@inproceedings{19869,
  abstract     = {{Given a connected graph $G$, let a $dT$-spanning tree of $G$ be a spanning tree of $G$ of maximum degree bounded by $dT$. It is well known that for each $dT ge 2$ the problem of deciding whether a connected graph has a $dT$-spanning tree is NP-complete. In this paper we investigate this problem when additionally connectivity and maximum degree of the graph are given. A complete characterization of this problem for 2- and 3-connected graphs, for planar graphs, and for $dT=2$ is provided. Our first result is that given a biconnected graph of maximum degree $2dT-2$, we can find its $dT$-spanning tree in time $O(m+n^3/2)$. For graphs of higher connectivity we design a polynomial-time algorithm that finds a $dT$-spanning tree in any $k$-connected graph of maximum degree $k(dT-2)+2$. On the other hand, we prove that deciding whether a $k$-connected graph of maximum degree $k(dT-2)+3$ has a $dT$-spanning tree is NP-complete, provided $k le 3$. For arbitrary $k ge 3$ we show that verifying whether a $k$-connected graph of maximum degree $k(dT-1)$ has a $dT$-spanning tree is NP-complete. In particular, we prove that the Hamiltonian path (cycle) problem is NP-complete for $k$-connected $k$-regular graphs, if $k>2$. This extends the well known result for $k=3$ and fully characterizes the case $dT=2$. For planar graphs it is NP-complete to decide whether a $k$-connected planar graph of maximum degree $dG$ has a $dT$-spanning tree for $k=1$ and $dG > dT ge 2$, for $k=2$ and $dG > 2(dT-1) ge 2$, and for $k=3$ and $dG > dT = 2$. On the other hand, we show how to find in polynomial (linear or almost linear) time a $dT$-spanning tree for all other parameters of $k$, $dG$, and $dT$.}},
  author       = {{Czumaj, Artur and Strothmann, Willy-Bernhard}},
  booktitle    = {{Proceedings of the Fifth Annual European Symposium on Algorithms (ESA'97)}},
  isbn         = {{9783540633976}},
  issn         = {{0302-9743}},
  title        = {{{Bounded degree spanning trees}}},
  doi          = {{10.1007/3-540-63397-9_9}},
  year         = {{1997}},
}

@inbook{3029,
  author       = {{Blömer, Johannes}},
  booktitle    = {{Algorithms — ESA '97}},
  isbn         = {{9783540633976}},
  issn         = {{0302-9743}},
  pages        = {{53--63}},
  publisher    = {{Springer Berlin Heidelberg}},
  title        = {{{Denesting by bounded degree radicals}}},
  doi          = {{10.1007/3-540-63397-9_5}},
  year         = {{1997}},
}

@inbook{16569,
  author       = {{Meyer auf der Heide, Friedhelm and Vöcking, Berthold}},
  booktitle    = {{Euro-Par'97 Parallel Processing}},
  isbn         = {{9783540634409}},
  issn         = {{0302-9743}},
  title        = {{{Static and dynamic data management in networks}}},
  doi          = {{10.1007/bfb0002716}},
  year         = {{1997}},
}

@inbook{16605,
  author       = {{Bäumker, Armin and Meyer auf der Heide, Friedhelm}},
  booktitle    = {{Solving Irregularly Structured Problems in Parallel}},
  isbn         = {{9783540631385}},
  issn         = {{0302-9743}},
  title        = {{{Communication efficient parallel searching}}},
  doi          = {{10.1007/3-540-63138-0_21}},
  year         = {{1997}},
}

@inbook{16687,
  author       = {{Karaivazoglou, Efstratios and Meyer auf der Heide, Friedhelm}},
  booktitle    = {{Euro-Par'97 Parallel Processing}},
  isbn         = {{9783540634409}},
  issn         = {{0302-9743}},
  title        = {{{Routing on asyncronous processor networks}}},
  doi          = {{10.1007/bfb0002741}},
  year         = {{1997}},
}

@inproceedings{16568,
  abstract     = {{We present a data structure problem which describes the requirements of a simple variant of fully dynamic walk-through animation: We assume the scene to consist of unit size balls in R2 or higher dimensions. The scene may be arbitrarily large and has to be stored in secondary memory (discs) with relatively slow access. We allow a visitor to walk in the scene, and a modeler to update the scene by insertions and deletions of balls. We focus on the realtime requirement of animation systems: For some t (specified by the computation power of (the rendering hardware of) the graphic workstation) the data structure has to guarantee that the balls within distance t of the current visitor's position are presented to the rendering hardware, 20 times per second. Insertions and deletions should also be available to the visitor with small delay, independent of the size of the scene. We present a data structure that fulfills the above task in realtime. Its runtime is output-sensitive, i.e. linear in a quantity close to the output size of the query. We further present (preliminary) experimental results indicating that our structure is efficient in practice.
}},
  author       = {{Fischer, Matthias and Meyer auf der Heide, Friedhelm and Strothmann, Willy-Bernhard}},
  booktitle    = {{5th Annual European Symposium on Algorithms (ESA '97)}},
  isbn         = {{9783540633976}},
  issn         = {{0302-9743}},
  pages        = {{157--170}},
  publisher    = {{Springer}},
  title        = {{{Dynamic data structures for realtime management of large geometric scenes}}},
  doi          = {{10.1007/3-540-63397-9_13}},
  volume       = {{1284}},
  year         = {{1997}},
}

@inbook{19816,
  author       = {{Kleine Büning, Hans and Lettmann, Theodor}},
  booktitle    = {{Lecture Notes in Computer Science}},
  isbn         = {{9783540618638}},
  issn         = {{0302-9743}},
  title        = {{{Learning a representation for optimizable formulas}}},
  doi          = {{10.1007/3-540-61863-5_33}},
  year         = {{1996}},
}

@inbook{17564,
  author       = {{Bäumker, Armin and Dittrich, Wolfgang and Meyer auf der Heide, Friedhelm and Rieping, Ingo}},
  booktitle    = {{Lecture Notes in Computer Science}},
  isbn         = {{9783540616276}},
  issn         = {{0302-9743}},
  pages        = {{369--376}},
  title        = {{{Realistic parallel algorithms: Priority queue operations and selection for the BSP* Model}}},
  doi          = {{10.1007/bfb0024725}},
  year         = {{1996}},
}

@book{16702,
  editor       = {{Meyer auf der Heide, Friedhelm and Monien, Burkhard}},
  isbn         = {{9783540614401}},
  issn         = {{0302-9743}},
  title        = {{{Automata, Languages and Programming, 23rd International Colloquium, ICALP96}}},
  doi          = {{10.1007/3-540-61440-0}},
  year         = {{1996}},
}

@inbook{16703,
  author       = {{Berenbrink, Petra and Meyer auf der Heide, Friedhelm and Stemann, Volker}},
  booktitle    = {{STACS 96}},
  isbn         = {{9783540609223}},
  issn         = {{0302-9743}},
  title        = {{{Fault-tolerant shared memory simulations}}},
  doi          = {{10.1007/3-540-60922-9_16}},
  year         = {{1996}},
}

@inbook{16704,
  author       = {{Meyer auf der Heide, Friedhelm and Vöcking, Berthold}},
  booktitle    = {{STACS 95}},
  isbn         = {{9783540590422}},
  issn         = {{0302-9743}},
  title        = {{{A packet routing protocol for arbitrary networks}}},
  doi          = {{10.1007/3-540-59042-0_81}},
  year         = {{1995}},
}

@inbook{16705,
  author       = {{Czumaj, Artur and Meyer auf der Heide, Friedhelm and Stemann, Volker}},
  booktitle    = {{Lecture Notes in Computer Science}},
  isbn         = {{9783540603139}},
  issn         = {{0302-9743}},
  title        = {{{Shared memory simulations with triple-logarithmic delay}}},
  doi          = {{10.1007/3-540-60313-1_133}},
  year         = {{1995}},
}

@inbook{16717,
  author       = {{Meyer auf der Heide, Friedhelm and Westermann, Matthias}},
  booktitle    = {{Graph-Theoretic Concepts in Computer Science}},
  isbn         = {{9783540606185}},
  issn         = {{0302-9743}},
  title        = {{{Hot-potato routing on multi-dimensional tori}}},
  doi          = {{10.1007/3-540-60618-1_77}},
  year         = {{1995}},
}

@inbook{16874,
  author       = {{Bäumker, Armin and Dittrich, Wolfgang and Meyer auf der Heide, Friedhelm}},
  booktitle    = {{Lecture Notes in Computer Science}},
  isbn         = {{9783540603139}},
  issn         = {{0302-9743}},
  title        = {{{Truly efficient parallel algorithms: c-optimal multisearch for an extension of the BSP model}}},
  doi          = {{10.1007/3-540-60313-1_131}},
  year         = {{1995}},
}

@book{17477,
  editor       = {{Meyer auf der Heide, Friedhelm and Monien, B. and Rosenberg, A. L.}},
  isbn         = {{9783540567318}},
  issn         = {{0302-9743}},
  publisher    = {{Springer}},
  title        = {{{Parallel Architectures and Their Efficient Use}}},
  doi          = {{10.1007/3-540-56731-3}},
  year         = {{1993}},
}

@inbook{16730,
  author       = {{Meyer auf der Heide, Friedhelm and Oesterdiekhoff, Brigitte and Wanka, Rolf}},
  booktitle    = {{Automata, Languages and Programming}},
  isbn         = {{9783540569398}},
  issn         = {{0302-9743}},
  title        = {{{Strongly adaptive token distribution}}},
  doi          = {{10.1007/3-540-56939-1_89}},
  year         = {{1993}},
}

@inbook{16732,
  author       = {{Lürwer-Brüggemeier, Katharina and Meyer auf der Heide, Friedhelm}},
  booktitle    = {{Lecture Notes in Computer Science}},
  isbn         = {{9783540565031}},
  issn         = {{0302-9743}},
  title        = {{{Capabilities and complexity of computations with integer division}}},
  doi          = {{10.1007/3-540-56503-5_46}},
  year         = {{1993}},
}

@inbook{3046,
  author       = {{Alt, Helmut and Blömer, Johannes}},
  booktitle    = {{Data structures and efficient algorithms}},
  isbn         = {{9783540554882}},
  issn         = {{0302-9743}},
  pages        = {{1--24}},
  publisher    = {{Springer Berlin Heidelberg}},
  title        = {{{Resemblance and symmetries of geometric patterns}}},
  doi          = {{10.1007/3-540-55488-2_19}},
  year         = {{1992}},
}

@inbook{16733,
  author       = {{Dietzfelbinger, Martin and Meyer auf der Heide, Friedhelm}},
  booktitle    = {{Data structures and efficient algorithms}},
  isbn         = {{9783540554882}},
  issn         = {{0302-9743}},
  title        = {{{High performance universal hashing, with applications to shared memory simulations}}},
  doi          = {{10.1007/3-540-55488-2_31}},
  year         = {{1992}},
}

@inbook{16734,
  author       = {{Meyer auf der Heide, Friedhelm}},
  booktitle    = {{Lecture Notes in Computer Science}},
  isbn         = {{9783540567318}},
  issn         = {{0302-9743}},
  title        = {{{Hashing strategies for simulating shared memory on distributed memory machines}}},
  doi          = {{10.1007/3-540-56731-3_3}},
  year         = {{1992}},
}