We provide a rather general asymptotic scheme for combinatorial parameters that asymptotically follow a discrete double-exponential distribution. It is based on analysing generating functions Gh(z) whose dominant singularities converge to a certain value at an exponential rate. This behaviour is typically found by means of a bootstrapping approach. Our scheme is illustrated by a number of class...

One popular and efficient scheme for solving combinatorial optimization problems over graphical models exactly is depth-first Branch and Bound. However, when the algorithm exploits problem decomposition using AND/OR search spaces, its anytime behavior breaks down. This article 1) analyzes and demonstrates this inherent conflict between effective exploitation of problem decomposition (through AN...

In this paper, we introduce an interesting tool to construct the k-out-of-N threshold signature schemes, which we call as message block sharing. To achieve our goal, we first separate an original message with large size into multiple message blocks with random size. Then, we give a partial number of message blocks to N signers with combinatorial approach. We propose an example scheme with our t...

Following the work of Okounkov-Pandharipande [OP1, OP2], Diaconescu [D], and the recent work [CDKM] studying the equivariant quantum cohomology QH∗ (C∗)2(Hilbn) of the Hilbert scheme and the relative Donaldson-Thomas theory of P ×C, we establish a connection between the J-function of the Hilbert scheme and a certain combinatorial identity in two variables. This identity is then generalized to a...

This paper deals with performance evaluation of rasterto-vector conversion algorithms. We briefly review the past work, and focus our attention on a method proposed by Phillips and Chhabra [6]. We show that the matching algorithm used in their method can be improved by introducing new metrics and reformulating the problem as a combinatorial optimization scheme. Improvements brought by our appro...

The concept of symmetric recursive algorithm leads to new, sdimensional spline spaces. We present a general scheme for constructing a collection of multivariate S-splines with k-l continuous derivatives whose linear span contains all polynomials of degree at most k . This scheme is different from the one developed earlier by Dahmen and Micchelli and, independently, by Höllig, which was based on...

Local rank modulation scheme was suggested recently for representing information in flash memories in order to overcome drawbacks of rank modulation. For 0 < s ≤ t ≤ n with s divides n, an (s, t, n)-LRM scheme is a local rank modulation scheme where the n cells are locally viewed cyclically through a sliding window of size t resulting in a sequence of small permutations which requires less comp...

The combinatorial effect of an exponential backoff scheme and retransmission cutoff on the stability of frequencyhopping slotted ALOHA systems with finite population is investigated in terms of the catastrophe theory. In the systems, the packet retransmission probabilities are geometrically distributed with respect to the number of experienced unsuccessful transmissions and a packet will be dis...

Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes constitutes an expensive task because of a combinatorial explosion in the complex size. For n points in R, we present a scheme to construct a 3 √ 2approximation of the multi-scale filtration of the L∞-Rips complex, which extends to a O(d0.25)approximation of the...

Two novel suboptimal algorithms for mutual exclusion in distributed systems are presented. One is based on the modi cation of Maekawa's grid based quorum scheme. The size of quorums is approximately p 2 p N where N is the number of sites in a network, as compared to 2 p N of the original method. The method is simple and geometrically evident. The second one is based on the idea of di erence set...