This paper presents a novel method for sharing rectangular objects in a video conference. During these sessions, users often want to share a printed document or other planar rectangular objects (a photograph, the whiteboard on the wall, etc.) with the other participants. If the object is simply held in front of the camera (or if the camera is turned towards the object), the object will undergo perspective distortion and a rectangular object will appear in the video as a quadrilateral. In addition, a handheld document will not be steady and it will be difficult for other users to read its contents. In this paper, we present an algorithm that uses real-time predictive keystone correction to automatically lock on to object and present it with the proper orientation and shape.

We propose and analyze a simple new randomized algorithm, called ResolveSat, for finding satisfying assignments of Boolean formulas in conjunctive normal form. The algorithm consists of two stages: a preprocessing stage in which resolution is applied to enlarge the set of clauses of the formula, followed by a search stage that uses a simple randomized greedy procedure to look for a satisfying assignment. Currently, this is the fastest known probabilistic algorithm for k -CNF satisfiability for k ≥ 4 (with a running time of O (2 0.5625 n ) for 4-CNF). In addition, it is the fastest known probabilistic algorithm for k -CNF, k ≥ 3, that have at most one satisfying assignment (unique k -SAT) (with a running time O (2 (2 ln 2 − 1) n + o ( n ) ) = O (2 0.386 … n ) in the case of 3-CNF). The analysis of the algorithm also gives an upper bound on the number of the codewords of a code defined by a k -CNF. This is applied to prove a lower bounds on depth 3 circuits accepting codes with nonconstant distance. In particular we prove a lower bound Ω(2 1.282…√>i /i< ) for an explicitly given Boolean function of n variables. This is the first such lower bound that is asymptotically bigger than 2 √>i /i< + o (√>i /i<) .

Ternary content-addressable memories (TCAMs) are becoming very popular for designing high-throughput forwarding engines on routers: they are fast, cost-effective and simple to manage. However, a major drawback of TCAMs is their high power consumption. This paper presents architectures and algorithms for making TCAM-based routing tables more power efficient. The proposed architectures and algorithms are simple to implement, use commodity TCAMs, and provide worst-case power consumption guarantees (independent of routing table contents).

We consider the problem of client assignment in a distributed system of content servers. We present a system called Webmapper for clustering IP addresses and assigning each cluster to an optimal content server. The system is passive in that the only information it uses comes from monitoring the TCP connections between the clients and the servers. It is also flexible in that it makes no a priori assumptions about network topology and server placement and it can react quickly to changing network conditions. We present experimental results to evaluate the performance of Webmapper.

For several NP-complete problems, there have been a progression of better but still exponential algorithms. In this paper, we address the relative likelihood of sub-exponential algorithms for these problems. We introduce a generalized reduction which we call Sub-Exponential Reduction Family (SERF) that preserves sub-exponential complexity. We show that CircuitSAT is SERF-complete for all NP-search problems, and that for any fixed k, k-SAT, k-Colorability, k-Set Cover, Independent Set, Clique, Vertex Cover, are SERF--complete for the class SNP of search problems expressible by second order existential formulas whose first order part is universal. In particular, sub-exponential complexity for any one of the above problems implies the same for all others. We also look at the issue of proving strongly exponential lower bounds for AC 0 ; that is, bounds of the form 2 \\Omega\\Gamma n) . This problem is even open for depth-3 circuits. In fact, such a bound for depth-3 circuits with even l...

We propose and analyze a simple new algorithm for finding satisfying assignments of Boolean formulae in conjunctive normal form. The algorithm, ResolveSat, is a randomized variant of the DDL procedure by M. Davis et al. (1962) or Davis-Putnam procedure. Rather than applying the DLL procedure to the input formula F, however; ResolveSat enlarges F by adding additional clauses using limited resolution before performing DLL. The basic idea behind our analysis is the same as by R. Paturi (1997): a critical clause for a variable at a satisfying assignment gives rise to a unit clause in the DLL procedure with sufficiently high probability, thus increasing the probability of finding a satisfying assignment. In the current paper, we analyze the effect of multiple critical clauses (obtained through resolution) in producing unit clauses. We show that, for each k, the running time of ResolveSat on a k-CNF formula is significantly better than 2/sup n/, even in the worst case. In particular we show that the algorithm finds a satisfying assignment of a general 3-CNF in time O(2/sup .446n/) with high probability; where the best previous algorithm has running time O(2/sup .582n/). We obtain a better upper bound of O(2/sup (2ln2-1)/n+0(n))=O(2/sup 0.387n/) for 3-CNF that have at most one satisfying assignment (unique k-SAT). For each k, the bounds for general k-CNF are the best known for the worst-case complexity of finding a satisfying solution for k-SAT, the idea of succinctly encoding satisfying solutions can be applied to obtain lower bounds on circuit site. Here, we exhibit a function f such that any depth-3 AND-OR circuit with bottom fan-in bounded by k requires /spl Omega/(2(c/sub k/n/k)) gates (with c/sub k/>1). This is the first such lower bound with c/sub k/>1.

A projection is a subset of {0,1}n given by equations of theform xi = xj, xi = \bar{x}j, xi = 0, and xi = 1, where for $1\leq i \leq n$, xi are Boolean variables and $\bar{x} i are their complements. We study monochromatic projections in 2-colorings of an n-dimensional Boolean cube. We also study the dimension of the largest projection contained in a set specified by its density. We prove almost matching lower and upper bounds on the density of a set required to guarantee the existence of a d-dimensional projection. We also prove almost tight upper and lower bounds on the dimension of monochromatic projections in arbitrary Boolean functions. We then prove almost tight upper and lower bounds on the dimension of monochromatic projections in Boolean functions represented by low degree GF(2) polynomials. It follows from these lower bounds that low-degree GF(2) polynomials can define Boolean functions which are close to being extremal with respect to the property of having no large dimensional monochromatic projections.

We present and analyze two simple algorithms for finding satisfying assignments of /spl kappa/-CNFs (Boolean formulae in conjunctive normal form with at most /spl kappa/ literals per clause). The first is a randomized algorithm which, with probability approaching 1, finds a satisfying assignment of a satisfiable /spl kappa/-CNF formula F in time O(n/sup 2/|F|2/sup n-n//spl kappa//). The second algorithm is deterministic, and its running time approaches 2/sup n-n/2/spl kappa// for large n and /spl kappa/. The randomized algorithm is the best known algorithm for /spl kappa/>3; the deterministic algorithm is the best known deterministic algorithm for /spl kappa/>4. We also show an /spl Omega/(n/sup 1/4/2/sup /spl radic/n/) lower bound on the size of depth 3 circuits of AND and OR gates computing the parity function. This bound is tight up to a constant factor. The key idea used in these upper and lower bounds is what we call the Satisfiability Coding Lemma. This basic lemma shows how to encode satisfying solutions of a /spl kappa/-CNF succinctly.

ExponentialLower Bounds for Depth 3