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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Bosek, B. Krawczyk, T. |
| Copyright Year | 2010 |
| Abstract | The main question in the on-line chain partitioning problem is to determine whether there exists an algorithm that partitions on-line posets of width at most $w$ into polynomial number of chains – see Trotter's chapter Partially ordered sets in the Handbook of Combinatorics. So far the best known on-line algorithm of Kier stead used at most $(5^w-1)/4$ chains, on the other hand Szemer\'{e}di proved that any on-line algorithm requires at least $\binom{w+1}{2}$ chains. These results were obtained in the early eighties and since then no progress in the general case has been done. We provide an on-line algorithm that partitions orders of width $w$ into at most $w^{16\log{w}}$ chains. This yields the first sub-exponential upper bound for on-line chain partitioning problem. |
| Starting Page | 347 |
| Ending Page | 354 |
| File Size | 430976 |
| Page Count | 8 |
| File Format | |
| ISBN | 9781424485253 |
| ISSN | 02725428 |
| DOI | 10.1109/FOCS.2010.40 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2010-10-23 |
| Publisher Place | USA |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Games Partitioning algorithms Color Upper bound Computer science Bismuth Polynomials algorithm on-line chain partitioning |
| Content Type | Text |
| Resource Type | Article |
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