We study the problem of minimizing the number of guards positioned at a xed height h such that each triangle on a given 2.5-dimensional triangulated terrain T is completely visible from at least one guard. We prove this problem to be N P-hard, and we show that it cannot be approximated by a polynomial time algorithm within a ratio of (1 ?) 1 35 ln n for any > 0, unless N P T IM E(n O(log log n)...

In this paper, we set up a framework to study approximation of manipulation, control, and bribery in elections. We show existence of approximation algorithms (even fully polynomial-time approximation schemes) as well as obtain inapproximability results. In particular, we show that a large subclass of scoring protocols admits fully polynomial-time approximation schemes for the coalitional weight...

In this paper we investigate the computational complexity of motivating time-inconsistent agents to complete long term projects. We resort to an elegant graph-theoretic model, introduced by Kleinberg and Oren [4], which consists of a task graph G with n vertices, including a source s and target t, and an agent that incrementally constructs a path from s to t in order to collect rewards. The twi...

In this paper we study a problem named graph partitioning with supply and demand (GPSD), motivated by applications in energy transmission. The input consists of an undirected graph G with the nodes partitioned into two sets: suppliers and consumers. Each supply node has associated a capacity and each consumer node has associated a demand. The goal is to find a subgraph of G and to partition it ...