On Symmetric Signatures in Holographic Algorithms
In holographic algorithms, symmetric signatures have been particularly useful. We give a complete characterization of these symmetric signatures over all bases of size 1. These improve previous results by Cai and Choudhary (ICALP 2006, vol. 4051, pp. ...
Small Space Representations for Metric Min-sum k-Clustering and Their Applications
The min-sum k -clustering problem is to partition a metric space (P,d) into k clusters C 1,…,C k ⊆P such that $\sum_{i=1}^{k}\sum_{p,q\in C_{i}}d(p,q)$is minimized. We show the first efficient construction of a coreset for this problem. Our coreset ...
Sturmian Trees
We consider Sturmian trees as a natural generalization of Sturmian words. A Sturmian tree is a tree having n+1 distinct subtrees of height n for each n. As for the case of words, Sturmian trees are irrational trees of minimal complexity.
We prove that a ...
A Search Algorithm for Subshift Attractors of Cellular Automata
We describe a heuristic algorithm which searches for spreading clopen sets of a cellular automaton. Then the algorithms searches for the corresponding subshift attractors (which are omega-limits of spreading sets found) as forward images of joins of ...
Arithmetizing Classes Around $\textsf{NC}$1 and $\textsf{L}$
The parallel complexity class $\textsf{NC}$1 has many equivalent models such as polynomial size formulae and bounded width branching programs. Caussinus et al. (J. Comput. Syst. Sci. 57:200–212, 1992) considered arithmetizations of two of these classes, ...
Why Almost All k-Colorable Graphs Are Easy to Color
Coloring a k-colorable graph using k colors (k≥3) is a notoriously hard problem. Considering average case analysis allows for better results. In this work we consider the uniform distribution over k-colorable graphs with n vertices and exactly cn edges, ...
A Cubic Kernel for Feedback Vertex Set and Loop Cutset
The Feedback Vertex Set problem on unweighted, undirected graphs is considered. Improving upon a result by Burrage et al. (Proceedings 2nd International Workshop on Parameterized and Exact Computation, pp. 192–202, 2006), we show that this problem has a ...
Kolmogorov-Loveland Stochasticity and Kolmogorov Complexity
Merkle et al. (Ann. Pure Appl. Logic 138(1–3):183–210, 2006) showed that all Kolmogorov-Loveland stochastic infinite binary sequences have constructive Hausdorff dimension 1. In this paper, we go even further, showing that from an infinite sequence of ...
