@inproceedings{BorndoerferArslanElijazyferetal., author = {Bornd{\"o}rfer, Ralf and Arslan, Oytun and Elijazyfer, Ziena and G{\"u}ler, Hakan and Renken, Malte and Sahin, Guvenc and Schlechte, Thomas}, title = {Line Planning on Path Networks with Application to the Istanbul Metrob{\"u}s}, series = {Operations Research Proceedings 2016}, booktitle = {Operations Research Proceedings 2016}, doi = {10.1007/978-3-319-55702-1_32}, pages = {235 -- 241}, abstract = {Bus rapid transit systems in developing and newly industrialized countries often consist of a trunk with a path topology. On this trunk, several overlapping lines are operated which provide direct connections. The demand varies heavily over the day, with morning and afternoon peaks typically in reverse directions. We propose an integer programming model for this problem, derive a structural property of line plans in the static (or single period) ``unimodal demand'' case, and consider approaches to the solution of the multi-period version that rely on clustering the demand into peak and off-peak service periods. An application to the Metrob{\"u}s system of Istanbul is discussed.}, language = {en} } @misc{BorndoerferArslanElijazyferetal., author = {Bornd{\"o}rfer, Ralf and Arslan, Oytun and Elijazyfer, Ziena and G{\"u}ler, Hakan and Renken, Malte and Sahin, G{\"u}venc and Schlechte, Thomas}, title = {Line Planning on Path Networks with Application to the Istanbul Metrob{\"u}s}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60119}, abstract = {Bus rapid transit systems in developing and newly industrialized countries often consist of a trunk with a path topology. On this trunk, several overlapping lines are operated which provide direct connections. The demand varies heavily over the day, with morning and afternoon peaks typically in reverse directions. We propose an integer programming model for this problem, derive a structural property of line plans in the static (or single period) ``unimodal demand'' case, and consider approaches to the solution of the multi-period version that rely on clustering the demand into peak and off-peak service periods. An application to the Metrob{\"u}s system of Istanbul is discussed.}, language = {en} } @misc{Elijazyfer, type = {Master Thesis}, author = {Elijazyfer, Ziena}, title = {L{\"a}ngenbeschr{\"a}nkte Teilgraphenbildung zur Maut-Kontrollstreckenoptimierung}, language = {de} } @misc{BorndoerferElijazyferSchwartz, author = {Bornd{\"o}rfer, Ralf and Elijazyfer, Ziena and Schwartz, Stephan}, title = {Approximating Balanced Graph Partitions}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73675}, abstract = {We consider the problem of partitioning a weighted graph into k connected components of similar weight. In particular, we consider the two classical objectives to maximize the lightest part or to minimize the heaviest part. For a partitioning of the vertex set and for both objectives, we give the first known approximation results on general graphs. Specifically, we give a \$\Delta\$-approximation where \$\Delta\$ is the maximum degree of an arbitrary spanning tree of the given graph. Concerning the edge partition case, we even obtain a 2-approximation for the min-max and the max-min problem, by using the claw-freeness of line graphs.}, language = {en} }