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New spectral lower bounds on the bisection width of graphs. <i>Theoretical Computer Science</i>. 2004:155-174. doi:<a href=\"https://doi.org/10.1016/j.tcs.2004.03.059\">10.1016/j.tcs.2004.03.059</a>","bibtex":"@article{Bezrukov_Elsässer_Monien_Preis_Tillich_2004, title={New spectral lower bounds on the bisection width of graphs}, DOI={<a href=\"https://doi.org/10.1016/j.tcs.2004.03.059\">10.1016/j.tcs.2004.03.059</a>}, journal={Theoretical Computer Science}, author={Bezrukov, S. and Elsässer, R. and Monien, B. and Preis, R. and Tillich, J.-P.}, year={2004}, pages={155–174} }"},"type":"journal_article","department":[{"_id":"101"}],"date_created":"2020-04-15T08:05:40Z"},{"date_created":"2020-04-15T08:17:18Z","department":[{"_id":"101"}],"type":"journal_article","citation":{"short":"S. Day, O. Junge, K. Mischaikow, SIAM Journal on Applied Dynamical Systems (2004) 117–160.","ama":"Day S, Junge O, Mischaikow K. A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems. <i>SIAM Journal on Applied Dynamical Systems</i>. 2004:117-160. doi:<a href=\"https://doi.org/10.1137/030600210\">10.1137/030600210</a>","chicago":"Day, S., O. Junge, and K. 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Elsässer, B. Monien, R. Preis, A. Frommer, Parallel Processing Letters (2004) 61–73.","chicago":"Elsässer, Robert, Burkhard Monien, Robert Preis, and Andreas Frommer. “Optimal Diffusion Schemes and Load Balancing on Product Graphs.” <i>Parallel Processing Letters</i>, 2004, 61–73. <a href=\"https://doi.org/10.1142/s0129626404001714\">https://doi.org/10.1142/s0129626404001714</a>.","apa":"Elsässer, R., Monien, B., Preis, R., &#38; Frommer, A. (2004). Optimal Diffusion Schemes and Load Balancing on Product Graphs. <i>Parallel Processing Letters</i>, 61–73. <a href=\"https://doi.org/10.1142/s0129626404001714\">https://doi.org/10.1142/s0129626404001714</a>","ieee":"R. Elsässer, B. Monien, R. Preis, and A. Frommer, “Optimal Diffusion Schemes and Load Balancing on Product Graphs,” <i>Parallel Processing Letters</i>, pp. 61–73, 2004.","ama":"Elsässer R, Monien B, Preis R, Frommer A. Optimal Diffusion Schemes and Load Balancing on Product Graphs. <i>Parallel Processing Letters</i>. 2004:61-73. doi:<a href=\"https://doi.org/10.1142/s0129626404001714\">10.1142/s0129626404001714</a>","bibtex":"@article{Elsässer_Monien_Preis_Frommer_2004, title={Optimal Diffusion Schemes and Load Balancing on Product Graphs}, DOI={<a href=\"https://doi.org/10.1142/s0129626404001714\">10.1142/s0129626404001714</a>}, journal={Parallel Processing Letters}, author={Elsässer, Robert and Monien, Burkhard and Preis, Robert and Frommer, Andreas}, year={2004}, pages={61–73} }","mla":"Elsässer, Robert, et al. “Optimal Diffusion Schemes and Load Balancing on Product Graphs.” <i>Parallel Processing Letters</i>, 2004, pp. 61–73, doi:<a href=\"https://doi.org/10.1142/s0129626404001714\">10.1142/s0129626404001714</a>."},"publication":"Parallel Processing Letters","abstract":[{"text":"<jats:p> We discuss nearest neighbor load balancing schemes on processor networks which are represented by a cartesian product of graphs and present a new optimal diffusion scheme for general graphs. In the first part of the paper, we introduce the Alternating-Direction load balancing scheme, which reduces the number of load balance iterations by a factor of 2 for cartesian products of graphs. The resulting flow is theoretically analyzed and can be very high for certain cases. Therefore, we further present the Mixed-Direction scheme which needs the same number of iterations but computes in most cases a much smaller flow. In the second part of the paper, we present a simple optimal diffusion scheme for general graphs, calculating a balancing flow which is minimal in the l<jats:sub>2</jats:sub> norm. It is based on the spectra of the graph representing the network and needs only m-1 iterations to balance the load with m being the number of distinct eigenvalues. Known optimal diffusion schemes have the same performance, however the optimal scheme presented in this paper can be implemented in a very simple manner. The number of iterations of optimal diffusion schemes is independent of the load scenario and, thus, they are practical for networks which represent graphs with known spectra. Finally, our experiments exhibit that the new optimal scheme can successfully be combined with the Alternating-Direction and Mixed-Direction schemes for efficient load balancing on product graphs. </jats:p>","lang":"eng"}],"date_created":"2020-04-16T05:46:56Z","department":[{"_id":"101"}],"type":"journal_article"},{"publication":"ESAIM: Control, Optimisation and Calculus of Variations","citation":{"ieee":"O. Junge and H. M. Osinga, “A set oriented approach to global optimal control,” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, pp. 259–270, 2004.","apa":"Junge, O., &#38; Osinga, H. M. (2004). A set oriented approach to global optimal control. <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, 259–270. <a href=\"https://doi.org/10.1051/cocv:2004006\">https://doi.org/10.1051/cocv:2004006</a>","chicago":"Junge, Oliver, and Hinke M. Osinga. “A Set Oriented Approach to Global Optimal Control.” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, 2004, 259–70. <a href=\"https://doi.org/10.1051/cocv:2004006\">https://doi.org/10.1051/cocv:2004006</a>.","short":"O. Junge, H.M. Osinga, ESAIM: Control, Optimisation and Calculus of Variations (2004) 259–270.","mla":"Junge, Oliver, and Hinke M. Osinga. “A Set Oriented Approach to Global Optimal Control.” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, 2004, pp. 259–70, doi:<a href=\"https://doi.org/10.1051/cocv:2004006\">10.1051/cocv:2004006</a>.","bibtex":"@article{Junge_Osinga_2004, title={A set oriented approach to global optimal control}, DOI={<a href=\"https://doi.org/10.1051/cocv:2004006\">10.1051/cocv:2004006</a>}, journal={ESAIM: Control, Optimisation and Calculus of Variations}, author={Junge, Oliver and Osinga, Hinke M.}, year={2004}, pages={259–270} }","ama":"Junge O, Osinga HM. A set oriented approach to global optimal control. <i>ESAIM: Control, Optimisation and Calculus of Variations</i>. 2004:259-270. doi:<a href=\"https://doi.org/10.1051/cocv:2004006\">10.1051/cocv:2004006</a>"},"date_created":"2020-04-16T08:11:16Z","type":"journal_article","department":[{"_id":"101"}],"title":"A set oriented approach to global optimal control","year":"2004","status":"public","publication_identifier":{"issn":["1292-8119","1262-3377"]},"author":[{"first_name":"Oliver","last_name":"Junge","full_name":"Junge, Oliver"},{"full_name":"Osinga, Hinke M.","last_name":"Osinga","first_name":"Hinke M."}],"publication_status":"published","date_updated":"2022-01-06T06:52:53Z","page":"259-270","_id":"16619","user_id":"15701","doi":"10.1051/cocv:2004006"},{"date_updated":"2022-01-06T06:52:53Z","publication_status":"published","publication_identifier":{"isbn":["0780386825"]},"author":[{"full_name":"Junge, O.","last_name":"Junge","first_name":"O."},{"first_name":"J.E.","last_name":"Marsden","full_name":"Marsden, J.E."},{"full_name":"Mezic, I.","first_name":"I.","last_name":"Mezic"}],"status":"public","title":"Uncertainty in the dynamics of conservative maps","year":"2004","doi":"10.1109/cdc.2004.1430379","user_id":"15701","_id":"16620","language":[{"iso":"eng"}],"citation":{"mla":"Junge, O., et al. “Uncertainty in the Dynamics of Conservative Maps.” <i>2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. 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No.04CH37601)","department":[{"_id":"101"}],"type":"conference","date_created":"2020-04-16T08:12:31Z"},{"_id":"51469","series_title":"Contemporary Mathematics","language":[{"iso":"eng"}],"editor":[{"full_name":"Agranowsky, M.","first_name":"M.","last_name":"Agranowsky"}],"volume":364,"user_id":"49063","author":[{"id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim"},{"full_name":"Mayer, D.","last_name":"Mayer","first_name":"D."}],"corporate_editor":["et al."],"title":"The Dynamical Zeta Function and Transfer Operators for the Kac-Baker Model","status":"public","year":"2004","intvolume":"       364","date_updated":"2024-02-20T13:27:15Z","publication_status":"published","date_created":"2024-02-19T08:14:51Z","department":[{"_id":"91"}],"type":"book_chapter","citation":{"bibtex":"@inbook{Hilgert_Mayer_2004, series={Contemporary Mathematics}, title={The Dynamical Zeta Function and Transfer Operators for the Kac-Baker Model}, volume={364}, booktitle={Complex Analysis and Dynamical Systems}, author={Hilgert, Joachim and Mayer, D.}, editor={Agranowsky, M. and et al.}, year={2004}, collection={Contemporary Mathematics} }","ama":"Hilgert J, Mayer D. 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