We present an algorithm that computes the Lempel-Ziv decomposition in O(n(log σ+log log n)) time and n log σ+ǫn bits of space, where ǫ is a constant rational parameter, n is the length of the input string, and σ is the alphabet size. The n log σ bits in the space bound are for the input string itself which is treated as read-only.

We explicitly compute the 2-group of self-equivalences and (homotopy classes of) chain homotopies between them for any split chain complex A• in an arbitrary K-linear abelian category (K any commutative ring with unit). In particular, it is shown that it is a split 2-group whose equivalence class depends only on the homology of A•, and that it is equivalent to the trivial 2-group when A• is a s...

We give a construction of quantum LDPC codes dimension $\Theta(\log N)$ and distance $\Theta(N/\log as the code length $N\to\infty$. Using product chain complexes this also provides family $\Omega(N^{1-\alpha/2}/\log $\Omega(N^\alpha \log N)$, where $0 \le \alpha < 1$. introduce study new operation called lifted product, which naturally generalizes operations for complexes. Moreover, simple byp...

An improved method for deformable shape-based image segmentation is described. Image regions are merged together and/or split apart, based on their agreement with an a priori distribution on the global deformation parameters for a shape template. Perceptually-motivated criteria are used to determine where/how to split regions, based on the local shape properties of the region group’s bounding c...

The stationary set splitting game is a game of perfect information of length ω1 between two players, unsplit and split, in which unsplit chooses stationarily many countable ordinals and split tries to continuously divide them into two stationary pieces. We show that it is possible in ZFC to force a winning strategy for either player, or for neither. This gives a new counterexample to Σ2 maximal...

An optimal O(log log n) time CRCW-PRAM algorithm for computing all period lengths of a string is presented. Previous parallel algorithms compute the period only if it is shorter than half of the length of the string. The algorithm can be used to nd all initial palindromes of a string in the same time and processor bounds. Both algorithms are the fastest possible over a general alphabet. We deri...

We introduce a tree-based method to find short Double-Base chains. As compared to the classical greedy approach, this new method is not only simpler to implement and faster, experimentally it also returns shorter chains on average. The complexity analysis shows that the average length of a chain returned by this tree-based approach is log2 n 4.6419 · This tends to suggest that the average lengt...