Step Optimal Implementations of Large Single-Writer Registers

We present two wait-free algorithms for simulating an l-bit single-writer register from k-bit single-writer registers, for any k >= 1. Our first algorithm has big-theta(l/k) step complexity for both Read and Write and uses big-theta (4^(l-k)) registers. An interesting feature of the algorithm is that Read operations do not write to shared variables. Our second algorithm has big-theta (l/k + (log n)/k) step complexity for both Read and Write, where n is the number of readers, but uses only big-theta (nl/k + n(log n)/k) registers. Combining both algorithms gives an implementation with big-theta (l/k) step complexity using big-theta (nl/k) space for any 1 <= k < l. We also prove that any implementation with big-O (l/k) step complexity for Read requires big-omega (l/k) step complexity for Write. Since reading l-bits requires at least ceiling(l/k) reads of k-bit registers, our lower bound shows that our implementation is step optimal

Log-space Algorithms for Paths and Matchings in k-trees

Reachability and shortest path problems are NL-complete for general graphs. They are known to be in L for graphs of tree-width 2 [JT07]. However, for graphs of tree-width larger than 2, no bound better than NL is known. In this paper, we improve these bounds for k-trees, where k is a constant. In particular, the main results of our paper are log-space algorithms for reachability in directed k-trees, and for computation of shortest and longest paths in directed acyclic k-trees. Besides the path problems mentioned above, we also consider the problem of deciding whether a k-tree has a perfect macthing (decision version), and if so, finding a perfect match- ing (search version), and prove that these two problems are L-complete. These problems are known to be in P and in RNC for general graphs, and in SPL for planar bipartite graphs [DKR08]. Our results settle the complexity of these problems for the class of k-trees. The results are also applicable for bounded tree-width graphs, when a tree-decomposition is given as input. The technique central to our algorithms is a careful implementation of divide-and-conquer approach in log-space, along with some ideas from [JT07] and [LMR07].Comment: Accepted in STACS 201

COMPARISON OF TWO NOVEL LIST SPHERE DETECTOR ALGORITHMS FOR MIMO-OFDM SYSTEMS

In this paper, the complexity and performance of two novel list sphere detector (LSD) algorithms are studied and evaluated in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system. The LSDs are based on the K-best and the Schnorr-Euchner enumeration (SEE) algorithms. The required list sizes for LSD algorithms are determined for a 2×2 system with 4- quadrature amplitude modulation (QAM), 16-QAM, and 64-QAM. The complexity of the algorithms is compared by studying the number of visited nodes per received symbol vector by the algorithm in computer simulations. The SEE based LSD algorithm is found to be a less complex and a feasible choice for implementation compared to the K-best based LSD algorithm.ElekrobitNokiaTexas InstrumentsFinnish Funding Agency for Technology and InnovationTeke

On Cavity Approximations for Graphical Models

We reformulate the Cavity Approximation (CA), a class of algorithms recently introduced for improving the Bethe approximation estimates of marginals in graphical models. In our new formulation, which allows for the treatment of multivalued variables, a further generalization to factor graphs with arbitrary order of interaction factors is explicitly carried out, and a message passing algorithm that implements the first order correction to the Bethe approximation is described. Furthermore we investigate an implementation of the CA for pairwise interactions. In all cases considered we could confirm that CA[k] with increasing $k$ provides a sequence of approximations of markedly increasing precision. Furthermore in some cases we could also confirm the general expectation that the approximation of order $k$, whose computational complexity is $O(N^{k+1})$ has an error that scales as $1/N^{k+1}$ with the size of the system. We discuss the relation between this approach and some recent developments in the field.Comment: Extension to factor graphs and comments on related work adde