5884615
The Directed Planar Reachability Problem
We investigate the s-t-connectivity problem for directed planar graphs, which is hard for L and is contained in NL but is not known to be complete. We show that this problem is logspace-reducible to its complement, and we show that the problem of searching graphs of genus 1 reduces to the planar case. 
 
We also consider a previously-studied subclass of planar graphs known as grid graphs. We show that the directed planar s-t-connectivity problem reduces to the reachability problem for directed grid graphs. 
 
A special case of the grid-graph reachability problem where no edges are directed from right to left is known as the “layered grid graph reachability problem”. We show that this problem lies in the complexity class UL.
14665111
Oblivious Symmetric Alternation
We introduce a new class $\rm {O}^p_2$ as a subclass of the symmetric alternation class $\rm {S}^p_2$. An $\rm {O}^p_2$ proof system has the flavor of an $\rm {S}^p_2$ proof system, but it is more restrictive in nature. In an $\rm {S}^p_2$ proof system, we have two competing provers and a verifier such that for any input, the honest prover has an irrefutable certificate. In an $\rm {O}^p_2$ proof system, we require that the irrefutable certificates depend only on the length of the input, not on the input itself. In other words, the irrefutable proofs are oblivious of the input. For this reason, we call the new class oblivious symmetric alternation. While this might seem slightly contrived, it turns out that this class helps us improve some existing results. For instance, we show that if NP⊂P/poly then $\rm PH = {O}^p_2$, whereas the best known collapse under the same hypothesis was $\rm PH = {S}^p_2$. 
 
We also define classes $\rm Y{O}^p_2$ and $\rm N{O}^p_2$, bearing relations to $\rm {O}^p_2$ as NP and coNP are to P, and show that these along with $\rm {O}^p_2$ form a hierarchy, similar to the polynomial hierarchy. We investigate other inclusions involving these classes and strengthen some known results. For example, we show that $\rm MA \subseteq N{O}^p_2$ which sharpens the known result $\rm MA \subseteq {S}^p_2$ [16]. Another example is our result that $\rm AM \subseteq O_2 \cdot NP \subseteq {\prod}^p_2$, which is an improved upper bound on AM. Finally, we also prove better collapses for the 2-queries problem as discussed by [12,1,7]. We prove that $\rm P^{NP[1]} = P^{NP[2]} \Longrightarrow PH = {NO}^p_2 \cap Y{O}^p_2$.
7441506
Derandomization and distinguishing complexity
We continue an investigation of resource-bounded Kolmogorov complexity and derandomization techniques begun in [E. Allender (2001), E. Allender et al., (2002)]. We introduce nondeterministic time-bounded Kolmogorov complexity measures (KNt and KNT) and examine the properties of these measures using constructions of hitting set generators for nondeterministic circuits [P. B. Miltersen et al., (1999), R. Shaltiel et al., (2001)]. We observe that KNt bears many similarities to the nondeterministic distinguishing complexity CND of [H. Buhrman et al., (2002)]. This motivates the definition of a new notion of time-bounded distinguishing complexity KDt, as an intermediate notion with connections to the class FewEXP. The set of KDt-random strings is complete for EXP under P/poly reductions. Most of the notions of resource-bounded Kolmogorov complexity discussed here and in [E. Allender (2001), E. Allender et al., (2002)] have close connections to circuit size (on different types of circuits). We extend this framework to define notions of Kolmogorov complexity KB and KF that are related to branching program size and formula size, respectively. The sets of KB- and KF-random strings lie in coNP; we show that oracle access to these sets enables one to factor Blum integers. We obtain related intractability results for approximating minimum formula size, branching program size, and circuit size. The NEXP/spl sube/NC and NEXP/spl sube/L/poly questions are shown to be equivalent to conditions about the KF and KB complexity of sets in P.
9598402
Time-space tradeoffs in the counting hierarchy
Extends the lower-bound techniques of L. Fortnow (2000) to the unbounded-error probabilistic model. A key step in the argument is a generalization of V.A. Nepomnjas/spl caron/c/spl caron/ii/spl breve/'s (1970) theorem from the Boolean setting to the arithmetic setting. This generalization is made possible due to the recent discovery of logspace-uniform TC/sup 0/ circuits for iterated multiplication (A. Chiu et al., 2000). As an example of the sort of lower bounds that we obtain, we show that MAJ-MAJSAT is not contained in PrTiSp(n/sup 1+o(1)/, n/sup /spl epsiv//) for any /spl epsiv/<1. We also extend one of Fortnow's lower bounds, from showing that S~A~T~ does not have uniform NC/sup 1/ circuits of size n/sup 1+o(1)/, to a similar result for SAC/sup 1/ circuits.
2670464
Grid graph reachability problems
We study the complexity of reachability problems on various classes of grid graphs. Reachability on certain classes of grid graphs gives natural examples of problems that are hard for NC1 under AC0 reductions but are not known to be hard far L; they thus give insight into the structure of L. In addition to explicating the structure of L, another of our goals is to expand the class of digraphs for which connectivity can be solved in logspace, by building on the work of Jakoby et al. (2001), who showed that reachability in series-parallel digraphs is solvable in L. We show that reachability for single-source multiple sink planar dags is solvable in L
411400
Parity Problems in Planar Graphs
We consider the problem of counting the number of spanning trees in planar graphs. We prove tight bounds on the complexity of the problem, both in general and especially in the modular setting. We exhibit the problem to be complete for Logspace when the modulus is 2k, for constant k. On the other hand, we show that for any other modulus and in the non-modular case, our problem is as hard in the planar case as for the case of arbitrary graphs. This completely settles the question regarding the complexity of modular computation of the number of spanning trees in planar graphs. The techniques used rely heavily on algebraic-topology. In the spirit of counting problems modulo 2k, we also exhibit a highly parallel oplusL algorithm for finding the value of a Permanent modulo 2k. Previously, the best known result in this direction was Valiant's result that this problem lies in P.
6539802
Robot localization using uncalibrated camera invariants
We describe a set of image measurements which are invariant to the camera internals but are location variant. We show that using these measurements it is possible to calculate the self-localization of a robot using known landmarks and uncalibrated cameras. We also show that it is possible to compute, using uncalibrated cameras, the Euclidean structure of 3-D world points using multiple views from known positions. We are free to alter the internal parameters of the camera during these operations. Our initial experiments demonstrate the applicability of the method.
11274155
Minimum-Energy Broadcast Using Practical Directional Antennas in All-Wireless Networks
Energy-efficient broadcast communication is an important problem in wireless ad hoc networks. Previously, minimum-energy broadcast that exploits the broadcast nature of radio transmission has been studied and shown to be NP-complete for omnidirectional antennas. In this paper, we investigate the minimum-energy broadcast problem under a wide spectrum of directional antenna models, including sectored antennas with fixed sectors and beamwidth and antenna array-based smart antennas with varying degrees of beam orientation and beamwidth. We first propose the RF design and implementation of each model, which suggests the practical parameters of antennas under that model. We then show that the minimum-energy broadcast problem under each of the antenna models is NP-complete. Lastly, we present a heuristic algorithm based on BIP for the above problem under each directional antenna model and experimentally compare the energy efficiency of using different directional antennas using these heuristics. Our results show that using antennas with adjustable orientation and variable beamwidth gives the best results. For such antennas, the scanning angle is the dominant factor in improving the quality of the broadcast trees. The number of antennas per node is not that critical to obtaining a better broadcast tree as long as it is large enough to cover the entire 360◦ around a node so as to prevent network partitioning.
9807325
A Fast Algorithm for Point Labeling Problem
In the map labeling problem, we are given a set P = {p1, p2, . . . , pn} of point sites distributed on a 2D map. The label of a point pi is an axis-parallel rectangle of specified size. The objective is to label maximum number of points on the map so that the placed labels are mutually non-overlapping. Here, we investigate a special class of map labeling problem where (i) the height of the label of each point is the same but its length may be different from the others, (ii) the label of a point pi touches the point at one of its four corners and (iii) it does not obscure any other point in P . We describe an efficient heuristic algorithm for this problem which runs in O(n √ n) time in the worst case. We run our algorithm as well as the algorithm proposed in [14] on the available benchmarks [13]. The results produced by our algorithm is same as that of [14] in most of the cases, and is one less in few cases. But the time taken by our algorithm is much less than [14].
2052039
Overlay Node Placement: Analysis, Algorithms and Impact on Applications
Overlay routing has emerged as a promising approach to improving performance and reliability of Internet paths. To fully realize the potential of overlay routing under the constraints of deployment costs in terms of hardware, network connectivity and human effort, it is critical to carefully place infrastructure overlay nodes to balance the trade-off between performance and resource constraints. In this paper, we investigate approaches to perform intelligent placement of overlay nodes to facilitate (i) resilient routing and (ii) TCP performance improvement. We formulate objective functions to accurately capture application behavior: reliability and TCP performance, and develop several placement algorithms, which offer a wide range of trade-offs in complexity and required knowledge of the client- server location and traffic load. Using simulations on synthetic and real Internet topologies, and PlanetLab experiments, we demonstrate the effectiveness of the placement algorithms and objective functions developed, respectively. We conclude that an approach, hybrid of random and greedy approaches, provides the best tradeoff between computational efficiency and accuracy. We also uncover the fundamental challenge in simultaneously optimizing for reliability and TCP performance, and propose a simple unified algorithm to achieve the same.
1480265
Evaluation of cluster interconnects for a distributed shared memory
Clusters of Symmetrical Multiprocessors (SMPs) have recently become popular as low-cost, high-performance computing solutions. The type of interconnection hardware used in these clusters can become a deciding factor in their overall performance. This paper evaluates the performance of three different communication systems, 10 Mbps Ethernet, 100 Mbps FastEthernet and 155 Mbps ATM, using a multithreaded Distributed Shared Memory system, Strings. The raw performance of each network is first measured using netperf. Ten different applications are then used for performance evaluation, including programs from the SPLASH-2 benchmarks, a medical computing application, and some computational kernels. It is found that half of the programs tested are not significantly affected by changes in the bandwidth. Though the ATM network provides the highest overall bandwidth, the remaining applications show that the increase in latency compared to FastEthernet prevents any performance improvement. On the other hand, applications that require only moderately high bandwidths perform substantially better with FastEthernet.