Due to the lack of unconditional polynomial lower bounds, it is now in fashion to prove
conditional lower bounds in order to advance our understanding of the class P. The vast …

Beginning in the 1960s, techniques from operations research began to be used to generate
political districting plans. A classical example is the integer programming model of Hess et …

We give an O(n\log^3n) algorithm that, given an n-node directed planar graph with arc
capacities, a set of source nodes, and a set of sink nodes finds a maximum flow from the …

Every undirected graph G has a (weighted) cut-equivalent tree T, commonly named after
Gomory and Hu who discovered it in 1961. Both T and G have the same node set, and for …

The dynamic shortest paths problem on planar graphs asks us to preprocess a planar graph
G such that we may support insertions and deletions of edges in G as well as distance …

When constructing political districting plans, prominent criteria include population balance,
contiguity, and compactness. The compactness of a districting plan, which is often judged by …

Given a triangulated planar graph G on n vertices and an integer r< n, an r--division of G with
few holes is a decomposition of G into O (n/r) regions of size at most r such that each region …

Min-Cut queries are fundamental: Preprocess an undirected edge-weighted graph, to
quickly report a minimum-weight cut that separates a query pair of nodes s, t. The best data …

We investigate the time-complexity of the All-Pairs Max-Flow problem: Given a graph with n
nodes and m edges, compute for all pairs of nodes the maximum-flow value between them …

The All-Pairs Min-Cut problem (aka All-Pairs Max-Flow) asks to compute a minimum $ s $-$ t
$ cut (or just its value) for all pairs of vertices $ s, t $. We study this problem in directed …