Alexander Golynski

Rank/select operations on large alphabets: a tool for text indexing

We consider a generalization of the problem of supporting rank and select queries on binary strings. Given a string of length <i>n</i> from an alphabet of size σ, we give the first representation that supports <i>rank</i> and <i>access</i> operations in <i>O</i>(lg lg σ) time, and <i>select</i> in <i>O</i>(1) time while using the optimal <i>n</i> lg σ + <i>o</i>(<i>n</i> lg σ) bits. The best known previous structure for this problem required <i>O</i>(lg σ) time, for general values of σ. Our results immediately improve the search times of a variety of text indexing methods.

On the size of succinct indices

A succinct data structure occupies an amount of space that is close to the information-theoretic minimum plus an additional term. The latter is not necessarily a lower-order term and, in several cases, completely dominates the space occupancy both in theory and in practice. In this paper, we present several solutions to partially overcome this problem, introducing new techniques of independent interest that allow us to improve over previously known upper and lower bounds.

An Efficient Bounds Consistency Algorithm for the Global Cardinality Constraint

Previous studies have demonstrated that designing special purpose constraint propagators can significantly improve the efficiency of a constraint programming approach. In this paper we present an efficient algorithm for bounds consistency propagation of the generalized cardinality constraint (gcc). Using a variety of benchmark and random problems, we show that on some problems our bounds consistency algorithm can dramatically outperform existing state-of-the-art commercial implementations of constraint propagators for the gcc. We also present a new algorithm for domain consistency propagation of the gcc which improves on the worst-case performance of the best previous algorithm for problems that occur often in applications.

Longest increasing subsequences in sliding windows

We consider the problem of finding the longest increasing subsequence in a sliding window over a given sequence (LISW). We propose an output-sensitive data structure that solves this problem in time O(n log log n+OUTPUT) for a sequence of n elements. This data structure substantially improves over the naive generalization of the longest increasing subsequence algorithm and in fact produces an output-sensitive optimal solution.

On the Redundancy of Succinct Data Structures

The redundancyof a succinct data structure is the difference between the space it uses and the appropriate information-theoretic lower bound. We consider the problem of representing binary sequences and strings succinctly using small redundancy. We improve the redundancy required to support the important operations of rank and select efficiently for binary sequences and for strings over small alphabets. We also show optimal density-sensitiveupper and lower bounds on the redundancy for systematicencodings of binary sequences.

Optimal strategies for the list update problem under the MRM alternative cost model

We give an explicit representation for the offline optimum strategy for list update under the MRM model of Martinez and Roura [C. Martinez, S. Roura, On the competitiveness of the move-to-front rule, Theoret. Comput. Sci. 242 (1-2) (2000) 3130-325] and Munro [J.I. Munro, On the competitiveness of linear search, in: Proc. 8th Annual European Symposium on Algorithms (ESA 2000), in: Lecture Notes in Comput. Sci., vol. 1879, 2000, pp. 338-345] and give an O(n^3) algorithm to compute it. This is in contrast to the standard model of Sleator and Tarjan [D.D. Sleator, R.E. Tarjan, Amortized efficiency of list update and paging rules, Commun. ACM 28 (2) (1985) 202-208] under which computing the offline optimum was shown to be NP-hard [C. Ambuhl, Offline list update is NP-hard, in: Proc. 8th Annual European Symposium on Algorithms (ESA 2000), in: Lecture Notes in Comput. Sci., vol. 1879, 2000, pp. 42-51]. This algorithm follows from a new characterization theorem for realizable visiting sequences in the MRM model.

Optimal Dynamic Video-on-Demand Using Adaptive Broadcasting

We consider the transmission of a movie over a broadcast network to support several viewers who start watching at arbitrary times, after a wait of at most t wait minutes. A recent approach called harmonic broadcasting optimally solves the case of many viewers watching a movie using a constant amount of bandwidth. We consider the more general setting and v changes dynamically. A natural objective is to minimize the amount of resources required to achieve this task. We introduce two natural measures of resource consumption and performance—total bandwidth usage and maximum momentary bandwidth usage—and propose strategies which are optimal for each of them. In particular, we show that an adaptive form of pyramid broadcasting is optimal for both measures simultaneously, up to constant factors. We also show that the maximum throughput for a fixed network bandwidth cannot be obtained by any online strategy.

On the complexity of routing in wireless multihop network

Wireless backbone networks represent an attractive alternative to wired networks in situations where cost, speed of deployment, and flexibility in network design are important. In typical configurations, users connect to wireless routers of the backbone network, which then redirect the traffic to one of the existing network gateways. To improve the network performance, wireless backbone routers redirect their traffic to the network gateways so as to maximize amount of traffic that can be supported by the network. In this paper, we prove that this problem is NP-hard as a result of the wireless interference that is created between geographically close transmission links. We consequently design and investigate the performance of interference-aware algorithms suitable for multi-channel environments against more traditional routing approaches. We evaluate their performance in simulated environments based on data taken from existing networks, and show that interference-based heuristics exhibit advantageous performance in non-uniform deployment.

Bandwidth reduction for video-on-demand broadcasting using secondary content insertion

An optimal broadcasting scheme under the presence of secondary content (i.e. advertisements) is proposed. The proposed scheme works both for movies encoded in a Constant Bit Rate (CBR) or a Variable Bit Rate (VBR) format. It is shown experimentally that secondary content in movies can make Video-on-Demand (VoD) broadcasting systems more efficient. An efficient algorithm is given to compute the optimal broadcasting schedule with secondary content, which in particular significantly improves over the best previously known algorithm for computing the optimal broadcasting schedule without secondary content.