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The complexity of unions of disjoint sets
 In Proceedings 24th Symposium on Theoretical Aspects of Computer Science
, 2007
"... This paper is motivated by the open question whether the union of two disjoint NPcomplete sets always is NPcomplete. We discover that such unions retain much of the complexity of their single components. More precisely, they are complete with respect to more general reducibilities. Moreover, we app ..."
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This paper is motivated by the open question whether the union of two disjoint NPcomplete sets always is NPcomplete. We discover that such unions retain much of the complexity of their single components. More precisely, they are complete with respect to more general reducibilities. Moreover, we approach the main question in a more general way: We analyze the scope of the complexity of unions of mequivalent disjoint sets. Under the hypothesis that NE � = coNE, we construct degrees in NP where our main question has a positive answer, i.e., these degrees are closed under unions of disjoint sets. 1
Logspace Mitoticity
, 2007
"... We study the relation of autoreducibility and mitoticity for polylogspace manyone reductions and logspace manyone reductions. For polylogspace these notions coincide, while proving the same for logspace is out of reach. More precisely, we show the following results with respect to nontrivial s ..."
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We study the relation of autoreducibility and mitoticity for polylogspace manyone reductions and logspace manyone reductions. For polylogspace these notions coincide, while proving the same for logspace is out of reach. More precisely, we show the following results with respect to nontrivial sets and manyone reductions. 1. polylogspace autoreducible ⇔ polylogspace mitotic 2. logspace mitotic ⇒ logspace autoreducible ⇒ (log n · log log n)space mitotic 3. relative to an oracle, logspace autoreducible � ⇒ logspace mitotic 1
Mitosis in computational complexity
 IN THEORY AND APPLICATIONS OF MODELS OF COMPUTATION (TAMC
, 2006
"... This expository paper describes some of the results of two recent research papers [GOP + 05,GPSZ05]. The first of these papers proves that every NPcomplete set is manyone autoreducible. The second paper proves that every manyone autoreducible set is manyone mitotic. It follows immediately that ..."
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This expository paper describes some of the results of two recent research papers [GOP + 05,GPSZ05]. The first of these papers proves that every NPcomplete set is manyone autoreducible. The second paper proves that every manyone autoreducible set is manyone mitotic. It follows immediately that every NPcomplete set is manyone mitotic. Hence, we have the compelling result that every NPcomplete set A splits into two NPcomplete sets A1 and A2.
unknown title
, 2006
"... We show the following results regarding complete sets. • NPcomplete sets and PSPACEcomplete sets are polynomialtime manyone autoreducible. • Complete sets of any level of PH, MODPH, or the Boolean hierarchy over NP are polynomialtime manyone autoreducible. • EXPcomplete sets are polynomialt ..."
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We show the following results regarding complete sets. • NPcomplete sets and PSPACEcomplete sets are polynomialtime manyone autoreducible. • Complete sets of any level of PH, MODPH, or the Boolean hierarchy over NP are polynomialtime manyone autoreducible. • EXPcomplete sets are polynomialtime manyone mitotic. • If there is a tally language in NP ∩ coNP−P, then, for every > 0, NPcomplete sets are not 2n(1+)immune. These results solve several of the open questions raised by Buhrman and Torenvliet in their 1994 survey paper on the structure of complete sets. 1
Research Statement
"... My research interests are algorithms for massive data, data structures, and approximation/online algorithms. ..."
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My research interests are algorithms for massive data, data structures, and approximation/online algorithms.
The Fault Tolerance of NPHard Problems
"... Abstract. We study the effects of faulty data on NPhard sets. We consider hard sets for several polynomial time reductions, add corrupt data and then analyze whether the resulting sets are still hard for NP. We explain that our results are related to a weakened deterministic variant of the notion o ..."
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Abstract. We study the effects of faulty data on NPhard sets. We consider hard sets for several polynomial time reductions, add corrupt data and then analyze whether the resulting sets are still hard for NP. We explain that our results are related to a weakened deterministic variant of the notion of program selfcorrection by Blum, Luby, and Rubinfeld. Among other results, we use the LeftSet technique to prove that mcomplete sets for NP are nonadaptively weakly deterministically selfcorrectable while bttcomplete sets for NP are weakly deterministically selfcorrectable. Our results can also be applied to the study of Yesha’s pcloseness. In particular, we strengthen a result by Ogiwara and Fu. 1