NDLI: Reducibility among Fractional Stability Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Rajaraman, Rajmohan Sundaram, Ravi Teng, Shang-Hua Poplawski, Laura J. Kintali, Shiva
Copyright Year	2013
Abstract	We resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be ${\bf{PPAD}}$-complete, along with the domains of practical significance: fractional stable paths problem (FSPP)---Internet routing; core of balanced games---economics and game theory; Scarf's lemma---combinatorics; hypergraph matching---social choice and preference systems; fractional bounded budget connection games (FBBC)---social networks; and strong fractional kernel---graph theory. In fact, we show that no fully polynomial-time approximation schemes exist (unless ${\bf{PPAD}}$ is in ${\bf{FP}}$). This paper is entirely a series of reductions that build in nontrivial ways on the framework established in previous work. In the course of deriving these reductions, we created two new concepts---preference games and personalized equilibria. The entire set of new reductions can be presented as a lattice with the above problems sandwiched between preference games (at the easy end) and personalized equilibria (at the hard end). Our completeness results extend to natural approximate versions of most of these problems.
Starting Page	2063
Ending Page	2113
Page Count	51
File Format	PDF
ISSN	00975397
DOI	10.1137/120874655
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	6 (Special Section on the Fiftieth Annual IEEE Symposium on Foundations of Computer Science (FOCS 2009))
Volume Number	42
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-11-05
Access Restriction	Subscribed
Subject Keyword	Computational difficulty of problems complexity Noncooperative games game theory network connection games Nash equilibrium Cooperative games Complexity classes social choice core economics PPAD-completeness kernels stable paths problem preference systems Scarf's lemma
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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