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.
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.
8876890
Overlay mesh construction using interleaved spanning trees
In this paper we evaluate a method of using interleaved spanning trees to compose a resilient, high performance overlay mesh. Though spanning trees of arbitrary type could be used to construct an overlay mesh, we focus on a distributed algorithm that computes k minimum spanning trees on an arbitrary graph. The principal motivation behind this strategy is to provide applications with a k-redundant, high quality mesh suitable for demanding applications like A/V broadcast, video conferencing, data collection, multi-path routing, and file mirroring/transfer. We elaborate details of k-MST, pointing out advantages and potential problem points of the protocol, and then analyze its performance using a variety of metrics with simulation as well as a functional PlanetLab implementation.
691108
Utilization-based admission control for real-time applications
In this paper, we present a methodology to use utilization-based admission control in guaranteed real-time communication in a scalable fashion. We make admission control scalable by using a configuration-time test to determine a safe utilization level of servers. Admission control at run-time then is reduced to simple utilization tests on the servers along the path of the new flow. Furthermore, we discuss how appropriate route selection improve utilization levels, design a safe route selection heuristic algorithm to achieve high utilization of resources, and derive two bounds on the maximum utilization level for given traffic in a network. We compare the results of our route selection heuristics with that of a shortest-path based algorithm, and find that our heuristics can achieve a much higher maximum utilization level than that of the shortest-path based algorithm.
1373438
On Approximating Minimum Vertex Cover for Graphs with Perfect Matching
It has been a challenging open problem whether there is a polynomial time approximation algorithm for the VERTEX COVER problem whose approximation ratio is bounded by a constant less than 2. In this paper, we study the VERTEX COVER problem on graphs with perfect matching (shortly, VC-PM). We show that if the VC-PM problem has a polynomial time approximation algorithm with approximation ratio bounded by a constant less than 2, then so does the VERTEX COVER problem on general graphs. Approximation algorithms for VC-PM are developed, which induce improvements over previously known algorithms on sparse graphs. For example, for graphs of average degree 5, the approximation ratio of our algorithm is 1.414, compared with the previously best ratio 1.615 by Halldorsson and Radhakrishnan.
11661855
Theoretical Analysis of XL over Small Fields
XL was first introduced to solve determined or overdetermined systems of equations over a finite field as an “algebraic attack” against multivariate cryptosystems. There has been a steady stream of announcements of cryptanalysis of primitives by such attacks, including stream ciphers (e.g. Toyocrypt), PKC’s, and more controversially block ciphers (AES/Rijndael and Serpent).
18640612
On approximating minimum vertex cover for graphs with perfect matching
It has been a challenging open problem whether there is a polynomial time approximation algorithm for the VERTEX COVER problem whose approximation ratio is bounded by a constant less than 2. In this paper, we study the VERTEX COVER problem on graphs with perfect matching (shortly, VC-PM). We show that if the VC-PM problem has a polynomial time approximation algorithm with approximation ratio bounded by a constant less than 2, then so does the VERTEX COVER problem on general graphs. Approximation algorithms for VC-PM are developed, which induce improvements over previously known algorithms on sparse graphs. For example, for graphs of average degree 5, the approximation ratio of our algorithm is 1.414, compared with the previously best ratio 1.615 by Halldorsson and Radhakrishnan.
31382426
Strong Fault-Tolerance: Parallel Routing in Networks with Faults
A d-regular network G is strongly fault-tolerant if for any copy Gf of G with at most d - 2 faulty nodes, every pair of nonfaulty nodes u and v in Gf admits min{df(u), df (v)} node-disjoint paths in Gf from u to v, where df(u) and df(v) are the degrees of the nodes u and v in Gf. We show that popular network structures, such as hypercube and star networks, are strongly fault-tolerant. We develop efficient algorithms that construct the maximum number of node-disjoint paths of optimal or nearly optimal length in these networks with faulty nodes. Our algorithms are optimal in terms of their running time.