#### DMCA

## Orienting Fully Dynamic Graphs with Worst-Case Time Bounds (2014)

Citations: | 2 - 0 self |

### Citations

96 |
Edge-disjoint spanning trees of finite graphs,
- Nash-Williams
- 1961
(Show Context)
Citation Context ... and bounded-treewidth graphs. A key property of bounded arboricity graphs that has been exploited in various algorithmic applications is the following Nash-Williams Theorem. Theorem 1 (Nash-Williams =-=[11,12]-=-). A graph G = (V, E) has arboricity α(G) if and only if α(G) > 0 is the smallest number of sets E1, . . . , E α(G) that E can be partitioned into, such that each subgraph (V, Ei) is a forest. This th... |

96 | Nash-Williams, \Edge-disjoint spanning trees of graphs - A - 1961 |

70 | Nash-Williams, Decompositions of finite graphs in forests - A - 1964 |

67 |
Decomposition of finite graphs into forests,
- Nash-Williams
- 1964
(Show Context)
Citation Context ... and bounded-treewidth graphs. A key property of bounded arboricity graphs that has been exploited in various algorithmic applications is the following Nash-Williams Theorem. Theorem 1 (Nash-Williams =-=[11,12]-=-). A graph G = (V, E) has arboricity α(G) if and only if α(G) > 0 is the smallest number of sets E1, . . . , E α(G) that E can be partitioned into, such that each subgraph (V, Ei) is a forest. This th... |

46 | Planar orientations with low out-degree and compaction of adjacency matrices
- CHROBAK, EPPSTEIN
- 1991
(Show Context)
Citation Context ...g” [1], where orientations are used to develop more efficient algorithms for finding simple cycles and paths. Another fundamental example is in data structures for quickly answering adjacency queries =-=[2,3,4]-=-, where a corientation of a (dynamic) graph G is used to answer adjacency queries in O(c) time using only linear space. These techniques [2,3,4] were further generalized to answer short-path queries [... |

22 |
Forests, frames, and games: Algorithms for matroid sums and applications.
- GABOW, N, et al.
- 1992
(Show Context)
Citation Context ...ry vertex is at most 1, hence the union of the oriented forests has out-degree bounded by α(G). There exists a polynomial-time algorithm that computes for a (static) graph G the exact arboricity α(G) =-=[13]-=-, and a linear-time algorithm that computes a (2α(G) − 1)-orientation [14]. For every (static) graph G, the minimum-possible maximum out-degree is closely related to α(G): the argument above provides ... |

22 |
games: Algorithms for matroid sums and applications
- Forests
- 1992
(Show Context)
Citation Context ... each vertex is at most 1, hence in the union of the oriented forests the out-degree of each vertex is at most α(G). There 2 exists a polynomial-time algorithm for computing the exact arboricity α(G) =-=[GW92]-=-, and a linear-time algorithm for computing a (2α(G) − 1)-orientation for a static graph G [AMZ97]. For every graph G, the maximum out-degree (of its edge orientations) is closely related to α(G): The... |

21 | The random graph threshold for k-orientiability and a fast algorithm for optimal multiple-choice allocation
- Cain, Sanders, et al.
- 2007
(Show Context)
Citation Context ...ng only linear space. These techniques [2,3,4] were further generalized to answer short-path queries [5]. Additional examples for the algorithmic use of low-degree orientations include load balancing =-=[6]-=-, maximal matchings [7], counting subgraphs in sparse graphs [8], prize-collecting TSPs and Steiner Trees [9], reporting all maximal independent sets [10], answering dominance queries [10], subgraph l... |

16 | maximal independent sets and dynamic dominance for sparse graphs
- All
(Show Context)
Citation Context ...low-degree orientations include load balancing [6], maximal matchings [7], counting subgraphs in sparse graphs [8], prize-collecting TSPs and Steiner Trees [9], reporting all maximal independent sets =-=[10]-=-, answering dominance queries [10], subgraph listing problems (listing triangles and 4-cliques) in planar graphs [2], and computing the girth [5]. Efficient Data Communication. The efficiency of netwo... |

14 | Dynamic Representations of Sparse Graphs
- Brodal, Fagerberg
- 1999
(Show Context)
Citation Context ...g” [1], where orientations are used to develop more efficient algorithms for finding simple cycles and paths. Another fundamental example is in data structures for quickly answering adjacency queries =-=[2,3,4]-=-, where a corientation of a (dynamic) graph G is used to answer adjacency queries in O(c) time using only linear space. These techniques [2,3,4] were further generalized to answer short-path queries [... |

13 | Efficient computation of implicit representations of sparse graphs
- Arikati, Maheshwari, et al.
- 1997
(Show Context)
Citation Context ...gree bounded by α(G). There exists a polynomial-time algorithm that computes for a (static) graph G the exact arboricity α(G) [13], and a linear-time algorithm that computes a (2α(G) − 1)-orientation =-=[14]-=-. For every (static) graph G, the minimum-possible maximum out-degree is closely related to α(G): the argument above provides an orientation with maximum out-degree at most α(G), but the maximum out-d... |

13 | Maintaining a large matching and a small vertex cover,” - Onak, Rubinfeld - 2010 |

12 | Fully dynamic maintenance of vertex cover,” - Ivkovic, Lloyd - 1994 |

10 | Simple deterministic algorithms for fully dynamic maximal matching.
- Neiman, Solomon
- 2013
(Show Context)
Citation Context ...hese techniques [2,3,4] were further generalized to answer short-path queries [5]. Additional examples for the algorithmic use of low-degree orientations include load balancing [6], maximal matchings =-=[7]-=-, counting subgraphs in sparse graphs [8], prize-collecting TSPs and Steiner Trees [9], reporting all maximal independent sets [10], answering dominance queries [10], subgraph listing problems (listin... |

8 |
Oracles for bounded-length shortest paths in planar graphs
- Kowalik, Kurowski
(Show Context)
Citation Context ...], where a corientation of a (dynamic) graph G is used to answer adjacency queries in O(c) time using only linear space. These techniques [2,3,4] were further generalized to answer short-path queries =-=[5]-=-. Additional examples for the algorithmic use of low-degree orientations include load balancing [6], maximal matchings [7], counting subgraphs in sparse graphs [8], prize-collecting TSPs and Steiner T... |

8 | An efficient polynomial-time approximation scheme for Steiner forest in planar graphs
- Eisenstat, Klein, et al.
- 2012
(Show Context)
Citation Context ...itional examples for the algorithmic use of low-degree orientations include load balancing [6], maximal matchings [7], counting subgraphs in sparse graphs [8], prize-collecting TSPs and Steiner Trees =-=[9]-=-, reporting all maximal independent sets [10], answering dominance queries [10], subgraph listing problems (listing triangles and 4-cliques) in planar graphs [2], and computing the girth [5]. Efficien... |

4 |
A dynamic data structure for counting subgraphs in sparse graphs
- Dvorak, Tuma
(Show Context)
Citation Context ...ralized to answer short-path queries [5]. Additional examples for the algorithmic use of low-degree orientations include load balancing [6], maximal matchings [7], counting subgraphs in sparse graphs =-=[8]-=-, prize-collecting TSPs and Steiner Trees [9], reporting all maximal independent sets [10], answering dominance queries [10], subgraph listing problems (listing triangles and 4-cliques) in planar grap... |

3 | Adjacency queries in dynamic sparse graphs
- Kowalik
(Show Context)
Citation Context ...g” [1], where orientations are used to develop more efficient algorithms for finding simple cycles and paths. Another fundamental example is in data structures for quickly answering adjacency queries =-=[2,3,4]-=-, where a corientation of a (dynamic) graph G is used to answer adjacency queries in O(c) time using only linear space. These techniques [2,3,4] were further generalized to answer short-path queries [... |

3 | Maintaining approximate maximum weighted matching in fully dynamic graphs - Anand, Baswana, et al. |

2 |
Maintaining assignments online: Matching, scheduling, and flows
- Gupta, Kumar, et al.
- 2014
(Show Context)
Citation Context ...) time and deletions in worst-case O(1) time by using an O(log n)-orientation. These algorithms have been used as black-box components in several applications of dynamic graphs. Recently Gupta et.al. =-=[16]-=- showed that 4if only insertions are allowed then an amortized 2 edge reorientations suffice for maintaining a maximum out-degree of O(α(G)). Algorithms with amortized runtime bounds may be insuffici... |

1 |
http://www.cs.uiuc.edu/~jeffe/teaching/datastructures/2006/ problems/Bill-arboricity.pdf (2006) Retrieved
- Erickson
- 2013
(Show Context)
Citation Context ...ned efficient amortized update time bounds, in contrast to our bounds which are all in the worst-case. Our results address an open question raised by Brodal and Fagerberg [3] and restated by Erickson =-=[15]-=-, of obtaining good worstcase bounds (although the ultimate goal is obviously worst-case time O(1) for all updates, if that is at all possible). 1.2 Comparison with Previous Work The dynamic setting i... |

1 | Fully dynamic (1 + ǫ)-approximate matchings - Gupta, Peng - 2013 |