Who coined the term “empirical entropy”?
I know of Shannon’s work with entropy, but lately I have worked on succinct data structures in which empirical entropy is often used as part of the storage analysis. Empirical entropy (as I understand...
View ArticleDynamic and/or practical succinct data structures for triangulations
Does anybody know of any results on succinct data structures for triangulations that can be constructed efficiently, and preferably also updated efficiently? Does anybody know of practical...
View ArticleSuccinct graphs with ability to perform random walk
Suppose I have an exponentially large graph $G$ ($|G|=2^n$) supplied with an efficient (of size $poly(n)$) randomized circuit $C_G$ implementing the random walk on $G$ – that is, $C_G$ takes a vertex...
View ArticleSuccinct Representation and Communication complexity
Succinct representation is often used to define NEXP or EXP complete problems. For example, when a graph is given as a circuit to compute the existence of edge between vertex $i,j$ for indices of $i,j$...
View ArticleProblem unsolvable in $2^{o(n)}$ on inputs with $n$ bits, assuming ETH?
If we assume the Exponential-Time Hypothesis, then there is no $2^{o(n)}$ algorithm for $n$-variable 3-SAT, and many other natural problems, such as 3-COLORING on graphs with $n$ vertices. Notice...
View ArticleUsing Kolmogorov complexity as input "size"
Say we have a computational problem, e.g. 3-SAT, that has a set of problem instances (possible inputs) $S$. Normally in the analysis of algorithms or computational complexity theory, we have some sets...
View ArticlePractical algorithms for finding small arithmetic circuits
I have a multivariate integer polynomial $f : mathbb{Z}^n to mathbb{Z}$ given as either as a circuit or as a list of monomials. I am interested in practical (though obviously exponential time)...
View ArticleWho coined the term "empirical entropy"?
I know of Shannon’s work with entropy, but lately I have worked on succinct data structures in which empirical entropy is often used as part of the storage analysis. Shannon defined the entropy of the...
View ArticleWhat is the name of this data structure? (hash table with a limit on the...
Denote $[n] triangleq {1,2,ldots,n}$. Assume we would like to have a data structure $S$ which kinda works as a dictionary from $[k]$ to $[v]$, and supports add/remove/update/query functionality,...
View ArticleIs there a counting complexity class for succint problems?
Encoding NP-complete problems succintly often makes them NEXP-complete. I am wondering if counting the number of solutions to such a problem with a succint encoding would be any harder than solving the...
View ArticleUsing Kolmogorov complexity as input “size”
Say we have a computational problem, e.g. 3-SAT, that has a set of problem instances (possible inputs) $S$. Normally in the analysis of algorithms or computational complexity theory, we have some sets...
View Article