Polynomial Learning of Distribution Families
The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major progress, the general ...
Multicommodity Flows and Cuts in Polymatroidal Networks
We consider multicommodity flow and cut problems in polymatroidal networks where there are submodular capacity constraints on the edges incident to a node. Polymatroidal networks were introduced by Lawler and Martel [Math. Oper. Res., 7 (1982), pp. 334--347]...
Approximating Minimization Diagrams and Generalized Proximity Search
We investigate the classes of functions whose minimization diagrams can be approximated efficiently in $\mathbb{R}^d$. We present a general framework and a data-structure that can be used to approximate the minimization diagram of such functions. The ...
Cutting Corners Cheaply, or How to Remove Steiner Points
Our main result is that the Steiner point removal (SPR) problem can always be solved with polylogarithmic distortion, which answers in the affirmative a question posed by Chan, Xia, Konjevod, and Richa in 2006. Specifically, we prove that for every edge-...
Steiner Shallow-Light Trees Are Exponentially Lighter than Spanning Ones
For a pair of parameters $\alpha,\beta \ge 1$, a spanning tree $T$ of a weighted undirected $n$-vertex graph $G = (V,E,w)$ is called an $(\alpha,\beta)$-shallow-light tree (shortly, $(\alpha,\beta)$-SLT) of $G$ with respect to a designated vertex $rt \in V$ ...
Operator Precedence Languages: Their Automata-Theoretic and Logic Characterization
Operator precedence languages were introduced half a century ago by Robert Floyd to support deterministic and efficient parsing of context-free languages. Recently, we renewed our interest in this class of languages thanks to a few distinguishing properties ...
Counting List Matrix Partitions of Graphs
Given a symmetric $D\times D$ matrix $M$ over \0,1,*\, a list $M$-partition of a graph $G$ is a partition of the vertices of $G$ into $D$ parts which are associated with the rows of $M$. The part of each vertex is chosen from a given list in such a way that no ...
Space Complexity in Polynomial Calculus
During the last 10 to 15 years, an active line of research in proof complexity has been to study space complexity and time-space trade-offs for proofs. Besides being a natural complexity measure of intrinsic interest, space is also an important concern in ...
On the Number of Iterations for Dantzig--Wolfe Optimization and Packing-Covering Approximation Algorithms
We give a lower bound on the iteration complexity of a natural class of Lagrangian-relaxation algorithms for approximately solving packing/covering linear programs. We show that, given an input with $m$ random 0/1-constraints on $n$ variables, with high ...