1,054 research outputs found
Derandomized Parallel Repetition via Structured PCPs
A PCP is a proof system for NP in which the proof can be checked by a
probabilistic verifier. The verifier is only allowed to read a very small
portion of the proof, and in return is allowed to err with some bounded
probability. The probability that the verifier accepts a false proof is called
the soundness error, and is an important parameter of a PCP system that one
seeks to minimize. Constructing PCPs with sub-constant soundness error and, at
the same time, a minimal number of queries into the proof (namely two) is
especially important due to applications for inapproximability.
In this work we construct such PCP verifiers, i.e., PCPs that make only two
queries and have sub-constant soundness error. Our construction can be viewed
as a combinatorial alternative to the "manifold vs. point" construction, which
is the only construction in the literature for this parameter range. The
"manifold vs. point" PCP is based on a low degree test, while our construction
is based on a direct product test. We also extend our construction to yield a
decodable PCP (dPCP) with the same parameters. By plugging in this dPCP into
the scheme of Dinur and Harsha (FOCS 2009) one gets an alternative construction
of the result of Moshkovitz and Raz (FOCS 2008), namely: a construction of
two-query PCPs with small soundness error and small alphabet size.
Our construction of a PCP is based on extending the derandomized direct
product test of Impagliazzo, Kabanets and Wigderson (STOC 09) to a derandomized
parallel repetition theorem. More accurately, our PCP construction is obtained
in two steps. We first prove a derandomized parallel repetition theorem for
specially structured PCPs. Then, we show that any PCP can be transformed into
one that has the required structure, by embedding it on a de-Bruijn graph
Conditional Hardness for Approximate Coloring
We study the coloring problem: Given a graph G, decide whether
or , where c(G) is the chromatic number of G. We derive conditional
hardness for this problem for any constant . For , our
result is based on Khot's 2-to-1 conjecture [Khot'02]. For , we base our
hardness result on a certain `fish shaped' variant of his conjecture.
We also prove that the problem almost coloring is hard for any constant
\eps>0, assuming Khot's Unique Games conjecture. This is the problem of
deciding for a given graph, between the case where one can 3-color all but a
\eps fraction of the vertices without monochromatic edges, and the case where
the graph contains no independent set of relative size at least \eps.
Our result is based on bounding various generalized noise-stability
quantities using the invariance principle of Mossel et al [MOO'05]
A New Multilayered PCP and the Hardness of Hypergraph Vertex Cover
Given a -uniform hyper-graph, the E-Vertex-Cover problem is to find the
smallest subset of vertices that intersects every hyper-edge. We present a new
multilayered PCP construction that extends the Raz verifier. This enables us to
prove that E-Vertex-Cover is NP-hard to approximate within factor
for any and any . The result is
essentially tight as this problem can be easily approximated within factor .
Our construction makes use of the biased Long-Code and is analyzed using
combinatorial properties of -wise -intersecting families of subsets
Derandomized Graph Product Results using the Low Degree Long Code
In this paper, we address the question of whether the recent derandomization
results obtained by the use of the low-degree long code can be extended to
other product settings. We consider two settings: (1) the graph product results
of Alon, Dinur, Friedgut and Sudakov [GAFA, 2004] and (2) the "majority is
stablest" type of result obtained by Dinur, Mossel and Regev [SICOMP, 2009] and
Dinur and Shinkar [In Proc. APPROX, 2010] while studying the hardness of
approximate graph coloring.
In our first result, we show that there exists a considerably smaller
subgraph of which exhibits the following property (shown for
by Alon et al.): independent sets close in size to the
maximum independent set are well approximated by dictators.
The "majority is stablest" type of result of Dinur et al. and Dinur and
Shinkar shows that if there exist two sets of vertices and in
with very few edges with one endpoint in and another in
, then it must be the case that the two sets and share a single
influential coordinate. In our second result, we show that a similar "majority
is stablest" statement holds good for a considerably smaller subgraph of
. Furthermore using this result, we give a more efficient
reduction from Unique Games to the graph coloring problem, leading to improved
hardness of approximation results for coloring
HUBUNGAN JUMLAH PARITAS DENGAN KEJADIAN RNPERDARAHAN POSTPARTUM DI RUMAH SAKITRNUMUM DAERAH DR. ZAINOEL ABIDINRNBANDA ACEH TAHUN 2011
ABSTRAKPerdarahan postpartum merupakan hilangnya 500 mL atau lebih darah setelah kala tiga persalinan pervaginam selesai, sedangkan 1000 mL atau lebih pada persalinan abdominal. Paritas tinggi merupakan salah satu faktor predisposisi untuk terjadinya perdarahan postpartum. Penelitian ini bertujuan untuk mengetahui hubungan jumlah paritas dengan kejadian perdarahan postpartum di Rumah Sakit Umum Daerah dr. Zainoel Abidin Banda Aceh Tahun 2011. Jenis penelitian ini adalah analitik dengan pendekatan retrospektif yang di lakukan selama bulan April dengan mengambil data rekam medik pada tahun 2011. Sampel diambil secara total sampling. Variabel penelitian adalah jumlah paritas dan perdarahan postpartum. Data dianalisis secara univariat dan biva riat. Hasil penelitian menunjukkan berdasarkan jumlah paritas sebagian penderita perdarahan postpartum multipara sebanyak 21 responden (45,6%). Berdasarkan uji analisis Chi Square menggunakan Fisher Exact Test terdapat hubungan antara jumlah paritas dengan kejadian perdarahan postpartum (p = 0,009). Kesimpulan dari penelitian ini adalah terdapat hubungan antara jumlah paritas dengan kejadian perdarahan postpartum.Kata Kunci: Jumlah Paritas, Perdarahan Postpartu
Toward the KRW Composition Conjecture: Cubic Formula Lower Bounds via Communication Complexity
One of the major challenges of the research in circuit complexity is proving super-polynomial lower bounds for de-Morgan formulas. Karchmer, Raz, and Wigderson suggested to approach this problem by proving that formula complexity behaves "as expected" with respect to the composition of functions f * g. They showed that this conjecture, if proved, would imply super-polynomial formula lower bounds.
The first step toward proving the KRW conjecture was made by Edmonds et al., who proved an analogue of the conjecture for the composition of "universal relations". In this work, we extend the argument of Edmonds et al. further to f * g where f is an arbitrary function and g is the parity function.
While this special case of the KRW conjecture was already proved implicitly in Hastad\u27s work on random restrictions, our proof seems more likely to be generalizable to other cases of the conjecture. In particular, our proof uses an entirely different approach, based on communication complexity technique of Karchmer and Wigderson. In addition, our proof gives a new structural result, which roughly says that the naive way for computing f * g is the only optimal way. Along the way, we obtain a new proof of the state-of-the-art formula lower bound of n^{3-o(1)} due to Hastad
- …