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Multi-parameter complexity analysis for constrained size graph problems: using greediness for parameterization [article]

Edouard Bonnet, Bruno Escoffier, Vangelis Th. Paschos, Emeric Tourniaire
2013 arXiv   pre-print
Then, we show how these results can be easily extended for getting standard-parameterization results (i.e., with parameter the value of the optimal solution) for a well known local graph partitioning problem  ...  We study the parameterized complexity of a broad class of problems called "local graph partitioning problems" that includes the classical fixed cardinality problems as max k-vertex cover, k-densest subgraph  ...  In this paper we develop a technique for obtaining multi-parameterized results for local graph partitioning problems. Informally, the basic idea behind it is the following.  ... 
arXiv:1306.2217v1 fatcat:4sookcb6bfdk7mxdkhwdrjvccq

Multi-parameter Complexity Analysis for Constrained Size Graph Problems: Using Greediness for Parameterization [chapter]

Édouard Bonnet, Bruno Escoffier, Vangelis Th. Paschos, Émeric Tourniaire
2013 Lecture Notes in Computer Science  
Then, we show how these results can be easily extended for getting standard-parameterization results (i.e., with parameter the value of the optimal solution) for a well known local graph partitioning problem  ...  We study the parameterized complexity of a broad class of problems called "local graph partitioning problems" that includes the classical fixed cardinality problems as max k-vertex cover, k-densest subgraph  ...  In this paper we develop a technique for obtaining multi-parameterized results for local graph partitioning problems. Informally, the basic idea behind it is the following.  ... 
doi:10.1007/978-3-319-03898-8_7 fatcat:c2oyxyd75jc2hd325q2rabvv74

A Flexible Algorithm for Sensor Network Partitioning and Self-partitioning Problems [chapter]

Sandip Roy, Yan Wan, Ali Saberi
2006 Lecture Notes in Computer Science  
We then review our stochastic automaton-based partitioning algorithm, and extend its use for network partitioning and self-partitioning problems.  ...  The remainder of this article introduces the graph partitioning problem, discusses the influence model and its use as a partitioning tool, and pursues the application of the distributed partitioning tool  ...  (The average number of hops could be used instead.) Thus, we partition the graph using this maximum number of hops when greedy routing is used.  ... 
doi:10.1007/11963271_14 fatcat:w7xszqzh7zc4vcv3soi4gcsw6y

Kernelization for Graph Packing Problems via Rainbow Matching [article]

Stéphane Bessy, Marin Bougeret, Dimitrios M. Thilikos, Sebastian Wiederrecht
2022 arXiv   pre-print
We apply the rainbow matching technique on two (di)graph packing problems, namely the Triangle-Packing in Tournament problem (), where we ask for a directed triangle packing in a tournament, and the Induced  ...  2-Path-Packing () where we ask for a packing of k induced paths of length two in a graph.  ...  Greedy localization. A wide family of parameterized problems that have extensively studied from the kernelization point of view are (di)graph packing problems.  ... 
arXiv:2207.06874v1 fatcat:2vz6uexdbza3xnrfrets5rh5iu

Solving hard cut problems via flow-augmentation [chapter]

Eun Jung Kim, Stefan Kratsch, Marcin Pilipczuk, Magnus Wahlström
2021 Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA)  
We present a new technique for designing xed-parameter algorithms for graph cut problems in undirected graphs, which we call ow augmentation.  ...  Our technique is applicable to problems that can be phrased as a search for an (edge) (s, t)cut of cardinality at most k in an undirected graph G with designated terminals s and t.  ...  To illustrate the need for the ow-augmentation framework, let us brie y review previous work on parameterized algorithms for graph separation problems.  ... 
doi:10.1137/1.9781611976465.11 fatcat:mrunr4gbbzbcporcm5fz5gnu4y

On Labeled Traveling Salesman Problems [chapter]

Basile Couëtoux, Laurent Gourvès, Jérôme Monnot, Orestis A. Telelis
2008 Lecture Notes in Computer Science  
For the maximization version we give a 1 2 -approximation algorithm based on local improvements, and a simpler 1 3 -approximation algorithm. We show that the problem is APX-hard.  ...  For all of the analyzed algorithms we exhibit tightness of their analysis by provision of appropriate worst-case instances. * The Center for Algorithmic Game Theory, funded by the Carlsberg Foundation,  ...  Tightness of Analysis of locim We describe a parameterized instance which shows that the analysis of locim is assymptotically tight.  ... 
doi:10.1007/978-3-540-92182-0_68 fatcat:ms6powyugrba3jzjjastxjtc4m

PAGER: A Distributed Algorithm for the Dead-end Problem of Location-based Routing in Sensor Networks

Mi Lu
2021 figshare.com  
The dead-end problem is an importance issue of location-based routing in sensor network, which occurs when a message falls into a local minimum using greedy forwarding.  ...  In this paper, we propose a novel algorithm, named Partial-partition Avoiding Geographic Routing (PAGER), to solve the problem.  ...  Therefore, messages originated from the resulting graph in Fig. 2 (c) will be forwarded to destination using greedy forwarding without encountering the dead-end problem.  ... 
doi:10.6084/m9.figshare.13664993.v1 fatcat:dlaycus2tnerhjr6cmmna3zq34

Labeled Traveling Salesman Problems: Complexity and approximation

Basile Couëtoux, Laurent Gourvès, Jérôme Monnot, Orestis A. Telelis
2010 Discrete Optimization  
For the maximization version we give a 1 2 -approximation algorithm based on local improvements and show that the problem is APX-hard.  ...  For all of the analyzed algorithms we exhibit tightness of their analysis by provision of appropriate worst-case instances.  ...  Tightness of analysis of locim We describe a parameterized instance which shows that the analysis of locim is asymptotically tight.  ... 
doi:10.1016/j.disopt.2010.02.003 fatcat:gefqjd3uardo3ee5pojf6jsabm

Page 1581 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
Mechthild Opperud (Kjeller) 2000b:90066 90C27 Pferschy, Ulrich (A-GRAZ-OR; Graz) Stochastic analysis of greedy algorithms for the subset sum problem. (English summary) CEJOR Cent. Eur. J. Oper.  ...  We show that these problems remain fixed-parameter tractable even under this parameterization.  ... 

Universal Framework for Wireless Scheduling Problems [article]

Magnus M. Halldorsson, Tigran Tonoyan
2017 arXiv   pre-print
We also show that the approximation obtained is provably the best possible for any conflict graph formulation.  ...  We propose the first framework for approximation algorithms in the physical model that addresses these questions in full, including rate control.  ...  This approximation allows us to bring to bear the large body of theory of graph algorithms, greatly simplifying both the exposition and the analysis.  ... 
arXiv:1705.10104v1 fatcat:xsxxemenk5honbds55sqlkayae

On the tractability of optimization problems on H-graphs [article]

Fedor V. Fomin, Petr A. Golovach, Jean-Florent Raymond
2020 arXiv   pre-print
We provide a more refined complexity analysis of these problems from the perspective of Parameterized Complexity.  ...  On the other hand, we prove that when H is a tree, then Minimum Dominating Set is fixed-parameter tractable parameterized (FPT) by the size of H.  ...  Later, invariants related to neighborhood equivalence were used in [8] as parameters of FPT algorithms for the vast class of locally checkable vertex subset and vertex partitioning problems (LC-VSP problems  ... 
arXiv:1709.09737v4 fatcat:af6txgy4andkbjvlex3bvlhsme

Selection and Optimization of Hyperparameters in Warm-Started Quantum Optimization for the MaxCut Problem

Felix Truger, Martin Beisel, Johanna Barzen, Frank Leymann, Vladimir Yussupov
2022 Electronics  
In this paper, we address the problem of hyperparameter selection in WS-QAOA for the maximum cut problem using the classical Goemans–Williamson algorithm for pre-computations.  ...  However, warm-starting requirements often depend on the quantum algorithm and problem at hand.  ...  Acknowledgments: We are grateful to the the authors of [27] for fruitful discussion on parts of the work presented in this paper.  ... 
doi:10.3390/electronics11071033 doaj:71023908d3534b93b93045502d8d6fbe fatcat:pyli33qh3jbdzodsyuimnvvov4

Optimization and Reoptimization in Scheduling Problems [article]

Yael Mordechai
2015 arXiv   pre-print
We show that makespan minimization on unrelated machines admits a parameterized approximation scheme, where the parameter used is the number of processing times that are large relative to the latest completion  ...  We also present an FPT algorithm for the graph-balancing problem, which corresponds to the instances of the restricted assignment problem where each job can be processed on at most 2 machines.  ...  Problems in which some parameter k is fixed are called parameterized problems.  ... 
arXiv:1509.01630v1 fatcat:ege7rcqprnaa5epuebjoc73ajm

Mixed-integer programming techniques for the connected max-k-cut problem

Christopher Hojny, Imke Joormann, Hendrik Lüthen, Martin Schmidt
2020 Mathematical Programming Computation  
We consider an extended version of the classical Max-k-Cut problem in which we additionally require that the parts of the graph partition are connected.  ...  For this problem we study two alternative mixed-integer linear formulations and review existing as well as develop new branch-and-cut techniques like cuts, branching rules, propagation, primal heuristics  ...  Pfetsch for helpful discussions and his agreement to use parts of the code developed in [28] as the basis for our code.  ... 
doi:10.1007/s12532-020-00186-3 fatcat:ispaycmmqbbunjfobn2e7iwzbi

Algorithm Engineering for Cut Problems [article]

Alexander Noe
2021 arXiv   pre-print
This work develops highly-efficient algorithms for the (global) minimum cut problem, the balanced graph partitioning problem and the multiterminal cut problem.  ...  All of these algorithms are efficient in practice and freely available for use.  ...  “ILP-based Local Search for Graph Partitioning”.  ... 
arXiv:2108.04566v1 fatcat:4tpyybkhsvg6toiuxkvdvychqu
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