Boxicity of a graph G(V, E), denoted by box(G), is the minimum integer k such that G can be represented as the intersection graph of axis parallel boxes in R. The problem of computing boxicity is inapproximable even for graph classes like bipartite, co-bipartite and split graphs within O(n)-factor, for any ǫ > 0 in polynomial time unless NP = ZPP . We give FPT approximation algorithms for compu...

We study the problem of finding a longest common increasing subsequence (LCIS) of multiple sequences of numbers. The LCIS problem is a fundamental issue in various application areas, including the whole genome alignment. In this paper we give an efficient algorithm to find the LCIS of two sequences in O(min(r log `, n`+r) log log n+Sort(n)) time where n is the length of each sequence and r is t...

We review recently developed theory for the Minimum Description Length principle, penalized likelihood and its statistical risk. An information theoretic condition on a penalty pen(f) yields the conclusion that the optimizer of the penalized log likelihood criterion log 1/likelihood(f) + pen(f) has risk not more than the index of resolvability, corresponding to the accuracy of the optimizer of ...

ylabpos <exp(pretty(log(unlist(jobs[,-7])), 100)) ylabels <paste(round(ylabpos),"\n(", log(ylabpos), ")", sep="") ## Create a date object ’startofmonth’; use this instead of ’Date’ startofmonth <seq(from=as.Date("1Jan1995", format="%d%b%Y"), by="1 month", length=24) atdates <seq(from=as.Date("1Jan1995", format="%d%b%Y"), by="6 month", length=4) datelabs <format(atdates, "%b%y") xyplot(BC+Albert...

We review recently developed theory for the Minimum Description Length principle, penalized likelihood and its statistical risk. An information theoretic condition on a penalty pen(f) yields the conclusion that the optimizer of the penalized log likelihood criterion log 1/likelihood(f) + pen(f) has risk not more than the index of resolvability, corresponding to the accuracy of the optimizer of ...

In this paper, we build morphological chains for agglutinative languages by using a log linear model for the morphological segmentation task. The model is based on the unsupervised morphological segmentation system called MorphoChains [1]. We extend MorphoChains log linear model by expanding the candidate space recursively to cover more split points for agglutinative languages such as Turkish, ...

A (k, ε)-non-malleable extractor is a function nmExt : {0, 1}×{0, 1} → {0, 1} that takes two inputs, a weak source X ∼ {0, 1} of min-entropy k and an independent uniform seed s ∈ {0, 1}, and outputs a bit nmExt(X, s) that is ε-close to uniform, even given the seed s and the value nmExt(X, s′) for an adversarially chosen seed s′ 6= s. Dodis and Wichs (STOC 2009) showed the existence of (k, ε)-no...

We explore relations between various variational problems for graphs: among the functionals considered are Euler characteristic χ(G), characteristic length μ(G), mean clustering ν(G), inductive dimension ι(G), edge density (G), scale measure σ(G), Hilbert action η(G) and spectral complexity ξ(G). A new insight in this note is that the local cluster coefficient C(x) in a finite simple graph can ...

This paper gives approximation algorithms for solving the following motion planning problem: Given a set of polyhedral obstacles and points s and t, find a shortest path from s to t that avoids the obstacles. The paths found by the algorithms are piecewise linear, and the length of a path is the sum of the lengths of the line segments making up the path. Approximation algorithms will be given f...