an application of overlap matching, we show how to reduce the string matching with swaps problem to the overlap matching prob- lem.  ... 

Page 79 of Journal of Aircraft Vol. 19, Issue 1 [page]

1982 Journal of Aircraft  
The picture also shows some of the problems encountered with the graphics logic used by the machine, namely, failure to fill all panels with the assigned color and color overlap.  ...  No attempt was made to solve these problems since time on this terminal was borrowed.  ... 

A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest [article]

Neil Olver, Frans Schalekamp, Suzanne van der Ster, Leen Stougie, Anke van Zuylen
2018 arXiv   pre-print
In addition, we show this linear program is stronger than previously known formulations, and we give a compact formulation, showing that it can be solved in polynomial time  ...  To prove the approximation guarantee, we construct a feasible dual solution for a novel linear programming formulation.  ...  Moreover, the compact formulation is amenable to use in commercial integer programming solvers.  ... 
arXiv:1811.05916v1 fatcat:mwvvjovh2fgt5iz3gc35rp3vsy

Improved Bounds for Sum Multicoloring and Scheduling Dependent Jobs with Minsum Criteria [chapter]

Rajiv Gandhi, Magnús M. Halldórsson, Guy Kortsarz, Hadas Shachnai
2005 Lecture Notes in Computer Science  
An input to our problems can be modeled as an instance of the sum multicoloring (SMC) problem: Given a graph and the number of colors required by each vertex, find a proper multicoloring which minimizes  ...  Building on the framework of Queyranne and Sviridenko (J. of Scheduling, 5:287-305, 2002 ), we present a general technique for reducing the sum multicoloring problem to classical graph multicoloring.  ...  Our problem of minimizing the sum of completion times can be formulated as the following integer program.  ... 
doi:10.1007/978-3-540-31833-0_8 fatcat:w4rvcm4nprcjhnthpcnppi3jxq

Hierarchies of Inefficient Kernelizability [article]

Danny Hermelin and Stefan Kratsch and Karolina Sołtys and Magnus Wahlström and Xi Wu
2011 arXiv   pre-print
(ICALP 2008) and Fortnow and Santhanam (STOC 2008) allows us to exclude the existence of polynomial kernels for a range of problems under reasonable complexity-theoretical assumptions.  ...  the clique problem parameterized by k log n.  ...  Multicolored Clique: Input: A graph G = (V, E) with |V | = n, a coloring function c : V → [k], and an integer k.  ... 
arXiv:1110.0976v1 fatcat:pulcvqyyzrft7edtf5re2ovfgi

Human appearance matching across multiple non-overlapping cameras

Yinghao Cai, Kaiqi Huang, Tieniu Tan
2008 Pattern Recognition (ICPR), Proceedings of the International Conference on  
The correspondence problem is solved under integer optimization framework where the cost function is determined by similarity of region signatures as well as geometric constraints between points.  ...  In this paper, we present a new solution to the problem of appearance matching across multiple nonoverlapping cameras.  ...  Acknowledgement This work is funded by research grants from the National Basic Research Program of China (2004CB318110), the National Science Foundation (60605014, 60332010, 60335010 and 2004DFA06900),  ... 
doi:10.1109/icpr.2008.4761704 dblp:conf/icpr/CaiHT08 fatcat:n6cygcur3zgarmh2uc7yslvv7m

Deconstructing intractability—A multivariate complexity analysis of interval constrained coloring

Christian Komusiewicz, Rolf Niedermeier, Johannes Uhlmann
2011 Journal of Discrete Algorithms  
Given a set of m integer intervals in the range 1 to n and a set of m associated multisets of colors (specifying for each interval the colors to be used for its elements), one asks whether there is a "  ...  The NP-hard Interval Constrained Coloring (ICC) problem appears in the interpretation of experimental data in biochemistry dealing with protein fragments.  ...  Fellows for early discussions about the deconstructive approach to NP-hard problems and Nadja Betzler for pointing us to the ICC problem.  ... 
doi:10.1016/j.jda.2010.07.003 fatcat:ikd7tqlze5atvncyd6cszwhu5q

Minimizing Movement: Fixed-Parameter Tractability [article]

Erik D. Demaine, MohammadTaghi Hajiaghayi, Dániel Marx
2012 arXiv   pre-print
Using our general tools, we determine the complexity of several concrete problems and fortunately show that many movement problems of interest can be solved efficiently.  ...  Thus the complexity of a particular problem can be determined by answering a purely combinatorial question.  ...  In this case, we can solve the problem with a simple application of Courcelle's Theorem [8] .  ... 
arXiv:1205.6960v2 fatcat:rg6t6xzwvfhujhfcvxqeek5hbm

Disentangling the Computational Complexity of Network Untangling [article]

Vincent Froese, Pascal Kunz, Philipp Zschoche
2022 arXiv   pre-print
We study the network untangling problem introduced by Rozenshtein, Tatti, and Gionis [DMKD 2021], which is a variant of Vertex Cover on temporal graphs – graphs whose edge set changes over discrete time  ...  They introduce two problem variants.  ...  If we use only the number n of vertices as a parameter, then we can use dynamic programming to show that both problems are in XP. Theorem 6.  ... 
arXiv:2204.02668v1 fatcat:tx73eg23ybfb3ckamnhkw2tgru

Scheduling Split Intervals

R. Bar-Yehuda, M. M. Halldórsson, J. (S.) Naor, H. Shachnai, I. Shapira
2006 SIAM journal on computing (Print)  
Our problem can be formulated as the problem of finding a maximum weight independent set in a t-interval graph (the special case of t = 1 is an ordinary interval graph).  ...  Each job J j is associated with an interval, I j , which consists of up to t segments, for some t ≥ 1, and a weight (profit), w j ; two jobs are in conflict if their intervals intersect.  ...  ., for video programs that are used in remote education [15] . Suppose that a client starts viewing a program at time t 0 .  ... 
doi:10.1137/s0097539703437843 fatcat:hbdzig772zconjpxsruhj43dom

Nonlinear optical microscopy for immunoimaging: a custom optimized system of high-speed, large-area, multicolor imaging

Hui Li, Quan Cui, Zhihong Zhang, Ling Fu, Qingming Luo
2015 Quantitative Imaging in Medicine and Surgery  
We built up a polygon-based nonlinear optical microscope system which was custom optimized for immunoimaging with high-speed, large-are and multicolor imaging abilities.  ...  Among numerous high-speed scanning mechanisms used in nonlinear optical imaging, polygon scanning is not only linearly but also dispersion-freely with high stability and tunable rotation speed, which can  ...  Acknowledgements This work was supported by the National Major Scientific Research Program of China (Grant No. 2011CB910401), and National Natural Science Foundation of China (No. 61178077).  ... 
doi:10.3978/j.issn.2223-4292.2014.11.07 pmid:25694951 pmcid:PMC4312289 fatcat:vjwwhveytvcwtkf6vs4566lmpm

Load-aware spectrum distribution in Wireless LANs

Thomas Moscibroda, Ranveer Chandra, Yunnan Wu, Sudipta Sengupta, Paramvir Bahl, Yuan Yuan
2008 Network Protocols (ICNP), Proceedings of the IEEE International Conference on  
This gives raise to a novel optimization problem that differs from previously studied channel assignment problems.  ...  Our results indicate that by allocating more spectrum to highly-loaded APs, the overall spectrum-utilization can be substantially improved and the notorious load-balancing problem in WLANs can be solved  ...  Optimal ILP Formulation The optimal solution of a problem instance can be characterized by the following integer linear program (ILP).  ... 
doi:10.1109/icnp.2008.4697032 dblp:conf/icnp/MoscibrodaCWSBY08 fatcat:iezwbtct6nd4jimqh7acjnknwi

Computer Graphics Display Technique for the Examination of Aircraft Design Data

1982 Journal of Aircraft  
The picture also shows some of the problems encountered with the graphics logic used by the machine, namely, failure to fill all panels with the assigned color and color overlap.  ...  The idea was to avoid the problems encountered above by only working with one integer group at a time.  ... 
doi:10.2514/3.57358 fatcat:oqmbmogz7vbrtjnl5xwdi6yxmi

Lightpath routing for maximum reliability in optical mesh networks

Shengli Yuan, Saket Varma, Jason P. Jue
2008 Journal of Optical Networking  
In these problems, every SRLG is represented by a distinct color and every fiber link is associated with one or more colors, depending on the SRLGs to which the link belongs.  ...  We consider the problem of maximizing the reliability of connections in optical mesh networks against simultaneous failures of multiple fiber links that belong to a shared-risk link group (SRLG).  ...  In addition to the heuristics, we also developed integer linear programming (ILP) formulations (Appendix A) in order to obtain the optimal solutions using CPLEX [30] .  ... 
doi:10.1364/jon.7.000449 fatcat:vxil632rxffp7c4swit5ygk2mi
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