Space--Time Tradeoffs for Subset Sum: An Improved Worst Case Algorithm

The technique of Schroeppel and Shamir (SICOMP, 1981) has long been the most efficient way to trade space against time for the SUBSET SUM problem. In the random-instance setting, however, improved tradeoffs exist. In particular, the recently discovered dissection method of Dinur et al. (CRYPTO 2012) yields a significantly improved space--time tradeoff curve for instances with strong randomness properties. Our main result is that these strong randomness assumptions can be removed, obtaining the same space--time tradeoffs in the worst case. We also show that for small space usage the dissection algorithm can be almost fully parallelized. Our strategy for dealing with arbitrary instances is to instead inject the randomness into the dissection process itself by working over a carefully selected but random composite modulus, and to introduce explicit space--time controls into the algorithm by means of a "bailout mechanism"

A PCP Characterization of AM

We introduce a 2-round stochastic constraint-satisfaction problem, and show that its approximation version is complete for (the promise version of) the complexity class AM. This gives a `PCP characterization' of AM analogous to the PCP Theorem for NP. Similar characterizations have been given for higher levels of the Polynomial Hierarchy, and for PSPACE; however, we suggest that the result for AM might be of particular significance for attempts to derandomize this class. To test this notion, we pose some `Randomized Optimization Hypotheses' related to our stochastic CSPs that (in light of our result) would imply collapse results for AM. Unfortunately, the hypotheses appear over-strong, and we present evidence against them. In the process we show that, if some language in NP is hard-on-average against circuits of size 2^{Omega(n)}, then there exist hard-on-average optimization problems of a particularly elegant form. All our proofs use a powerful form of PCPs known as Probabilistically Checkable Proofs of Proximity, and demonstrate their versatility. We also use known results on randomness-efficient soundness- and hardness-amplification. In particular, we make essential use of the Impagliazzo-Wigderson generator; our analysis relies on a recent Chernoff-type theorem for expander walks.Comment: 18 page

Random Unitaries Give Quantum Expanders

We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. We consider Hermitian and non-Hermitian cases, and we provide asymptotically tight bounds in the Hermitian case on the typical value of the second largest eigenvalue. The key idea is the use of Schwinger-Dyson equations from lattice gauge theory to efficiently compute averages over the unitary group.Comment: 14 pages, 1 figur

PENGARUH PEMBERIAN PUPUK KANDANG KAMBING DAN NITROGEN TERHADAP PERTUMBUHAN DAN PRODUKSI TANAMAN KACANG KEDELAI (Glycine max L).

Tanaman kedelai merupakan sumber protein nabati utama bagi sebagian besar penduduk Indonesia. Pupuk kandang kambing dan pupuk NPK yang mengandung nitrogen sangat efektif untuk memberikan nitrogen terhadap tanaman khusunya tanaman kedelai. Adapun tujuan dari penelitian ini untuk mengetahui “Pengaruh Pemberian Pupuk Kandang Kambing Dan Nitrogen Terhadap Pertumbuhan Dan Produksi Tanaman Kacang Kedalai, Penelitian ini disusun berdasarkan Rancangan Acak Kelompok (RAK) Faktorial dengan 2 faktor perlakuan dan 3 ulangan. Faktor pertama pemberian pupuk kandang kambing dengan 3 taraf yaitu : K0 =0 kg/plot, K1 = 1 kg/plot, K2 2 kg/plot. Faktor kedua adalah pemberian pupuk NPK dengan 4 taraf yaitu N0 = 0 g/plot, N1 = 15, g/plot, N2 = 30 g/plot, N3 = 45 g/plot.  Hasil penelitian pemberian pupuk kandang kambing menunjukkan berpengaruh tidak nyata terhadap pertumbuhan dan produksi kacang kedalai. Pemberian pupuk NPK berpengaruh nyata terhadap pertumbuhan dan produksi tanaman kacang kedelai, dengan perlakuan terbaik pada dosis 45 g/plot (N3) mengasilkan tanaman tertinggi 52,39 cm, jumlah cabang 10,44 cabang, jumlah daun 11,44 helai dan 75,56 buah. Interaksi antara antara pengaplikasian pupuk kandang kambing dan Nitrogen terhadap pertumbahan dan produksi tanaman kedalai menunjukan berpengaruh nyata terhadap jumlah cabang, dengan perlakuan terbaik pada dosis 2 kg/plot dan 45 g/plot (K2N3) menghasilkan cabang terbanyak 11,00 cabang. Kata kunci: Kedelai, NPK, Nitroge

Approximately coloring graphs without long induced paths

It is an open problem whether the 3-coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on $t$ vertices, for fixed $t$. We propose an algorithm that, given a 3-colorable graph without an induced path on $t$ vertices, computes a coloring with $\max\{5,2\lceil{\frac{t-1}{2}}\rceil-2\}$ many colors. If the input graph is triangle-free, we only need $\max\{4,\lceil{\frac{t-1}{2}}\rceil+1\}$ many colors. The running time of our algorithm is $O((3^{t-2}+t^2)m+n)$ if the input graph has $n$ vertices and $m$ edges

Dynamic hierarchies in temporal directed networks

The outcome of interactions in many real-world systems can be often explained by a hierarchy between the participants. Discovering hierarchy from a given directed network can be formulated as follows: partition vertices into levels such that, ideally, there are only forward edges, that is, edges from upper levels to lower levels. In practice, the ideal case is impossible, so instead we minimize some penalty function on the backward edges. One practical option for such a penalty is agony, where the penalty depends on the severity of the violation. In this paper we extend the definition of agony to temporal networks. In this setup we are given a directed network with time stamped edges, and we allow the rank assignment to vary over time. We propose 2 strategies for controlling the variation of individual ranks. In our first variant, we penalize the fluctuation of the rankings over time by adding a penalty directly to the optimization function. In our second variant we allow the rank change at most once. We show that the first variant can be solved exactly in polynomial time while the second variant is NP-hard, and in fact inapproximable. However, we develop an iterative method, where we first fix the change point and optimize the ranks, and then fix the ranks and optimize the change points, and reiterate until convergence. We show empirically that the algorithms are reasonably fast in practice, and that the obtained rankings are sensible

A Hypergraph Dictatorship Test with Perfect Completeness

A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based \PCP construction. Such a test has oracle access to a collection of functions and determines whether all the functions are the same dictatorship, or all their low degree influences are $o(1).$ Their test makes $q\geq3$ queries and has amortized query complexity $1+O(\frac{\log q}{q})$ but has an inherent loss of perfect completeness. In this paper we give an adaptive hypergraph dictatorship test that achieves both perfect completeness and amortized query complexity $1+O(\frac{\log q}{q})$.Comment: Some minor correction

On Coloring Resilient Graphs

We introduce a new notion of resilience for constraint satisfaction problems, with the goal of more precisely determining the boundary between NP-hardness and the existence of efficient algorithms for resilient instances. In particular, we study $r$-resiliently $k$-colorable graphs, which are those $k$-colorable graphs that remain $k$-colorable even after the addition of any $r$ new edges. We prove lower bounds on the NP-hardness of coloring resiliently colorable graphs, and provide an algorithm that colors sufficiently resilient graphs. We also analyze the corresponding notion of resilience for $k$-SAT. This notion of resilience suggests an array of open questions for graph coloring and other combinatorial problems.Comment: Appearing in MFCS 201

Peer-to-Peer Secure Multi-Party Numerical Computation Facing Malicious Adversaries

We propose an efficient framework for enabling secure multi-party numerical computations in a Peer-to-Peer network. This problem arises in a range of applications such as collaborative filtering, distributed computation of trust and reputation, monitoring and other tasks, where the computing nodes is expected to preserve the privacy of their inputs while performing a joint computation of a certain function. Although there is a rich literature in the field of distributed systems security concerning secure multi-party computation, in practice it is hard to deploy those methods in very large scale Peer-to-Peer networks. In this work, we try to bridge the gap between theoretical algorithms in the security domain, and a practical Peer-to-Peer deployment. We consider two security models. The first is the semi-honest model where peers correctly follow the protocol, but try to reveal private information. We provide three possible schemes for secure multi-party numerical computation for this model and identify a single light-weight scheme which outperforms the others. Using extensive simulation results over real Internet topologies, we demonstrate that our scheme is scalable to very large networks, with up to millions of nodes. The second model we consider is the malicious peers model, where peers can behave arbitrarily, deliberately trying to affect the results of the computation as well as compromising the privacy of other peers. For this model we provide a fourth scheme to defend the execution of the computation against the malicious peers. The proposed scheme has a higher complexity relative to the semi-honest model. Overall, we provide the Peer-to-Peer network designer a set of tools to choose from, based on the desired level of security.Comment: Submitted to Peer-to-Peer Networking and Applications Journal (PPNA) 200

KLEIN: A New Family of Lightweight Block Ciphers

Resource-efficient cryptographic primitives become fundamental for realizing both security and efficiency in embedded systems like RFID tags and sensor nodes. Among those primitives, lightweight block cipher plays a major role as a building block for security protocols. In this paper, we describe a new family of lightweight block ciphers named KLEIN, which is designed for resource-constrained devices such as wireless sensors and RFID tags. Compared to the related proposals, KLEIN has advantage in the software performance on legacy sensor platforms, while in the same time its hardware implementation can also be compact