Realizable Paths and the NL vs L Problem

Realizable paths and the NL vs L problem

Adding Relations in Multi-levels to an Organization Structure of a Complete Binary Tree Maximizing Total Shortening Path Length

This paper proposes a model of adding relations in multi-levels to an organization structure which is a complete binary tree such that the communication of information between every member in the organization becomes the most efficient. When edges between every pair of nodes with the same depth in L (L = 1, 2, · · · , H ) levels are added to a complete binary tree of height H, an optimal set of...

Computing Shortest Paths in Series-Parallel Graphs in Logarithmic Space

Series-parallel graphs, which are built by repeatedly applying series or parallel composition operations to paths, play an important role in computer science as they model the flow of information in many types of programs. For directed series-parallel graphs, we study the problem of finding a shortest path between two given vertices. Our main result is that we can find such a path in logarithmi...

Isolation, Matching, and Counting Uniform and Nonuniform Upper Bounds

We show that the perfect matching problem is in the complexity class SPL (in the nonuniform setting). This provides a better upper bound on the complexity of the matching problem, as well as providing motivation for studying the complexity class SPL. Using similar techniques, we show that counting the number of accepting paths of a nondeterministic logspace machine can be done in NL/poly, if th...

Some results on the symmetric doubly stochastic inverse eigenvalue problem

‎The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$‎, ‎to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$‎. ‎If there exists an $ntimes n$ symmetric doubly stochastic ...