## Bicriteria Network Design Problems (1995)

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Citations: | 75 - 13 self |

### BibTeX

@MISC{Ravi95bicriterianetwork,

author = {Madhav Marathe Ravi and R. Ravi and Ravi Sundaram and S. S. Ravi and Daniel J. Rosenkrantz and Harry B. Hunt Iii},

title = {Bicriteria Network Design Problems},

year = {1995}

}

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### Abstract

We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a subgraph from a given subgraph-class that minimizes the second objective subject to the budget on the first. We consider three different criteria - the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, we develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same we present a "black box" parametric search technique. This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorit...

### Citations

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Citation Context ...are typically sought to be minimized in the construction of these trees. Network design problems where even one cost measure must be minimized, are often NP-hard. (See Section A2 on Network Design in =-=[GJ79]-=-.) But, in real-life applications, it is often the case that the network to be built is required to minimize multiple cost measures simultaneously, with different cost functions for each measure. For ... |

8530 |
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Citation Context ...ms for minimum diameter spanning trees [CG82]; while the result for (Total cost, Total cost, Spanning tree) follows by combining Theorem 6.3 with an exact algorithm to compute a minimum spanning tree =-=[CLR]-=-. Finally, we present a cluster based approximation algorithm and a solution based decomposition technique for devising approximation algorithms for problems when the two objectives are different. Our... |

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Citation Context ...problem, termed the multi-objective shortest path problem (MOSP) in the literature, is NP-complete and Warburton [Wa87] presented the first fully polynomial approximation scheme (FPAS) for it. Hassin =-=[Ha92]-=- provided a strongly polynomial FPAS for the problem which improved the running time of Warburton [Wa87]. This result was further improved by Phillips [Ph+93]. The (Total cost, Total cost, Spanning tr... |

146 | Improved low-degree testing and its applications - Arora, Sudan |

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Citation Context ..., Raghavachari and Young [KR+93] studied an extension called Light, approximate Shortest-path Trees (LAST) and gave an approximation algorithm with (O(1),O(1)) performance guarantee. Kadaba and Jaffe =-=[KJ83]-=-, Kompella et al. [KP+92A], and Zhu et al. [ZP+94] considered the (Diameter, Total cost, Steiner tree) problem with two edge costs and presented heuristics without any guarantees. It is easy to con6 T... |

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Citation Context ... between two pre-specified vertices s and t, or (Diameter, Total cost, s-t path). This problem, termed the multi-objective shortest path problem (MOSP) in the literature, is NP-complete and Warburton =-=[Wa87]-=- presented the first fully polynomial approximation scheme (FPAS) for it. Hassin [Ha92] provided a strongly polynomial FPAS for the problem which improved the running time of Warburton [Wa87]. This re... |

47 | Linear-time computation of optimal subgraphs of decomposable graphs - Bern, Lawler, et al. - 1987 |

45 |
Rapid rumor ramification: Approximating the minimum broadcast time
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Citation Context ...ee-bounded minimum cost spanning tree problem and provided an approximation algorithm with performance guarantee (O(log n),O(log n)). The (Degree, Diameter, Spanning tree) problem was studied by Ravi =-=[Ra94]-=- in the context of finding good broadcast networks. There he provides an approximation algorithm for the (Degree, Diameter, Spanning tree) problem with performance guarantee (O(log 2 n),O(log n)) 6 . ... |

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Citation Context ...also extend to Steiner trees in a straightforward way. Our results for treewidth-bounded graphs have an interesting application in the context of finding optimum broadcast schemes. Kortsarz and Peleg =-=[KP92]-=- gave O(log n)-approximation algorithms for the minimum broadcast time problem for series-parallel graphs. Combining our results for the (Degree, Diameter, Spanning tree) for treewidth-bounded graphs ... |

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18 |
Approximating Shallow-light Trees
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(Show Context)
Citation Context ...pproximation scheme for the (Total Cost, Total Cost, Spanning tree) problem. Their approach does not seem to extend to devising approximation algorithms for more general subgraphs considered here. In =-=[KP97]-=-, Kortsarz and Peleg consider the (Diameter, Total Cost, Steiner tree) problem. They provide polynomial time approximation algorithms for this problem with performance guarantees (2,O(log n)) for cons... |

9 | Hunt III, "Many Birds with One Stone: Multi-objective Approximation Algorithms - Ravi, Marathe, et al. - 1993 |

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5 |
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Citation Context ... propagation, transmission and queuing delays. Such multi-criteria network design problems, with separate cost functions for each optimization criterion, also occur naturally in Information Retrieval =-=[BK90]-=- and VLSI designs (see [ZP+94] and the references therein). With the advent of deep micron VLSI designs, the feature size has shrunk to sizes of 0.5 microns and less. As a result, the interconnect res... |

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3 |
The bounded path problem
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(Show Context)
Citation Context ...e, Spanning tree)-bicriteria problem. Similarly, the entry for (Diameter, Diameter, Spanning tree) follows by combining Theorem 6.3 with the known exact algorithms for minimum diameter spanning trees =-=[CG82]-=-; while the result for (Total cost, Total cost, Spanning tree) follows by combining Theorem 6.3 with an exact algorithm to compute a minimum spanning tree [CLR]. Finally, we present a cluster based ap... |

3 | A compendium of NP-optimization problems - Creszenci, Kann - 1998 |

2 | The multi-weighted spanning tree problem - Ganley, Golin, et al. - 1995 |

2 | The constrained spanning tree problem," to appear - Ravi, Goemans - 1996 |

1 |
The constrained spanning tree problem,” to appear
- Ravi, Goemans
- 1996
(Show Context)
Citation Context ...treewidth-bounded graphs. Subsequent work During the time when this paper was under review, important progress has been made in improving some of the results in this paper. Recently, Ravi and Goemans =-=[RG95]-=- have devised a (1,1 + ǫ) approximation scheme for the (Total Cost, Total Cost, Spanning tree) problem. Their approach does not seem to extend to devising approximation algorithms for more general sub... |

1 | Minimum Ratio Spanning - Chandrasekaran - 1977 |