Optimal Point Placement for Mesh Smoothing

We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using generalized linear programming. We also give efficient algorithms for some mesh smoothing problems that do not fit into the generalized linear programming paradigm.Comment: 12 pages, 3 figures. A preliminary version of this paper was presented at the 8th ACM/SIAM Symp. on Discrete Algorithms (SODA '97). This is the final version, and will appear in a special issue of J. Algorithms for papers from SODA '9

Quasiconvex Programming

We define quasiconvex programming, a form of generalized linear programming in which one seeks the point minimizing the pointwise maximum of a collection of quasiconvex functions. We survey algorithms for solving quasiconvex programs either numerically or via generalizations of the dual simplex method from linear programming, and describe varied applications of this geometric optimization technique in meshing, scientific computation, information visualization, automated algorithm analysis, and robust statistics.Comment: 33 pages, 14 figure

Audit Games with Multiple Defender Resources

Modern organizations (e.g., hospitals, social networks, government agencies) rely heavily on audit to detect and punish insiders who inappropriately access and disclose confidential information. Recent work on audit games models the strategic interaction between an auditor with a single audit resource and auditees as a Stackelberg game, augmenting associated well-studied security games with a configurable punishment parameter. We significantly generalize this audit game model to account for multiple audit resources where each resource is restricted to audit a subset of all potential violations, thus enabling application to practical auditing scenarios. We provide an FPTAS that computes an approximately optimal solution to the resulting non-convex optimization problem. The main technical novelty is in the design and correctness proof of an optimization transformation that enables the construction of this FPTAS. In addition, we experimentally demonstrate that this transformation significantly speeds up computation of solutions for a class of audit games and security games