## Exhaustive search, combinatorial optimization and enumeration: Exploring the potential of raw computing power (2000)

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Venue: | In SOFSEM 2000, number 1963 in LNCS |

Citations: | 4 - 1 self |

### BibTeX

@INPROCEEDINGS{Nievergelt00exhaustivesearch,,

author = {Jürg Nievergelt},

title = {Exhaustive search, combinatorial optimization and enumeration: Exploring the potential of raw computing power},

booktitle = {In SOFSEM 2000, number 1963 in LNCS},

year = {2000},

pages = {18--35},

publisher = {Springer}

}

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### Abstract

Abstract. For half a century since computers came into existence, the goal of finding elegant and efficient algorithms to solve “simple ” (welldefined and well-structured) problems has dominated algorithm design. Over the same time period, both processingand storage capacity of computers have increased by roughly a factor of a million. The next few decades may well give us a similar rate of growth in raw computing power, due to various factors such as continuingminiaturization, parallel and distributed computing. If a quantitative change of orders of magnitude leads to qualitative advances, where will the latter take place? Only empirical research can answer this question. Asymptotic complexity theory has emerged as a surprisingly effective tool for predictingrun times of polynomial-time algorithms. For NPhard problems, on the other hand, it yields overly pessimistic bounds. It asserts the non-existence of algorithms that are efficient across an entire problem class, but ignores the fact that many instances, perhaps

### Citations

152 | Reverse search for enumeration
- Avis, Fukuda
- 1996
(Show Context)
Citation Context ...ves, such as Erathostenes’ prime number sieve. 5 Reverse Search The more information is known a priori about a graph, the less book-keeping data needs to be kept during the traversal. Avis and Fukuda =-=[2]-=- presentaset of conditions that enable graph traversal without auxiliary data structures such as stacks, queues, or node marks. The amount of memory used for book-keeping is constant, i. e. independen... |

19 | Harnessing computational resources for efficient exhaustive search
- Gasser
- 1995
(Show Context)
Citation Context ... far has resisted most efforts at systematization. Several recent Ph. D. thesis’ have attempted to extract general rules of how to attack compute-intensive problem instances from massive case studies =-=[4,3,7]-=-. Data allocation on disk is a central issue, trying to achieve some locality of data access despite the combinatorial chaos typical of such problems. In problems involving retrograde analysis (e. g. ... |

18 |
The solution of the four-color-map problem
- Appel, Haken
- 1977
(Show Context)
Citation Context ...as entry points into the pertinent literature: – the continuing race for large primes, for example Mersenne primes of form 2 p − 1, – the landmark proof of the “four-color theorem” by Appel and Haken =-=[1]-=-, – more recent work in Ramsey theory or cellular-automata [5]. For such cases we need a complexity measure that applies to problem instances, rather than to over-sized problem classes. Counting indiv... |

17 |
The machine tools of combinatorics
- Lehmer
- 1964
(Show Context)
Citation Context ... the team computation + conjecture, and Derrick Lehmer was a pioneer in using search algorithms such as sieves or backtrack in pursuit of theorems whose proof requires a massive amount of computation =-=[6]-=-. We make no attempt to survey the many results obtained thanks to computer-based mathematics, but merely recall a few as entry points into the pertinent literature: – the continuing race for large pr... |

16 |
The Death of Proof
- HORGAN
- 1993
(Show Context)
Citation Context ...g race for large primes, for example Mersenne primes of form 2 p − 1, – the landmark proof of the “four-color theorem” by Appel and Haken [1], – more recent work in Ramsey theory or cellular-automata =-=[5]-=-. For such cases we need a complexity measure that applies to problem instances, rather than to over-sized problem classes. Counting individual operations and measuring the running time of numerous pr... |

9 | ZRAM: A library of parallel search algorithms and its use in enumeration and combinatorial optimization
- Marzetta
- 1998
(Show Context)
Citation Context ... far has resisted most efforts at systematization. Several recent Ph. D. thesis’ have attempted to extract general rules of how to attack compute-intensive problem instances from massive case studies =-=[4,3,7]-=-. Data allocation on disk is a central issue, trying to achieve some locality of data access despite the combinatorial chaos typical of such problems. In problems involving retrograde analysis (e. g. ... |

7 | All the needles in a haystack: Can exhaustive search overcome combinatorial chaos?, Invited paper
- Nievergelt, Gasser, et al.
- 1995
(Show Context)
Citation Context ... may run for months and generatesPotential of Raw Computer Power 35 data bases of many GigaBytes, independent verification of the result is a necessity. Some of the experience gained is summarized in =-=[10]-=-. Attacking computationally hard problem instances has so far never been near the center of algorithm research. It has rather been relegated to the niche of puzzles and games, pursued by a relatively ... |

5 |
Retrograde analysis of certain endgames
- Thomson
- 1986
(Show Context)
Citation Context .... Data allocation on disk is a central issue, trying to achieve some locality of data access despite the combinatorial chaos typical of such problems. In problems involving retrograde analysis (e. g. =-=[11,13]-=-), where every state (e. g. a board position in a game) in the state space is assigned a unique index in a huge array, construction of a suitable index function is critical. Since such computations ma... |

2 |
Forecasting: An impossible necessity
- Maurer
- 2000
(Show Context)
Citation Context ...ed were generally not foreseen. Evidence for this is provided by quotes from famous pioneers, such as DEC founder Ken Olsen’s dictum “there is no reason why anyone would want a computer in his home” (=-=[9]-=- is an amusing collection of predictions). If past predictions fell short of reality, we cannot assume that our gaze into the crystal ball will be any clearer today. We do not know what problems can b... |

2 |
Exhaustive and heuristic retrograde analysis of the KPPKP endgame
- Wirth, Nievergelt
- 1999
(Show Context)
Citation Context .... Data allocation on disk is a central issue, trying to achieve some locality of data access despite the combinatorial chaos typical of such problems. In problems involving retrograde analysis (e. g. =-=[11,13]-=-), where every state (e. g. a board position in a game) in the state space is assigned a unique index in a huge array, construction of a suitable index function is critical. Since such computations ma... |

1 |
Solving hard combinatorial optimization problems in parallel. Two case studies
- Bruengger
- 1997
(Show Context)
Citation Context ... far has resisted most efforts at systematization. Several recent Ph. D. thesis’ have attempted to extract general rules of how to attack compute-intensive problem instances from massive case studies =-=[4,3,7]-=-. Data allocation on disk is a central issue, trying to achieve some locality of data access despite the combinatorial chaos typical of such problems. In problems involving retrograde analysis (e. g. ... |

1 |
Enumerating the k best plane spanningtrees
- Marzetta, Nievergelt
- 2000
(Show Context)
Citation Context ...plane spanning trees over a given set of points in the plane, i. e. those trees constructed with straight line segments in such a manner that no two edgessPotential of Raw Computer Power 31 intersect =-=[8]-=-. [2] present an algorithm for enumerating all plane spanning trees, in some uncontrolled order that results from the arbitrary labeling of points. We attack this same problem under the additional con... |

1 |
The physical basis of digital computing
- Houten
- 2000
(Show Context)
Citation Context ...f Raw Computer Power 19 the same rate observed over the past 3 decades, of doubling in any period of 1 to 2 years. An up-to-date summary of possibilities and limitations of technology can be found in =-=[12]-=-. What does it mean for a discipline to be technology-driven? Whatarethe implications? Consider the converse: disciplines that are demand-driven rather than technology-driven. In the 60s the US stated... |