Alternation-Trading Proofs, Linear Programming, and Lower Bounds

A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT, Majority-of-Majority-SAT, and Tautologies, to name a few. The proofs of these lower bounds follow a certain proof-by-contradiction strategy that we call alternation-trading. An important open problem is to determine how powerful such proofs can possibly be. We propose a methodology for studying these proofs that makes them amenable to both formal analysis and automated theorem proving. We prove that the search for better lower bounds can often be turned into a problem of solving a large series of linear programming instances. Implementing a small-scale theorem prover based on this result, we extract new human-readable time lower bounds for several problems. This framework can also be used to prove concrete limitations on the current techniques.Comment: To appear in STACS 2010, 12 page

Simple and Efficient Fully-Functional Succinct Trees

The fully-functional succinct tree representation of Navarro and Sadakane (ACM Transactions on Algorithms, 2014) supports a large number of operations in constant time using $2n+o(n)$ bits. However, the full idea is hard to implement. Only a simplified version with $O(\log n)$ operation time has been implemented and shown to be practical and competitive. We describe a new variant of the original idea that is much simpler to implement and has worst-case time $O(\log\log n)$ for the operations. An implementation based on this version is experimentally shown to be superior to existing implementations

Design of multimedia processor based on metric computation

Media-processing applications, such as signal processing, 2D and 3D graphics rendering, and image compression, are the dominant workloads in many embedded systems today. The real-time constraints of those media applications have taxing demands on today's processor performances with low cost, low power and reduced design delay. To satisfy those challenges, a fast and efficient strategy consists in upgrading a low cost general purpose processor core. This approach is based on the personalization of a general RISC processor core according the target multimedia application requirements. Thus, if the extra cost is justified, the general purpose processor GPP core can be enforced with instruction level coprocessors, coarse grain dedicated hardware, ad hoc memories or new GPP cores. In this way the final design solution is tailored to the application requirements. The proposed approach is based on three main steps: the first one is the analysis of the targeted application using efficient metrics. The second step is the selection of the appropriate architecture template according to the first step results and recommendations. The third step is the architecture generation. This approach is experimented using various image and video algorithms showing its feasibility

New Bounds for the Garden-Hose Model

We show new results about the garden-hose model. Our main results include improved lower bounds based on non-deterministic communication complexity (leading to the previously unknown $\Theta(n)$ bounds for Inner Product mod 2 and Disjointness), as well as an $O(n\cdot \log^3 n)$ upper bound for the Distributed Majority function (previously conjectured to have quadratic complexity). We show an efficient simulation of formulae made of AND, OR, XOR gates in the garden-hose model, which implies that lower bounds on the garden-hose complexity $GH(f)$ of the order $\Omega(n^{2+\epsilon})$ will be hard to obtain for explicit functions. Furthermore we study a time-bounded variant of the model, in which even modest savings in time can lead to exponential lower bounds on the size of garden-hose protocols.Comment: In FSTTCS 201

Benchmarking Summarizability Processing in XML Warehouses with Complex Hierarchies

Business Intelligence plays an important role in decision making. Based on data warehouses and Online Analytical Processing, a business intelligence tool can be used to analyze complex data. Still, summarizability issues in data warehouses cause ineffective analyses that may become critical problems to businesses. To settle this issue, many researchers have studied and proposed various solutions, both in relational and XML data warehouses. However, they find difficulty in evaluating the performance of their proposals since the available benchmarks lack complex hierarchies. In order to contribute to summarizability analysis, this paper proposes an extension to the XML warehouse benchmark (XWeB) with complex hierarchies. The benchmark enables us to generate XML data warehouses with scalable complex hierarchies as well as summarizability processing. We experimentally demonstrated that complex hierarchies can definitely be included into a benchmark dataset, and that our benchmark is able to compare two alternative approaches dealing with summarizability issues.Comment: 15th International Workshop on Data Warehousing and OLAP (DOLAP 2012), Maui : United States (2012

Narrow Proofs May Be Maximally Long

We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size n^Omega(w). This shows that the simple counting argument that any formula refutable in width w must have a proof in size n^O(w) is essentially tight. Moreover, our lower bound generalizes to polynomial calculus resolution (PCR) and Sherali-Adams, implying that the corresponding size upper bounds in terms of degree and rank are tight as well. Our results do not extend all the way to Lasserre, however, where the formulas we study have proofs of constant rank and size polynomial in both n and w