Shimon Even

On the Complexity of Timetable and Multicommodity Flow Problems

A very primitive version of Gotlieb’s timetable problem is shown to be NP-complete, and therefore all the common timetable problems are NP-complete. A polynomial time algorithm, in case all teachers are binary, is shown. The theorem that a meeting function always exists if all teachers and classes have no time constraints is proved. The multicommodity integral flow problem is shown to be NP-complete even if the number of commodities is two. This is true both in the directed and undirected cases.

Network Flow and Testing Graph Connectivity

An algorithm of Dinic for finding the maximum flow in a network is described. It is then shown that if the vertex capacities are all equal to one, the algorithm requires at most

A Local-Ratio Theorem for Approximating the Weighted Vertex Cover Problem

O(|V|^{1/2} \cdot |E|)

A linear-time approximation algorithm for the weighted vertex cover problem

time, and if the edge capacities are all equal to one, the algorithm requires at most

The complexity of promise problems with applications to public-key cryptography

O(|V|^{2/3} \cdot |E|)

On the complexity of time table and multi-commodity flow problems

time. Also, these bounds are tight for Dinic’s algorithm.These results are used to test the vertex connectivity of a graph in

Computing an st-numbering☆

O(|V|^{1/2} \cdot |E|^2 )

Linear Algorithm for Data Compression via String Matching

time and the edge connectivity in

A construction of a cipher from a single pseudorandom permutation

O(|V|^{5/3} \cdot |E|)

On-line/off-line digital signatures

time.