Constitutes the proceedings of the 4th International Conference on Theory and Applications of Models of Computation, TAMC 2007, held in Shanghai, China in May 2007. This book addresses major areas in computer science; mathematics, especially logic; and the physical sciences, particularly with regard to computation and computability theory.

Plenary Lectures.- Detecting Sharp Drops in PageRank and a Simplified Local Partitioning Algorithm.- Generalizations of the Compactness Theorem and Gödel’s Completeness Theorem for Nonstandard Finite Structures.- Contributed Papers.- Approximation Algorithms for 3D Orthogonal Knapsack.- A Comparative Study of Efficient Algorithms for Partitioning a Sequence into Monotone Subsequences.- The Hardness of Selective Network Design for Bottleneck Routing Games.- A Polynomial Time Algorithm for Finding Linear Interval Graph Patterns.- Elementary Differences Among Jump Hierarchies.- Working with the LR Degrees.- Computability on Subsets of Locally Compact Spaces.- A New Approach to Graph Recognition and Applications to Distance-Hereditary Graphs.- Finding a Duplicate and a Missing Item in a Stream.- Directed Searching Digraphs: Monotonicity and Complexity.- Protecting Against Key Escrow and Key Exposure in Identity-Based Cryptosystem.- Encapsulated Scalar Multiplications and Line Functions in the Computation of Tate Pairing.- A Provably Secure Blind Signature Scheme.- Construct Public Key Encryption Scheme Using Ergodic Matrices over GF(2).- New Left-to-Right Radix-r Signed-Digit Recoding Algorithm for Pairing-Based Cryptosystems.- The Strongest Nonsplitting Theorem.- There is an Sw-Cuppable Strongly c.e. Real.- On Computation Complexity of the Concurrently Enabled Transition Set Problem.- Synchronization of Some DFA.- On the Treewidth and Pathwidth of Biconvex Bipartite Graphs.- On Exact Complexity of Subgraph Homeomorphism.- Searching a Polygonal Region by Two Guards.- On the Internal Steiner Tree Problem.- Approximately Optimal Trees for Group Key Management with Batch Updates.- On Deciding Deep Holes of Reed-Solomon Codes.- Quantum Multiparty Communication Complexity andCircuit Lower Bounds.- Efficient Computation of Algebraic Immunity of Symmetric Boolean Functions.- Improving the Average Delay of Sorting.- Approximating Capacitated Tree-Routings in Networks.- Feedback Arc Set Problem in Bipartite Tournaments.- Studying on Economic-Inspired Mechanisms for Routing and Forwarding in Wireless Ad Hoc Network.- Enhancing Simulation for Checking Language Containment.- QBF-Based Symbolic Model Checking for Knowledge and Time.- A Characterization of the Language Classes Learnable with Correction Queries.- Learnable Algorithm on the Continuum.- Online Deadline Scheduling with Bounded Energy Efficiency.- Efficient Algorithms for Airline Problem.- Efficient Exact Arithmetic over Constructive Reals.- Bounding Run-Times of Local Adiabatic Algorithms.- A Note on Universal Composable Zero Knowledge in Common Reference String Model.- A Note on the Feasibility of Generalized Universal Composability.- t-Private and Secure Auctions.- Secure Multiparty Computations Using a Dial Lock.- A Time Hierarchy Theorem for Nondeterministic Cellular Automata.- Decidability of Propositional Projection Temporal Logic with Infinite Models.- Separation of Data Via Concurrently Determined Discriminant Functions.- The Undecidability of the Generalized Collatz Problem.- Combinatorial and Spectral Aspects of Nearest Neighbor Graphs in Doubling Dimensional and Nearly-Euclidean Spaces.- Maximum Edge-Disjoint Paths Problem in Planar Graphs.- An Efficient Algorithm for Generating Colored Outerplanar Graphs.- Orthogonal Drawings for Plane Graphs with Specified Face Areas.- Absolutely Non-effective Predicates and Functions in Computable Analysis.- Linear-Size Log-Depth Negation-Limited Inverter for k-Tonic Binary Sequences.- The Existence of Unsatisfiable Formulas in k-LCNF fork???3.- Improved Exponential Time Lower Bound of Knapsack Problem Under BT Model.- Phase Transition of Multivariate Polynomial Systems.- Approximation Algorithms for Maximum Edge Coloring Problem.- Two Improved Range-Efficient Algorithms for F 0 Estimation.- Approximation to the Minimum Rooted Star Cover Problem.- Approximability and Parameterized Complexity of Consecutive Ones Submatrix Problems.- Parameterized Algorithms for Weighted Matching and Packing Problems.- Kernelizations for Parameterized Counting Problems.- Revisiting the Impossibility for Boosting Service Resilience.- An Approximation Algorithm to the k-Steiner Forest Problem.- A Distributed Algorithm of Fault Recovery for Stateful Failover.- Path Embedding on Folded Hypercubes.- An Approximation Algorithm Based on Chain Implication for Constrained Minimum Vertex Covers in Bipartite Graphs.

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