Affine reductions for LPs and SDPs
We define a reduction mechanism for LP and SDP formulations that degrades approximation factors in a controlled fashion. Our reduction mechanism is a minor restriction of classical hardness reductions requiring an additional independence assumption and it allows for reusing many hardness reductions...
Gespeichert in:
Veröffentlicht in: | Mathematical programming 2019-01, Vol.173 (1-2), p.281-312 |
---|---|
Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | We define a reduction mechanism for LP and SDP formulations that degrades approximation factors in a controlled fashion. Our reduction mechanism is a minor restriction of classical hardness reductions requiring an additional independence assumption and it allows for reusing many hardness reductions that have been used to show inapproximability in the context of PCP theorems. As a consequence we establish strong linear programming inapproximability (for LPs with a polynomial number of constraints) for many problems. In particular we obtain a
3
2
-
ε
inapproximability for
answering an open question in Chan et al. (Proceedings of FOCS, pp. 350–359,
2013
,
https://doi.org/10.1109/FOCS.2013.45
) and prove an inapproximability factor of
1
2
+
ε
for bounded degree
. In the case of SDPs, we obtain inapproximability results for these problems relative to the SDP-inapproximability of
MaxCUT
. Moreover, using our reduction framework we are able to reproduce various results for CSPs from Chan et al. (Proceedings of FOCS, pp. 350–359,
2013
,
https://doi.org/10.1109/FOCS.2013.45
) via simple reductions from Max-
2
-XOR. |
---|---|
ISSN: | 0025-5610 1436-4646 |
DOI: | 10.1007/s10107-017-1221-9 |