Convex Analysis: (pms-28)

We present a new concept for optimization under uncertainty: recoverable robustness A solution is recovery robust if it can be recovered by limited means in all likely scenarios Specializing the general concept to linear programming we can show that recoverable robustness combines the flexibility of stochastic programming with the tractability and performances guarantee of the classical robust approach We exemplify recoverable robustness in delay resistant, periodic and aperiodic timetabling problems, and train platforming

The Concept of Recoverable Robustness, Linear Programming Recovery, and Railway Applications

A new approximation algorithm for maximum weighted matching in general edge-weighted graphs is presented. It calculates a matching with an edge weight of at least of the edge weight of a maximum weighted matching. Its time complexity is O(|E|), with |E| being the number of edges in the graph. This improves over the previously known -approximation algorithms for maximum weighted matching which require O(|E| log(|V|)) steps, where |V| is the number of vertices.

Linear Time 1/2-Approximation Algorithm for Maximum Weighted Matching in General Graphs

Designing Reliable Algorithms in Unreliable Memories.- From Balanced Graph Partitioning to Balanced Metric Labeling.- Fearful Symmetries: Quantum Computing, Factoring, and Graph Isomorphism.- Exploring an Unknown Graph Efficiently.- Online Routing in Faulty Meshes with Sub-linear Comparative Time and Traffic Ratio.- Heuristic Improvements for Computing Maximum Multicommodity Flow and Minimum Multicut.- Relax-and-Cut for Capacitated Network Design.- On the Price of Anarchy and Stability of Correlated Equilibria of Linear Congestion Games,,.- The Complexity of Games on Highly Regular Graphs.- Computing Equilibrium Prices: Does Theory Meet Practice?.- Efficient Exact Algorithms on Planar Graphs: Exploiting Sphere Cut Branch Decompositions.- An Algorithm for the SAT Problem for Formulae of Linear Length.- Linear-Time Enumeration of Isolated Cliques.- Finding Shortest Non-separating and Non-contractible Cycles for Topologically Embedded Graphs.- Delineating Boundaries for Imprecise Regions.- Exacus: Efficient and Exact Algorithms for Curves and Surfaces.- Min Sum Clustering with Penalties.- Improved Approximation Algorithms for Metric Max TSP.- Unbalanced Graph Cuts.- Low Degree Connectivity in Ad-Hoc Networks.- 5-Regular Graphs are 3-Colorable with Positive Probability.- Optimal Integer Alphabetic Trees in Linear Time.- Predecessor Queries in Constant Time?.- An Algorithm for Node-Capacitated Ring Routing.- On Degree Constrained Shortest Paths.- A New Template for Solving p-Median Problems for Trees in Sub-quadratic Time.- Roll Cutting in the Curtain Industry.- Space Efficient Algorithms for the Burrows-Wheeler Backtransformation.- Cache-Oblivious Comparison-Based Algorithms on Multisets.- Oblivious vs. Distribution-Based Sorting: An Experimental Evaluation.- Allocating Memory in a Lock-Free Manner.- Generating Realistic Terrains with Higher-Order Delaunay Triangulations.- I/O-Efficient Construction of Constrained Delaunay Triangulations.- Convex Hull and Voronoi Diagram of Additively Weighted Points.- New Tools and Simpler Algorithms for Branchwidth.- Treewidth Lower Bounds with Brambles.- Minimal Interval Completions.- A 2-Approximation Algorithm for Sorting by Prefix Reversals.- Approximating the 2-Interval Pattern Problem.- A Loopless Gray Code for Minimal Signed-Binary Representations.- Efficient Approximation Schemes for Geometric Problems?.- Geometric Clustering to Minimize the Sum of Cluster Sizes.- Approximation Schemes for Minimum 2-Connected Spanning Subgraphs in Weighted Planar Graphs.- Packet Routing and Information Gathering in Lines, Rings and Trees.- Jitter Regulation for Multiple Streams.- Efficient c-Oriented Range Searching with DOP-Trees.- Matching Point Sets with Respect to the Earth Mover's Distance.- Small Stretch Spanners on Dynamic Graphs.- An Experimental Study of Algorithms for Fully Dynamic Transitive Closure.- Experimental Study of Geometric t-Spanners.- Highway Hierarchies Hasten Exact Shortest Path Queries.- Preemptive Scheduling of Independent Jobs on Identical Parallel Machines Subject to Migration Delays.- Fairness-Free Periodic Scheduling with Vacations.- Online Bin Packing with Cardinality Constraints.- Fast Monotone 3-Approximation Algorithm for Scheduling Related Machines.- Engineering Planar Separator Algorithms.- Stxxl: Standard Template Library for XXL Data Sets.- Negative Cycle Detection Problem.- An Optimal Algorithm for Querying Priced Information: Monotone Boolean Functions and Game Trees.- Online View Maintenance Under a Response-Time Constraint.- Online Primal-Dual Algorithms for Covering and Packing Problems.- Efficient Algorithms for Shared Backup Allocation in Networks with Partial Information.- Using Fractional Primal-Dual to Schedule Split Intervals with Demands.- An Approximation Algorithm for the Minimum Latency Set Cover Problem.- Workload-Optimal Histograms on Streams.- Finding Frequent Patterns in a String in Sublinear Time.- Online Occlusion Culling.- Shortest Paths in Matrix Multiplication Time.- Computing Common Intervals of K Permutations, with Applications to Modular Decomposition of Graphs.- Greedy Routing in Tree-Decomposed Graphs.- Making Chord Robust to Byzantine Attacks.- Bucket Game with Applications to Set Multicover and Dynamic Page Migration.- Bootstrapping a Hop-Optimal Network in the Weak Sensor Model.- Approximating Integer Quadratic Programs and MAXCUT in Subdense Graphs.- A Cutting Planes Algorithm Based Upon a Semidefinite Relaxation for the Quadratic Assignment Problem.- Approximation Complexity of min-max (Regret) Versions of Shortest Path, Spanning Tree, and Knapsack.- Robust Approximate Zeros.- Optimizing a 2D Function Satisfying Unimodality Properties.

Algorithms -- ESA 2005 : 13th Annual European Symposium, Palma de Mallorca, Spain, October 3-6, 2005 : proceedings

The Critical Node Detection Problem in networks: A survey.

Many polynomial-time solvable combinatorial optimization problems become NP-hard if an additional complicating constraint is added to restrict the set of feasible solutions. In this paper, we consider two such problems, namely maximum-weight matching and maximum-weight matroid intersection with one additional budget constraint. We present the first polynomial-time approximation schemes for these problems. Similarly to other approaches for related problems, our schemes compute two solutions to the Lagrangian relaxation of the problem and patch them together to obtain a near-optimal solution. However, due to the richer combinatorial structure of the problems considered here, standard patching techniques do not apply. To circumvent this problem, we crucially exploit the adjacency relations on the solution polytope and, surprisingly, the solution to an old combinatorial puzzle.

/pdf/budgeted-matching-and-budgeted-matroid-intersection-via-the-2hi6azo1ex.pdf

Budgeted matching and budgeted matroid intersection via the gasoline puzzle

Delays in a railway network are a common problem that railway companies face in their daily operations. When a train is delayed, it may either be beneficial to let a connecting train wait so that passengers in the delayed train do not miss their connection, or it may be beneficial to let the connecting train depart on time to avoid further delays. These decisions naturally depend on the global structure of the network, on the schedule, on the passenger routes and on the imposed delays. The railway delay management (RDM) problem (in a broad sense) is to decide which trains have to wait for connecting trains and which trains have to depart on time. The offline version (i.e. when all delays are known in advance) is already NP-hard for very special networks. In this paper we show that the online railway delay management (ORDM) problem is PSPACE-hard. This result justifies the need for a simulation approach to evaluate wait policies for ORDM. For this purpose we present TOPSUâRDM, a simulation platform for evaluating and comparing different heuristics for the ORDM problem with stochastic delays. Our novel approach is to separate the actual simulation and the program that implements the decision-making policy, thus enabling implementations of different heuristics to ââcompeteââ on the same instances and delay distributions. We also report on computational results indicating the worthiness of developing intelligent wait policies. For RDM and other logistic planning processes, it is our goal to bridge the gap between theoretical models, which are accessible to theoretical analysis, but are often too far away from practice, and the methods which are used in practice today, whose performance is almost impossible to measure.

/pdf/online-railway-delay-management-hardness-simulation-and-1n4i870j18.pdf

Online railway delay management: Hardness, simulation and computation

In this article, we consider k-way vertex cut: the problem of finding a graph separator of a given size that decomposes the graph into the maximum number of components. Our main contribution is the derivation of an efficient polynomial-time approximation scheme for the problem on planar graphs. Also, we show that k-way vertex cut is polynomially solvable on graphs of bounded treewidth and fixed–parameter tractable on planar graphs with the size of the separator as the parameter. © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 63(2), 170–178 2014

Complexity and approximability of the k‐way vertex cut

We present a linear time algorithm exactly solving the 2-edge connected spanning subgraph (2-ECSS) problem in a graph of bounded treewidth. Using this with Klein's diameter reduction technique [15], we find a linear time PTAS for the problem in unweighted planar graphs, and the first PTAS for the problem in weighted planar graphs.

Minimum weight 2-edge-connected spanning subgraphs in planar graphs

We study implementability in dominant strategies of social choice functions when sets of types are multi-dimensional and convex, sets of outcomes are arbitrary, valuations for outcomes are convex functions in the type, and utilities over outcomes and payments are quasi-linear. Archer and Kleinberg [1] have proven that in case of valuation functions that are linear in the type monotonicity in combination with a local integrability condition are equivalent with implementability. We show that in the case of convex valuation functions one has to require in addition a property called decomposition monotonicity in order to conclude implementability from monotonicity and the integrability condition. Decomposition monotonicity is automatically satisfied in the linear case.

Saks and Yu [9] have shown that for the same setting as in Archer and Kleinberg [1], but finite set of outcomes, monotonicity alone is sufficient for implementability. Later Archer and Kleinberg [1], Monderer [6] and Vohra [10] have given alternative proofs for the same theorem. Using our characterization, we show that the Saks and Yu theorem generalizes to convex valuations. Again, decomposition monotonicity has to be added as a condition.

André Berger

Papers

Budgeted matching and budgeted matroid intersection via the gasoline puzzle

Online railway delay management: Hardness, simulation and computation

Complexity and approximability of the k‐way vertex cut

Minimum weight 2-edge-connected spanning subgraphs in planar graphs

Characterizing Incentive Compatibility for Convex Valuations