628849
Learning a circuit by injecting values
We propose a new model for exact learning of acyclic circuits using experiments in which chosen values may be assigned to an arbitrary subset of wires internal to the circuit, but only the value of the circuit's single output wire may be observed. We give polynomial time algorithms to learn (1) arbitrary circuits with logarithmic depth and constant fan-in and (2) Boolean circuits of constant depth and unbounded fan-in over AND, OR, and NOT gates. Thus, both AC0 and NC1 circuits are learnable in polynomial time in this model. Negative results show that some restrictions on depth, fan-in and gate types are necessary: exponentially many experiments are required to learn AND/OR circuits of unbounded depth and fan-in; it is NP-hard to learn AND/OR circuits of unbounded depth and fan-in 2; and it is NP-hard to learn circuits of bounded depth and unbounded fan-in over AND, OR, and threshold gates, even when the target circuit is known to contain at most one threshold gate and that threshold gate has threshold 2. We also consider the effect of adding an oracle for behavioral equivalence. In this case there are polynomial-time algorithms to learn arbitrary circuits of constant fan-in and unbounded depth and to learn Boolean circuits with arbitrary fan-in and unbounded depth over AND, OR, and NOT gates. A corollary is that these two classes are PAC-learnable if experiments are available.
33317527
Learning Large-Alphabet and Analog Circuits with Value Injection Queries
We consider the problem of learning an acyclic discrete circuit with n wires, fan-in bounded by k and alphabet size s using value injection queries. For the class of transitively reduced circuits, we develop the Distinguishing Paths Algorithm, that learns such a circuit using (ns)O(k) value injection queries and time polynomial in the number of queries. We describe a generalization of the algorithm to the class of circuits with shortcut width bounded by b that uses (ns)O(k+b) value injection queries. Both algorithms use value injection queries that fix only O(kd) wires, where d is the depth of the target circuit. We give a reduction showing that without such restrictions on the topology of the circuit, the learning problem may be computationally intractable when s = nΘ(1), even for circuits of depth O(log n). We then apply our large-alphabet learning algorithms to the problem of approximate learning of analog circuits whose gate functions satisfy a Lipschitz condition. Finally, we consider models in which behavioral equivalence queries are also available, and extend and improve the learning algorithms of [5] to handle general classes of gates functions that are polynomial time learnable from counterexamples.
3103973
Sprite: a simple, cheat-proof, credit-based system for mobile ad-hoc networks
Mobile ad hoc networking has been an active research area for several years. How to stimulate cooperation among selfish mobile nodes, however, is not well addressed yet. In this paper, we propose Sprite, a simple, cheat-proof, credit-based system for stimulating cooperation among selfish nodes in mobile ad hoc networks. Our system provides incentive for mobile nodes to cooperate and report actions honestly. Compared with previous approaches, our system does not require any tamper-proof hardware at any node. Furthermore, we present a formal model of our system and prove its properties. Evaluations of a prototype implementation show that the overhead of our system is small. Simulations and analysis show that mobile nodes can cooperate and forward each other's messages, unless the resource of each node is extremely low.
5765721
Architecture of TsinghuAeolus
RoboCup Simulation Server provides a wonderful challenge for all the participants. This paper explains key technology implemented by Tsinghuaeolus RoboCup team played in RoboCup environment, including basic adversarial skills, which is developed by using Dynamic Programming in combination with heuristic search algorithm, and reactive strategy architecture. Tsinghuaeolus was the winner of RoboCup2001.
15338297
Fast construction of overlay networks
An asynchronous algorithm is described for rapidly constructing an overlay network in a peer-to-peer system where all nodes can in principle communicate with each other directly through an underlying network, but each participating node initially has pointers to only a handful of other participants. The output of the mechanism is a linked list of all participants sorted by their identifiers, which can be used as a foundation for building various linear overlay networks such as Chord or skip graphs. Assuming the initial pointer graph is weakly-connected with maximum degree <i>d</i> and the length of a node identifier is <i>W</i>, the mechanism constructs a binary search tree of nodes of depth <i>O</i>(<i>W</i>) in expected <i>O</i>(<i>W</i> log <i>n</i>) time using expected <i>O</i>((<i>d</i>+<i>W</i>)<i>n</i> log <i>n</i>) messages of size <i>O</i>(<i>W</i>) each. Furthermore, the algorithm has low <i>contention</i>: at any time there are only <i>O</i>(<i>d</i>) undelivered messages for any given recipient. A lower bound of Ω(<i>d</i> + log <i>n</i>) is given for the running time of any procedure in a related synchronous model that yields a sorted list from a degree-<i>d</i> weakly-connected graph of <i>n</i> nodes. We conjecture that this lower bound is tight and could be attained by further improvements to our algorithms.
16222163
Learning a Hidden Hypergraph
We consider the problem of learning a hypergraph using edge-detecting queries. In this model, the learner may query whether a set of vertices induces an edge of the hidden hypergraph or not. We show that an r-uniform hypergraph with m edges and n vertices is learnable with O(2 4r m.poly(r,logn)) queries with high probability. The queries can be made in O(min(2 r r 2 log 2 n, r 3 log 3 n)) rounds. We also give an algorithm that learns a non-uniform hypergraph whose minimum edge size is r 1 and maximum edge size is r 2 using O(f 1 (r 1 ,r 2 ).m (r 2 -r 1 +2)/2 . poly(log n)) queries with high probability, and give a lower bound of Ω(f 2 (r 1 ,r 2 ).m (r 2 -r 1 +2)/2 for this class of hypergraphs, where fi and f 2 are functions depending only on r 1 and r 2 . The queries can also be made in O(min(2 r 2r 2 2 log 2 n, r 3 2 log 3 n)) rounds.
2221913
A Simple Linear-Time Approximation Algorithm for Multi-processor Job Scheduling on Four Processors
Multiprocessor job scheduling problem has become increasingly interesting, for both theoretical study and practical applications. Theoretical study of the problem has made significant progress recently, which, however, seems not to imply practical algorithms for the problem, yet. Practical algorithms have been developed only for systems with three processors and the techniques seem difficult to extend to systems with more than three processors. This paper offers new observations and introduces new techniques for the multiprocessor job scheduling problem on systems with four processors. A very simple and practical linear time approximation algorithm of ratio bounded by 1:5 is developed for the multi-processor job scheduling problem P4|fix|Cmax, which significantly improves previous results. Our techniques are also useful for multiprocessor job scheduling problems on systems with more than four processors.
36905463
Quasi-threshold Graphs
Abstract Quasi-threshold graphs are defined recursively by the following rules: 1. (1) K1 is a quasi-threshold graph, 2. (2) adding a new vertex adjacent to all vertices of a quasi-threshold graph results in a quasi-threshold graph, 3. (3) the disjoint union of two quasi-threshold graphs is a quasi-threshold graph. This paper gives some new equivalent definitions of a quasi-threshold graph. From them, linear time recognition algorithms follow. We also give linear time algorithms for the edge domination problem and the bandwidth problem in this class of graphs.
7794101
Effective Density Queries for Moving Objects in Road Networks
Recent research has focused on density queries for moving objects in highly dynamic scenarios. An area is dense if the number of moving objects it contains is above some threshold. Monitoring dense areas has applications in traffic control systems, bandwidth management, collision probability evaluation, etc. All existing methods, however, assume the objects moving in the Euclidean space. In this paper, we study the density queries in road networks, where density computation is determined by the length of the road segment and the number of objects on it. We define an effective road-network density query guaranteeing to obtain useful answers. We then propose the cluster-based algorithm for the efficient computation of density queries for objects moving in road networks. Extensive experimental results show that our methods achieve high efficiency and accuracy for finding the dense areas in road networks.
2426986
Quantifying Privacy Leakage through Answering Database Queries
We assume a database consists of records of individuals with private or sensitive fields. Queries on the distribution of a sensitive field within a selected population in the database can be submitted to the data center. The answers to the queries leak private information of individuals though no identification information is provided. Inspired by decision theory, we present a quantitative model for the privacy protection problem in such a database query or linkage environment in this paper. In the model, the value of information is estimated from the viewpoint of the querier.To estimate the value, we define the information state of the data user by a class of probability distributions on the set of possible confidential values. We further define the usefulness of information based on how easy the data user can locate individuals that fit the description given in the queries. These states and the usefulness of information can be modified and refined by the user's knowledge acquisition actions. The value of information is then defined as the expected gain of the privacy receiver and the privacy is protected by imposing costs on the answers of the queries for balancing the gain.
53307441
Circuit Bottom Fan-In and Computational Power
We investigate the relationship between circuit bottom fan-in and circuit size when circuit depth is fixed. We show that in order to compute certain functions, a moderate reduction in circuit bottom fan-in will cause significant increase in circuit size. In particular, we prove that there are functions that are computable by circuits of linear size and depth k with bottom fan-in 2 but require exponential size for circuits of depth k with bottom fan-in 1. A general scheme is established to study the trade-off between circuit bottom fan-in and circuit size. Based on this scheme, we are able to prove, for example, that for any integer c, there are functions that are computable by circuits of linear size and depth k with bottom fan-in $O(\log n)$ but that require exponential size for circuits of depth k with bottom fan-in c, and that for any constant $\epsilon > 0$, there are functions that are computable by circuits of linear size and depth k with bottom fan-in $\log n$ but that require superpolynomial size for circuits of depth k with bottom fan-in $O(\log^{1-\epsilon} n)$. A consequence of these results is that the three input read-modes of alternating Turing machines proposed in the literature are all distinct.