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On the span in channel assignment problems: bounds, computing and counting

Colin McDiarmid
2003 Discrete Mathematics  
The least t for which there is a feasible assignment is the span of the problem. We ÿrst derive two bounds on the span, an upper bound (from a sequential assignment method) and a lower bound.  ...  The channel assignment problem involves assigning radio channels to transmitters, using a small span of channels but without causing excessive interference.  ...  Acknowledgements I am grateful to the referees for detailed comments.  ... 
doi:10.1016/s0012-365x(02)00821-x fatcat:uuds5u7ag5ddpmfflweokuepqu

An exact algorithm for the channel assignment problem

Daniel Král'
2005 Discrete Applied Mathematics  
We present an algorithm running in time O(n(l + 2) n ) which outputs the span for l-bounded channel assignment problems with n vertices.  ...  An algorithm running in time O(nl(l + 2) n ) for computing the number of different proper assignments of span at most K is further presented.  ...  Acknowledgements The author would like to thank Jan Kára and Jan Kratochvíl for carefully reading the preliminary version of this manuscript.  ... 
doi:10.1016/j.dam.2004.01.020 fatcat:fw66yqxcfzchtne54kzoan5mj4

Fixed parameter complexity of distance constrained labeling and uniform channel assignment problems [article]

Jiří Fiala and Tomáš Gavenčiak and Dušan Knop and Martin Koutecký and Jan Kratochvíl
2015 arXiv   pre-print
Finally, we show that the uniform variant of the Channel Assignment problem becomes NP-complete when generalized to graphs of bounded clique width.  ...  The same consequence applies on Channel Assignment when the maximum weight is additionally included among the parameters.  ...  Only few partial results are known [19] , among others that the Channel Assignment is polynomially solvable on graphs of bounded tree width if the span λ is bounded by a constant.  ... 
arXiv:1507.00640v2 fatcat:2xlaquhqxbfc5gedz5hqjc4v6e

The Complexity of Design Automation Problems [chapter]

Sartaj Sahni, Atul Bhatt, Raghunath Raghavan
1988 Handbook of Advanced Semiconductor Technology and Computer Systems  
Emphasis is on problems involving the physical implementation and testing stages of the design process. Section 2 contains a brief description, in general terms, of the DA problems considered.  ...  To date, most of the effort in DA has concentrated on the following stages of the design process: physical implementation of the logic design, and testing.  ...  Rather, asymptotic bounds on the step count are obtained. Asymptotic analysis uses the notation Ο, Ω, Θ and o. These are defined below.  ... 
doi:10.1007/978-94-011-7056-7_17 fatcat:muwhoo6fgvfdlmszv4wheza53q

Tight lower bound for the channel assignment problem [article]

Arkadiusz Socala
2014 arXiv   pre-print
We study the complexity of the Channel Assignment problem.  ...  A major open problem asks whether Channel Assignment admits an O(c^n)-time algorithm, for a constant c independent of the weights on the edges.  ...  Acknowledgments We thank Łukasz Kowalik who was the originator of this studies for a comprehensive support.  ... 
arXiv:1407.7162v1 fatcat:v376hlne4jasvcmhktr3k3cqlq

The complexity of design automation problems

Sartaj Sahni, Atul Bhatt
1980 Proceedings of the seventeenth design automation conference on Design automation - DAC '80  
Emphasis is on problems involving the physical implementation and testing stages of the design process. Section 2 contains a brief description, in general terms, of the DA problems considered.  ...  To date, most of the effort in DA has concentrated on the following stages of the design process: physical implementation of the logic design, and testing.  ...  Rather, asymptotic bounds on the step count are obtained. Asymptotic analysis uses the notation Ο, Ω, Θ and o. These are defined below.  ... 
doi:10.1145/800139.804562 dblp:conf/dac/SahniB80 fatcat:h427snpf35gjdhub6ugvxkfpza

Distance geometry approach for special graph coloring problems [article]

Rosiane de Freitas, Bruno Dias, Nelson Maculan, Jayme Szwarcfiter
2016 arXiv   pre-print
They constitute models for real applications, such as channel assignment in mobile wireless networks.  ...  We also propose implicit enumeration methods for some of the optimization problems based on branch-and-prune methods proposed for distance geometry problems in the literature.  ...  on the edges and distance geometry problems, and for discussing some of the ideas presented here.  ... 
arXiv:1606.04978v1 fatcat:grzcsiarwbfrxoumuoj4jy6czi

The Orphan Problem in ZigBee Wireless Networks

Meng-Shiuan Pan, Chia-Hung Tsai, Yu-Chee Tseng
2009 IEEE Transactions on Mobile Computing  
In this paper, we show that the orphan problem can be divided into two subproblems: the bounded-degree-and-depth tree formation (BDDTF) problem and the end-device maximum matching (EDMM) problem.  ...  This assignment is easy to implement, but it restricts the number of children of a device and the depth of the network.  ...  Several works have investigated the bounded-degree spanning tree problem.  ... 
doi:10.1109/tmc.2009.60 fatcat:avphv54purdifgj3ezxm7kh2aa

Counting-Based Search: Branching Heuristics for Constraint Satisfaction Problems

G. Pesant, C. Quimper, A. Zanarini
2012 The Journal of Artificial Intelligence Research  
This paper concentrates on one family of candidates: counting-based search.  ...  Whereas most generic search heuristics in constraint programming rely on local information at the level of the individual variable, our search heuristics are based on more global information at the constraint  ...  We wish to thank Tyrel Russell who participated in the implementation and experimentation work.  ... 
doi:10.1613/jair.3463 fatcat:2cgckqpxszcg3pe3yype5nkesq

The k-Colorable Unit Disk Cover Problem [article]

Monith S. Reyunuru, Kriti Jethlia, Manjanna Basappa
2021 arXiv   pre-print
(of radius=1), both lying in the plane, and a parameter k, the objective is to compute a set D'⊆ D such that every point in P is covered by at least one disk in D' and there exists a function χ:D'→ C  ...  that assigns colors to disks in D' such that for any d and d' in D' if d∩ d'≠∅, then χ(d)≠χ(d'), where C denotes a set containing k distinct colors.  ...  Introduction Our motivation for studying the problem arises from practical applications in the frequency/channel assignment problem in wireless/cellular networks.  ... 
arXiv:2104.00207v2 fatcat:c6pfcurwgjhmnp6x4q5fi3hwx4

Bicriteria Network Design Problems [article]

Madhav V. Marathe, R. Ravi, Ravi Sundaram,S. S. Ravi, Daniel J. Rosenkrantz, Harry B. Hunt III
1998 arXiv   pre-print
A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a <subgraph \from a  ...  This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance  ...  We thank Sven Krumke (University of Würzberg) for reading the paper carefully and providing several useful comments. In particular, both pointed an error in the original proof of Theorem 5.3.  ... 
arXiv:cs/9809103v1 fatcat:kgal233ohncypjtkchs3asiabu

Linear Assignment Problems and Extensions [chapter]

Rainer E. Burkard, Eranda Çela
1999 Handbook of Combinatorial Optimization  
We consider different aspects of assignment problems, starting with the assignment polytope and the relationship between assignment and matching problems, and focusing then on deterministic and randomized  ...  This paper aims at describing the state of the art on linear assignment problems (LAPs).  ...  In the terminal assignment problem the terminals situated in two upper layers are to be assigned such that the resulting channel routing problem has minimum total density.  ... 
doi:10.1007/978-1-4757-3023-4_2 fatcat:zb3oagbemfg23l57jxd6d6vna4

Lower bounds for the virtual path layout problem in ATM networks [chapter]

Luca Becchetti, Carlo Gaibisso
1997 Lecture Notes in Computer Science  
In this paper we deal with the problem of designing virtual path layouts in ATM networks with given hop-count and minimum load, for which we prove a lower bound with respect to networks with arbitrary  ...  The result is then applied to derive a tight lower bound for the one-to-many communication pattern in networks with arbitrary topology, and for the many-to-many communication pattern in planar graphs and  ...  2. the maximum number of virtual paths in a virtual channel, denoted as hop count in what follows, should be kept as low as possible, so as to guarantee low set up times for the virtual channels and high  ... 
doi:10.1007/3-540-63774-5_116 fatcat:vnfvnf7opnhzxokupt5caop4nq

Lower Bounds for the Bandwidth Problem [article]

Franz Rendl, Renata Sotirov, Christian Truden
2021 arXiv   pre-print
This work focuses on investigating novel approaches to obtain lower bounds for the bandwidth problem. In particular, we use vertex partitions to bound the bandwidth of a graph.  ...  Our approach contains prior approaches for bounding the bandwidth as special cases. By varying sizes of partitions, we achieve a trade-off between quality of bounds and efficiency of computing them.  ...  [9] proposed two lower bounds based on SDP relaxations of the resulting Quadratic Assignment Problem (QAP).  ... 
arXiv:1904.06715v4 fatcat:ajmnzac35neuphpu7uoq73k7ka

A multi-period machine assignment problem

Xinhui Zhang, Jonathan F. Bard
2006 European Journal of Operational Research  
In this paper, a multi-period assignment problem is studied that arises as part of a weekly planning problem at mail processing and distribution centers.  ...  In a comparative study, high quality solutions were routinely provided by the heuristic in negligible time when compared to a commercial branch-and-bound code (Xpress).  ...  Introduction The classical assignment problem (AP) has a wide range of applications that span manufacturing, personnel scheduling and transportation, to name a few.  ... 
doi:10.1016/j.ejor.2004.07.051 fatcat:vimrtxc3undenag7e6vrm3gw7y
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