Improved on-line broadcast scheduling with deadlines

We study an on-line broadcast scheduling problem in which requests have deadlines, and the objective is to maximize the weighted throughput, i.e., the weighted total length of the satisfied requests. For the case where all requested pages have the same length, we present an online deterministic algorithm named BAR and prove that it is 4.56-competitive. This improves the previous algorithm of (Kim, J.-H., Chwa, K.-Y. in Theor. Comput. Sci. 325(3):479–488, 2004) which is shown to be 5-competitive by (Chan, W.-T., et al. in Lecture Notes in Computer Science, vol. 3106, pp. 210–218, 2004). In the case that pages may have different lengths, we give a ( )-competitive algorithm where Δ is the ratio of maximum to minimum page lengths. This improves the (4Δ+3)-competitive algorithm of (Chan, W.-T., et al. in Lecture Notes in Computer Science, vol. 3106, pp. 210–218, 2004). We also prove an almost matching lower bound of Ω(Δ/log Δ). Furthermore, for small values of Δ we give better lower bounds. The work described in this paper was fully supported by grants from the Research Grants Council of the Hong Kong SAR, China [CityU 1198/03E, HKU 7142/03E, HKU 5172/03E], an NSF Grant of China [No. 10371094], and a Nuffield Foundation Grant of UK [NAL/01004/G].     

All-Pairs Shortest Paths with Real Weights in <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis><Superscript>3</Superscript>/log <Emphasis Type="Italic">n</Emphasis>) Time

We describe an O(n ³/log n)-time algorithm for the all-pairs-shortest-paths problem for a real-weighted directed graph with n vertices. This slightly improves a series of previous, slightly subcubic algorithms by Fredman (SIAM J. Comput. 5:49–60, 1976), Takaoka (Inform. Process. Lett. 43:195–199, 1992), Dobosiewicz (Int. J. Comput. Math. 32:49–60, 1990), Han (Inform. Process. Lett. 91:245–250, 2004), Takaoka (Proc. 10th Int. Conf. Comput. Comb., Lect. Notes Comput. Sci., vol. 3106, pp. 278–289, Springer, 2004), and Zwick (Proc. 15th Int. Sympos. Algorithms and Computation, Lect. Notes Comput. Sci., vol. 3341, pp. 921–932, Springer, 2004). The new algorithm is surprisingly simple and different from previous ones. A preliminary version of this paper appeared in Proc. 9th Workshop Algorithms Data Struct. (WADS), Lect. Notes Comput. Sci., vol. 3608, pp. 318–324, Springer, 2005.     

Planar Polyline Drawings via Graph Transformations

We study the problem of transforming plane triangulations into irreducible triangulations, which are plane graphs with a quadrangular exterior face, triangular interior faces and no separating triangles. Our linear time transformation reveals important relations between the minimum Schnyder’s realizers of plane triangulations (Bonichon et al., Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, vol. 2607, pp. 499–510, Springer, Berlin, 2003; Research Report RR-1279-02, LaBRI, University of Bordeaux, France; Brehm, Diploma thesis, FB Mathematik und Informatik, Freie Universität Berlin, 2000) and the transversal structures of irreducible triangulations (Fusy, Proceedings of 13th International Symposium on Graph Drawing, Lecture Notes in Computer Science, vol. 3843, pp. 177–188, Springer, Berlin, 2005; He, SIAM J. Comput. 22:1218–1226, 1993). The transformation morphs a 3-connected plane graph into an internally 4-connected plane graph. Therefore some of the graph algorithms designed specifically for 4-connected plane graphs can be applied to 3-connected plane graphs indirectly. As an example of such applications, we present a linear time algorithm that produces a planar polyline drawing for a plane graph with n vertices in a grid of size bounded by W×H, where $W\leq\lfloor\frac{2n-2}{3}\rfloorWe study the problem of transforming plane triangulations into irreducible triangulations, which are plane graphs with a quadrangular exterior face, triangular interior faces and no separating triangles. Our linear time transformation reveals important relations between the minimum Schnyder’s realizers of plane triangulations (Bonichon et al., Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, vol. 2607, pp. 499–510, Springer, Berlin, 2003; Research Report RR-1279-02, LaBRI, University of Bordeaux, France; Brehm, Diploma thesis, FB Mathematik und Informatik, Freie Universit?t Berlin, 2000) and the transversal structures of irreducible triangulations (Fusy, Proceedings of 13th International Symposium on Graph Drawing, Lecture Notes in Computer Science, vol. 3843, pp. 177–188, Springer, Berlin, 2005; He, SIAM J. Comput. 22:1218–1226, 1993). The transformation morphs a 3-connected plane graph into an internally 4-connected plane graph. Therefore some of the graph algorithms designed specifically for 4-connected plane graphs can be applied to 3-connected plane graphs indirectly. As an example of such applications, we present a linear time algorithm that produces a planar polyline drawing for a plane graph with n vertices in a grid of size bounded by W×H, where W ￡ ?\frac2n-23?W\leq\lfloor\frac{2n-2}{3}\rfloor , and W+H ￡ ?\frac4n-43?W+H\leq\lfloor \frac{4n-4}{3}\rfloor . It uses at most ?\frac2n-53?\lfloor\frac{2n-5}{3}\rfloor bends, and each edge uses at most one bend. Our algorithm is area optimal. Compared with the existing area optimal polyline drawing algorithm proposed in Bonichon et al. (Proceedings of the 28th International Workshop on Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science, vol. 2573, pp. 35–46, Springer, Berlin, 2002), our algorithm uses a smaller number of bends. Their bend bound is (n−2).     

U-multimedia framework: a secure and intelligent multimedia service framework based on context information in U-home

In the last few years, intelligent secured multimedia services play a vital role along with ubiquitous home environment (Park et al. in Lecture Notes in Computer Science, vol. 4097, pp. 660–670, [2006]; Lecture Notes in Computer Science, vol. 4159, pp. 893–901, [2006]; IEICE Trans. Inf. Syst. E89-D(12):2831–2837, [2006]; Lecture Notes in Artificial Intelligence, vol. 4252, pp. 777–784, [2006]; Lecture Notes in Artificial Intelligence, vol. 3801, pp. 313–320, [2005]). There are certain constrains and limitations in providing effective and efficient services in U-home. The mechanism and applications are integrated to realize such services. Three different kinds of ubiquitous multimedia services are proposed in the framework. Based on the temporal and spatial context information, the surrounding situations are recognized. The contexts are collected and well analyzed with the preconditions to provide the final services. The proposed framework provides efficient services in the multimedia based deices based on the current context information.

A modular approach to shared-memory consensus,with applications to the probabilistic-write model

We show that consensus can be solved by an alternating sequence of adopt-commit objects (Gafni in Proceedings of the seventeenth annual ACM symposium on principles of distributed computing, pp 143–152, 1998; Alistarh et al. in ISAAC, Lecture notes in computer science, vol 5878. Springer, Berlin, pp 943–953, 2009), which detect agreement, and conciliators, which ensure agreement with some probability. We observe that most known randomized consensus algorithms have this structure. We give a deterministic implementation of an m-valued adopt-commit object for an unbounded number of processes that uses lg m + Θ(log log m) space and individual work. We also give a randomized conciliator for any number of values in the probabilistic-write model with n processes that guarantees agreement with constant probability while using one multi-writer register, O(log n) expected individual work, and Θ(n) expected total work. Combining these objects gives a consensus protocol for the probabilistic-write model that uses O(log m + log n) individual work and O(n log m) total work. No previous protocol in this model uses sublinear individual work or linear total work for constant m.     

Non-Uniform Reductions

We study properties of non-uniform reductions and related completeness notions. We strengthen several results of Hitchcock and Pavan (ICALP (1), Lecture Notes in Computer Science, vol. 4051, pp. 465–476, Springer, 2006) and give a trade-off between the amount of advice needed for a reduction and its honesty on NEXP. We construct an oracle relative to which this trade-off is optimal. We show, in a more systematic study of non-uniform reductions, among other things that non-uniformity can be removed at the cost of more queries. In line with Post’s program for complexity theory (Buhrman and Torenvliet in Bulletin of the EATCS 85, pp. 41–51, 2005) we connect such ‘uniformization’ properties to the separation of complexity classes.     

Digitally Continuous Multivalued Functions, Morphological Operations and Thinning Algorithms

In a recent paper (Escribano et al. in Discrete Geometry for Computer Imagery 2008. Lecture Notes in Computer Science, vol. 4992, pp. 81–92, 2008) we have introduced a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach, which uses multivalued functions, provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions.     

The Directed Orienteering Problem

This paper studies vehicle routing problems on asymmetric metrics. Our starting point is the directed k-TSP problem: given an asymmetric metric (V,d), a root r∈V and a target k≤|V|, compute the minimum length tour that contains r and at least k other vertices. We present a polynomial time O(\fraclog² nloglogn·logk)O(\frac{\log^{2} n}{\log\log n}\cdot\log k)-approximation algorithm for this problem. We use this algorithm for directed k-TSP to obtain an O(\fraclog² nloglogn)O(\frac{\log^{2} n}{\log\log n})-approximation algorithm for the directed orienteering problem. This answers positively, the question of poly-logarithmic approximability of directed orienteering, an open problem from Blum et al. (SIAM J. Comput. 37(2):653–670, 2007). The previously best known results were quasi-polynomial time algorithms with approximation guarantees of O(log ² k) for directed k-TSP, and O(log n) for directed orienteering (Chekuri and Pal in IEEE Symposium on Foundations in Computer Science, pp. 245–253, 2005). Using the algorithm for directed orienteering within the framework of Blum et al. (SIAM J. Comput. 37(2):653–670, 2007) and Bansal et al. (ACM Symposium on Theory of Computing, pp. 166–174, 2004), we also obtain poly-logarithmic approximation algorithms for the directed versions of discounted-reward TSP and vehicle routing problem with time-windows.     

Deterministically Isolating a Perfect Matching in Bipartite Planar Graphs

We present a deterministic Logspace procedure, which, given a bipartite planar graph on n vertices, assigns O(log n) bits long weights to its edges so that the minimum weight perfect matching in the graph becomes unique. The Isolation Lemma as described in Mulmuley et al. (Combinatorica 7(1):105–131, 1987) achieves the same for general graphs using randomness, whereas we can do it deterministically when restricted to bipartite planar graphs. As a consequence, we reduce both decision and construction versions of the perfect matching problem in bipartite planar graphs to testing whether a matrix is singular, under the promise that its determinant is 0 or 1, thus obtaining a highly parallel SPL\mathsf{SPL} algorithm for both decision and construction versions of the bipartite perfect matching problem. This improves the earlier known bounds of non-uniform SPL\mathsf{SPL} by Allender et al. (J. Comput. Syst. Sci. 59(2):164–181, 1999) and NC\mathsf{NC} ² by Miller and Naor (SIAM J. Comput. 24:1002–1017, 1995), and by Mahajan and Varadarajan (Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing (STOC), pp. 351–357, 2000). It also rekindles the hope of obtaining a deterministic parallel algorithm for constructing a perfect matching in non-bipartite planar graphs, which has been open for a long time. Further we try to find the lower bound on the number of bits needed for deterministically isolating a perfect matching. We show that our particular method for isolation will require Ω(log n) bits. Our techniques are elementary.     

Improved Approximation Algorithms for Maximum Resource Bin Packing and Lazy Bin Covering Problems

In this paper, we study two variants of the bin packing and covering problems called Maximum Resource Bin Packing (MRBP) and Lazy Bin Covering (LBC) problems, and present new approximation algorithms for them. For the offline MRBP problem, the previous best known approximation ratio is \frac65\frac{6}{5} (=1.2) achieved by the classical First-Fit-Increasing (FFI) algorithm (Boyar et al. in Theor. Comput. Sci. 362(1–3):127–139, 2006). In this paper, we give a new FFI-type algorithm with an approximation ratio of \frac8071\frac{80}{71} (≈1.12676). For the offline LBC problem, it has been shown in Lin et al. (COCOON, pp. 340–349, 2006) that the classical First-Fit-Decreasing (FFD) algorithm achieves an approximation ratio of \frac7160\frac{71}{60} (≈1.18333). In this paper, we present a new FFD-type algorithm with an approximation ratio of \frac1715\frac{17}{15} (≈1.13333). Our algorithms are based on a pattern-based technique and a number of other observations. They run in near linear time (i.e., O(nlog n)), and therefore are practical.     

Incremental Branching Programs

We propose a new model of restricted branching programs specific to solving GEN problems, which we call incremental branching programs. We show that syntactic incremental branching programs capture previously studied models of computation for the problem GEN, namely marking machines (Cook, S.A. in J. Comput. Syst. Sci. 9(3):308–316, 1974) and Poon’s extension (Proc. of the 34th IEEE Symp. on the Foundations of Computer Science, pp. 218–227, 1993) of jumping automata on graphs (Cook, S.A., Rackoff, C.W. in SIAM J. Comput. 9:636–652, 1980). We then prove exponential size lower bounds for our syntactic incremental model, and for some other variants of branching program computation for GEN. We further show that nondeterministic syntactic incremental branching programs are provably stronger than their deterministic counterpart when solving a natural NL-complete GEN sub-problem. It remains open if syntactic incremental branching programs are as powerful as unrestricted branching programs for GEN problems. A preliminary version of this paper appears as (Gál, A., Koucky, M., McKenzie, P., Incremental branching programs, in Proc. of the 2006 Computer Science in Russia Conference CSR06. Lecture Notes in Computer Science, vol. 3967, pp. 178–190, 2006). A. Gal supported in part by NSF Grant CCF-0430695 and an Alfred P. Sloan Research Fellowship. M. Koucky did part of this work while being a postdoctoral fellow at McGill University, Canada and at CWI, Amsterdam, Netherlands. Supported in part by NWO vici project 2004–2009, project No. 1M0021620808 of MŠMT ČR, grants 201/07/P276, 201/05/0124 of GA ČR, and Institutional Research Plan No. AV0Z10190503. P. McKenzie supported by the NSERC of Canada and the (Québec) FQRNT.     

Applying Approximate Counting for Computing the Frequency Moments of Long Data Streams

This paper takes up a remark in the well-known paper of Alon, Matias, and Szegedy (J. Comput. Syst. Sci. 58(1):137–147, 1999) about the computation of the frequency moments of data streams and shows in detail how any F _k with k≥1 can be approximately computed using space O(km ^1−1/k (k+log m+log log  n)) based on approximate counting. An important building block for this, which may be interesting in its own right, is a new approximate variant of reservoir sampling using space O(log log  n) for constant error parameters.     

The effect of malformed tiles on tile assemblies within the kinetic tile assembly model

Many different constructions of proofreading tile sets have been proposed in the literature to reduce the effect of deviations from ideal behaviour of the dynamics of the molecular tile self-assembly process. In this paper, we consider the effect on the tile assembly process of a different kind of non-ideality, namely, imperfections in the tiles themselves. We assume a scenario in which some small proportion of the tiles in a tile set are “malformed”. We study, through simulations, the effect of such malformed tiles on the self-assembly process within the kinetic Tile Assembly Model (kTAM). Our simulation results show that some tile set constructions show greater error-resilience in the presence of malformed tiles than others. For example, the 2- and 3-way overlay compact proofreading tile sets of Reif et al. (DNA Computing 10, Lecture Notes in Computer Science, vol 3384. Springer, 2005) are able to handle malformed tiles quite well. On the other hand, the snaked proofreading tile set of Chen and Goel (DNA Computing 10, Lecture Notes in Computer Science, vol 3384. Springer, 2005) fails to form even moderately sized tile assemblies when malformed tiles are present. We show how the Chen–Goel construction may be modified to yield new snaked proofreading tile sets that are resilient not only to errors intrinsic to the assembly process, but also to errors caused by malformed tiles.     

Investigating the usability of real-time scheduling theory with the Cheddar project

This article deals with real-time critical systems modelling and verification. Real-time scheduling theory provides algebraic methods and algorithms in order to make timing constraints verifications of these systems. Nevertheless, many industrial projects do not perform analysis with real-time scheduling theory even if demand for use of this theory is large and the industrial application field is wide (avionics, aerospace, automotive, autonomous systems, …). The Cheddar project investigates why real-time scheduling theory is not used and how its usability can be increased. The project was launched at the University of Brest in 2002. In Lecture Notes on Computer Sciences, vol. 5026, pp. 240–253, 2008, we have presented a short overview of this project. This article is an extended presentation of the Cheddar project, its contributions and also its ongoing works.     

A High Order Compact Scheme for the Pure-Streamfunction Formulation of the Navier-Stokes Equations

In this paper we continue the study, which was initiated in (Ben-Artzi et al. in Math. Model. Numer. Anal. 35(2):313–303, 2001; Fishelov et al. in Lecture Notes in Computer Science, vol. 2667, pp. 809–817, 2003; Ben-Artzi et al. in J. Comput. Phys. 205(2):640–664, 2005 and SIAM J. Numer. Anal. 44(5):1997–2024, 2006) of the numerical resolution of the pure streamfunction formulation of the time-dependent two-dimensional Navier-Stokes equation. Here we focus on enhancing our second-order scheme, introduced in the last three afore-mentioned articles, to fourth order accuracy. We construct fourth order approximations for the Laplacian, the biharmonic and the nonlinear convective operators. The scheme is compact (nine-point stencil) for the Laplacian and the biharmonic operators, which are both treated implicitly in the time-stepping scheme. The approximation of the convective term is compact in the no-leak boundary conditions case and is nearly compact (thirteen points stencil) in the case of general boundary conditions. However, we stress that in any case no unphysical boundary condition was applied to our scheme. Numerical results demonstrate that the fourth order accuracy is actually obtained for several test-cases.     

Lower Bounds for Kernelizations and Other Preprocessing Procedures

We first present a method to rule out the existence of parameter non-increasing polynomial kernelizations of parameterized problems under the hypothesis P≠NP. This method is applicable, for example, to the problem Sat parameterized by the number of variables of the input formula. Then we obtain further improvements of corresponding results in (Bodlaender et al. in Lecture Notes in Computer Science, vol. 5125, pp. 563–574, Springer, Berlin, 2008; Fortnow and Santhanam in Proceedings of the 40th ACM Symposium on the Theory of Computing (STOC’08), ACM, New York, pp. 133–142, 2008) by refining the central lemma of their proof method, a lemma due to Fortnow and Santhanam. In particular, assuming that the polynomial hierarchy does not collapse to its third level, we show that every parameterized problem with a “linear OR” and with NP-hard underlying classical problem does not have polynomial self-reductions that assign to every instance x with parameter k an instance y with |y|=k ^O(1)⋅|x|^1−ε (here ε is any given real number greater than zero). We give various applications of these results. On the structural side we prove several results clarifying the relationship between the different notions of preprocessing procedures, namely the various notions of kernelizations, self-reductions and compressions.     

Sublinear Fully Distributed Partition with Applications

We present new efficient deterministic and randomized distributed algorithms for decomposing a graph with n nodes into a disjoint set of connected clusters with radius at most k−1 and having O(n ^1+1/k ) intercluster edges. We show how to implement our algorithms in the distributed CONGEST\mathcal{CONGEST} model of computation, i.e., limited message size, which improves the time complexity of previous algorithms (Moran and Snir in Theor. Comput. Sci. 243(1–2):217–241, 2000; Awerbuch in J. ACM 32:804–823, 1985; Peleg in Distributed Computing: A Locality-Sensitive Approach, 2000) from O(n) to O(n ^1−1/k ). We apply our algorithms for constructing low stretch graph spanners and network synchronizers in sublinear deterministic time in the CONGEST\mathcal{CONGEST} model.     

Space Efficient Dynamic Orthogonal Range Reporting

In this paper we present new space efficient dynamic data structures for orthogonal range reporting. The described data structures support planar range reporting queries in time O(log n+klog log (4n/(k+1))) and space O(nlog log n), or in time O(log n+k) and space O(nlog  ^ε n) for any ε>0. Both data structures can be constructed in O(nlog n) time and support insert and delete operations in amortized time O(log ² n) and O(log nlog log n) respectively. These results match the corresponding upper space bounds of Chazelle (SIAM J. Comput. 17, 427–462, 1988) for the static case. We also present a dynamic data structure for d-dimensional range reporting with search time O(log  ^d−1 n+k), update time O(log  ^d n), and space O(nlog  ^d−2+ε n) for any ε>0. The model of computation used in our paper is a unit cost RAM with word size log n. A preliminary version of this paper appeared in the Proceedings of the 21st Annual ACM Symposium on Computational Geometry 2005. Work partially supported by IST grant 14036 (RAND-APX).     

Approximation Algorithms for Reconstructing the Duplication History of Tandem Repeats

Computing the duplication history of a tandem repeated region is an important problem in computational biology (Fitch in Genetics 86:623–644, 1977; Jaitly et al. in J. Comput. Syst. Sci. 65:494–507, 2002; Tang et al. in J. Comput. Biol. 9:429–446, 2002). In this paper, we design a polynomial-time approximation scheme (PTAS) for the case where the size of the duplication block is 1. Our PTAS is faster than the previously best PTAS in Jaitly et al. (J. Comput. Syst. Sci. 65:494–507, 2002). For example, to achieve a ratio of 1.5, our PTAS takes O(n ⁵) time while the PTAS in Jaitly et al. (J. Comput. Syst. Sci. 65:494–507, 2002) takes O(n ¹¹) time. We also design a ratio-6 polynomial-time approximation algorithm for the case where the size of each duplication block is at most 2. This is the first polynomial-time approximation algorithm with a guaranteed ratio for this case. Part of work was done during a Z.-Z. Chen visit at City University of Hong Kong.     

Checking extended <Emphasis Type="Italic">CTL</Emphasis> properties using guarded quotient structures

We extend CTL logic to a logic called COUNT CTL (CCTL) for specifying properties of concurrent programs with large number of processes. We present a model checking algorithm for symmetric or partially symmetric systems when their correctness specification is given in CCTL. The model-checking algorithm employs Guarded Quotient Structures introduced by Sistla and Godefroid (Lecture Notes in Comput. Sci., vol. 2102, 2001). The GQS structures can be succinct representations for the reachability graphs of partially symmetric or even asymmetric systems. Our algorithm exploits state symmetries for fast evaluation. The algorithm is top down in nature, and automatically incorporates formula decomposition and sub-formula tracking. This paper is supported in part by the NSF grants CCR-9988884, CCR-0205365.