Preliminary Definitions, Results and Motivation Stable Matching Problems: The Stable Marriage Problem: An Update SM and HR with Indifference The Stable Roommates Problem Further Stable Matching Problems Other Optimal Matching Problems: Pareto Optimal Matchings Popular Matchings Profile-Based Optimal Matchings.

/pdf/algorithmics-of-matching-under-preferences-2l3a9z5euq.pdf

Algorithmics of Matching Under Preferences

The rapidly growing field of computational social choice, at the intersection of computer science and economics, deals with the computational aspects of collective decision making. This handbook, written by thirty-six prominent members of the computational social choice community, covers the field comprehensively. Chapters devoted to each of the field's major themes offer detailed introductions. Topics include voting theory (such as the computational complexity of winner determination and manipulation in elections), fair allocation (such as algorithms for dividing divisible and indivisible goods), coalition formation (such as matching and hedonic games), and many more. Graduate students, researchers, and professionals in computer science, economics, mathematics, political science, and philosophy will benefit from this accessible and self-contained book.

/pdf/handbook-of-computational-social-choice-12i1xbv1b8.pdf

Handbook of Computational Social Choice

The concept of rainbow connection was introduced by Chartrand et al. in 2008. It is fairly interesting and recently quite a lot papers have been published about it. In this survey we attempt to bring together most of the results and papers that dealt with it. We begin with an introduction, and then try to organize the work into five categories, including (strong) rainbow connection number, rainbow $k$-connectivity, $k$-rainbow index, rainbow vertex-connection number, algorithms and computational complexity. This survey also contains some conjectures, open problems or questions.

Rainbow connections of graphs -- A survey

The concept of rainbow connection was introduced by Chartrand et al. [14] in 2008. It is interesting and recently quite a lot papers have been published about it. In this survey we attempt to bring together most of the results and papers that dealt with it. We begin with an introduction, and then try to organize the work into five categories, including (strong) rainbow connection number, rainbow k-connectivity, k-rainbow index, rainbow vertex-connection number, algorithms and computational complexity. This survey also contains some conjectures, open problems and questions.

Rainbow Connections of Graphs: A Survey

Invited Lectures.- Origami, Linkages, and Polyhedra: Folding with Algorithms.- Reliable and Efficient Geometric Computing.- Some Computational Challenges in Today's Bio-medicine.- Contributed Papers: Design and Analysis Track.- Kinetic Collision Detection for Convex Fat Objects.- Dynamic Connectivity for Axis-Parallel Rectangles.- Single Machine Precedence Constrained Scheduling Is a Vertex Cover Problem.- Cooperative TSP.- Frechet Distance for Curves, Revisited.- Resource Allocation in Bounded Degree Trees.- Dynamic Algorithms for Graph Spanners.- Latency Constrained Aggregation in Sensor Networks.- Competitive Analysis of Flash-Memory Algorithms.- Contention Resolution with Heterogeneous Job Sizes.- Deciding Relaxed Two-Colorability-A Hardness Jump.- Negative Examples for Sequential Importance Sampling of Binary Contingency Tables.- Estimating Entropy over Data Streams.- Necklaces, Convolutions, and X + Y.- Purely Functional Worst Case Constant Time Catenable Sorted Lists.- Taxes for Linear Atomic Congestion Games.- Spanners with Slack.- Compressed Indexes for Approximate String Matching.- Traversing the Machining Graph.- Efficient Computation of Nash Equilibria for Very Sparse Win-Lose Bimatrix Games.- Distributed Almost Exact Approximations for Minor-Closed Families.- Spectral Clustering by Recursive Partitioning.- Finite Termination of "Augmenting Path" Algorithms in the Presence of Irrational Problem Data.- Dynamic Programming and Fast Matrix Multiplication.- Near-Entropy Hotlink Assignments.- Subspace Sampling and Relative-Error Matrix Approximation: Column-Row-Based Methods.- Finding Total Unimodularity in Optimization Problems Solved by Linear Programs.- Preemptive Online Scheduling: Optimal Algorithms for All Speeds.- On the Complexity of the Multiplication Method for Monotone CNF/DNF Dualization.- Lower and Upper Bounds on FIFO Buffer Management in QoS Switches.- Graph Coloring with Rejection.- A Doubling Dimension Threshold ?(loglogn) for Augmented Graph Navigability.- Violator Spaces: Structure and Algorithms.- Region-Restricted Clustering for Geographic Data Mining.- An O(n 3 (loglogn/logn)5/4) Time Algorithm for All Pairs Shortest Paths.- Cheating by Men in the Gale-Shapley Stable Matching Algorithm.- Approximating Almost All Instances of Max-Cut Within a Ratio Above the Hastad Threshold.- Enumerating Spanning and Connected Subsets in Graphs and Matroids.- Less Hashing, Same Performance: Building a Better Bloom Filter.- A Unified Approach to Approximating Partial Covering Problems.- Navigating Low-Dimensional and Hierarchical Population Networks.- Popular Matchings in the Capacitated House Allocation Problem.- Inner-Product Based Wavelet Synopses for Range-Sum Queries.- Approximation in Preemptive Stochastic Online Scheduling.- Greedy in Approximation Algorithms.- I/O-Efficient Undirected Shortest Paths with Unbounded Edge Lengths.- Stochastic Shortest Paths Via Quasi-convex Maximization.- Path Hitting in Acyclic Graphs.- Minimum Transversals in Posi-modular Systems.- An LP-Designed Algorithm for Constraint Satisfaction.- Approximate k-Steiner Forests Via the Lagrangian Relaxation Technique with Internal Preprocessing.- Balancing Applied to Maximum Network Flow Problems.- Contributed Papers: Engineering and Applications Track.- Out-of-Order Event Processing in Kinetic Data Structures.- Kinetic Algorithms Via Self-adjusting Computation.- Parallel Machine Scheduling Through Column Generation: Minimax Objective Functions.- Reporting Flock Patterns.- On Exact Algorithms for Treewidth.- An Improved Construction for Counting Bloom Filters.- An MINLP Solution Method for a Water Network Problem.- Skewed Binary Search Trees.- Algorithmic Aspects of Proportional Symbol Maps.- Does Path Cleaning Help in Dynamic All-Pairs Shortest Paths?.- Multiline Addressing by Network Flow.- The Engineering of a Compression Boosting Library: Theory vs Practice in BWT Compression.- The Price of Resiliency: A Case Study on Sorting with Memory Faults.- How Branch Mispredictions Affect Quicksort.- Robust, Generic and Efficient Construction of Envelopes of Surfaces in Three-Dimensional Spaces.- Engineering Highway Hierarchies.- Univariate Polynomial Real Root Isolation: Continued Fractions Revisited.- Exact and Efficient Construction of Planar Minkowski Sums Using the Convolution Method.

Algorithms - ESA 2006 : 14th Annual European Symposium, Zurich, Switzerland, September 11-13, 2006 : proceedings

http://www.cse.iitm.ac.in/~meghana/papers/TCS11-2.pdf

Popular mixed matchings

http://www.cse.iitm.ac.in/~meghana/papers/DAM09.pdf

Optimal popular matchings

We present an incremental algorithm that updates the betweenness centrality (BC) score of all vertices in a graph G when a new edge is added to G, or the weight of an existing edge is reduced. Our incremental algorithm runs in O(v * · n) time, where v * is bounded by m *, the number of edges that lie on a shortest path in G. We achieve the same bound for the more general incremental vertex update problem. Even for a single edge update, our incremental algorithm is the first algorithm that is provably faster on sparse graphs than recomputing with the well-known static Brandes algorithm. It is also likely to be much faster than Brandes on dense graphs since m * is often close to linear in n. Our incremental algorithm is very simple, and we give an efficient cache-oblivious implementation that incurs O(n · sort(v *)) cache misses, where sort is a well-known measure for caching efficiency.

/pdf/betweenness-centrality-incremental-and-faster-1m4zym9r48.pdf

Betweenness Centrality - Incremental and Faster

A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices. The (strong) rainbow connectivity of a graph G, denoted by (src(G), respectively) rc(G) is the smallest number of colors required to edge color the graph such that G is (strongly) rainbow connected. In this paper we study the rainbow connectivity problem and the strong rainbow connectivity problem from a computational point of view. Our main results can be summarised as below: 1) For every fixed k >= 3, it is NP-Complete to decide whether src(G) = 3, it is NP-Complete to decide whether rc(G) <= k. This resolves one of the open problems posed by Chakraborty et al. (J. Comb. Opt., 2011) where they prove the hardness for the even case. 3) The following problem is fixed parameter tractable: Given a graph G, determine the maximum number of pairs of vertices that can be rainbow connected using two colors. 4) For a directed graph G, it is NP-Complete to decide whether rc(G) <= 2.

http://www.cse.iitm.ac.in/~meghana/papers/FSTTCS11.pdf

Rainbow Connectivity: Hardness and Tractability

We study the problem of matching applicants to jobs under one-sided preferences; that is, each applicant ranks a non-empty subset of jobs under an order of preference, possibly involving ties. A matching M is said to be more popular than T if the applicants that prefer M to T outnumber those that prefer T to M. A matching is said to be popular if there is no matching more popular than it. Equivalently, a matching M is popular if @f(M,T)>[email protected](T,M) for all matchings T, where @f(X,Y) is the number of applicants that prefer X to Y. Previously studied solution concepts based on the popularity criterion are either not guaranteed to exist for every instance (e.g., popular matchings) or are NP-hard to compute (e.g., least unpopular matchings). This paper addresses this issue by considering mixed matchings. A mixed matching is simply a probability distribution over matchings in the input graph. The function @f that compares two matchings generalizes in a natural manner to mixed matchings by taking expectation. A mixed matching P is popular if @f(P,Q)>[email protected](Q,P) for all mixed matchings Q. We show that popular mixed matchings always exist and we design polynomial time algorithms for finding them. Then we study their efficiency and give tight bounds on the price of anarchy and price of stability of the popular matching problem.

Meghana Nasre

Papers

Popular mixed matchings

Optimal popular matchings

Betweenness Centrality - Incremental and Faster

Rainbow Connectivity: Hardness and Tractability

Popular Mixed Matchings