40338736
The maximum resource bin packing problem
Usually, for bin packing problems, we try to minimize the number of bins used or in the case of the dual bin packing problem, maximize the number or total size of accepted items. This paper presents results for the opposite problems, where we would like to maximize the number of bins used or minimize the number or total size of accepted items. We consider off-line and on-line variants of the problems.For the off-line variant, we require that there be an ordering of the bins, so that no item in a later bin fits in an earlier bin. We find the approximation ratios of two natural approximation algorithms, First-Fit-Increasing and First-Fit-Decreasing for the maximum resource variant of classical bin packing.For the on-line variant, we define maximum resource variants of classical and dual bin packing. For dual bin packing, no on-line algorithm is competitive. For classical bin packing, we find the competitive ratio of various natural algorithms.We study the general versions of the problems as well as the parameterized versions where there is an upper bound of 1/k on the item sizes, for some integer k.
80794
Efficient Rebalancing of Chromatic Search Trees
Chromatic trees were defined by Nurmi and Soisalon-Soininen, as a new type of binary search tree for databases. The aim is to improve runtime performance by allowing a greater degree of concurrency, which, in turn, is obtained by uncoupling updating from rebalancing. This also allows rebalancing to be postponed completely or partially until after peak working hours. The advantages of the proposal of Nurmi and Soisalon-Soininen are quite significant, but there are definite problems with it. First, they give no explicit upper bound on the complexity of their algorithm. Second, some of their rebalancing operations can be applied many more times than necessary. Third, some of their operations, when removing one problem, create another. We define a new set of rebalancing operations which we prove give rise to at most @?log"2(N+1)@?-1 rebalancing operations per insertion and at most @?log"2(N+1)@?-2 rebalancing operations per deletion, where N is the maximum size the tree could ever have, given its initial size and the number of insertions performed. Most of these rebalancing operations, in fact, do no restructuring; they simply move weights around. The number of operations which actually change the structure of the tree is at most one per update.
30882911
Complexity of Layered Binary Search Trees with Relaxed Balance
When search trees are made relaxed, balance constraints are weakened such that updates can be made without immediate rebalancing. This can lead to a speed-up in some circumstances. However, the weakened balance constraints also make it more challenging to prove complexity results for relaxed structures.In our opinion, one of the simplest and most intuitive presentations of balanced search trees has been given via layered trees. We show that relaxed layered trees are among the best of the relaxed structures. More precisely, rebalancing is worst-case logarithmic and amortized constant per update, and restructuring is worst-case constant per update.
19914316
Extending the Accommodating Function
The applicability of the accommodating function, a relatively new measure for the quality of on-line algorithms, is extended. If a limited amount n of some resource is available, the accommodating function A(?) is the competitive ratio when input sequences are restricted to those for which the amount ?n of resources suffices for an optimal off-line algorithm. The accommodating function was originally used only for ? ? 1. We focus on ? < 1, observe that the function now appears interesting for a greater variety of problems, and use it to make new distinctions between known algorithms and to find new ones.
34233329
Search Trees with Relaxed Balance and Near-Optimal Height
We introduce the relaxed k-tree, a search tree with relaxed balance and a height bound, when in balance, of (1 + Ɛ) log2 n + 1, for any Ɛ > 0. The rebalancing work is amortized O(1/Ɛ) per update. This is the first binary search tree with relaxed balance having a height bound better than c ċ log2 n for a fixed constant c. In all previous proposals, the constant is at least 1/ log2 Φ > 1.44, where Φ is the golden ratio. 
 
As a consequence, we can also define a standard (non-relaxed) k-tree with amortized constant rebalancing per update, which is an improvement over the original definition. 
 
Search engines based on main-memory databases with strongly fluctuating workloads are possible applications for this line of work.
6986183
Efficient Simplification of Bisimulation Formulas
The problem of checking or optimally simplifying bisimulation formulas is likely to be computationally very hard. We take a different view at the problem: we set out to define a very fast algorithm, and then see what we can obtain. Sometimes our algorithm can simplify a formula perfectly, sometimes it cannot. However, the algorithm is extremely fast and can, therefore, be added to formula-based bisimulation model checkers at practically no cost. When the formula can be simplified by our algorithm, this can have a dramatic positive effect on the better, but also more time consuming, theorem provers which will finish the job.
6620376
Time-abstracted Bisimulation: Implicit Specifications and Decidability
In the last few years a number of real-time process calculi have emerged with the purpose of capturing important quantitative aspects of real-time systems. In addition, a number of process equivalences sensitive to time-quantities have been proposed, among these the notion of timed (bisimulation) equivalence in [RR86, DS89, HR91, BB89, NRSV90, MT90, Wan91b].
1222159
The Fork Calculus
The Fork Calculus FC presents a theory of communicating systems in family with CCS, but it differs in the way that processes are put in parallel. In CCS there is a binary parallel operator |, and two processes p and q are put in parallel by p|q. In FC there is a unary fork operator, and a process p is activated to "run in parallel with the rest of the program" by fork(p). An operational semantics is defined, and a congruence relation between processes is suggested. In addition, a sound and complete axiomatisation of the congruence is provided. FC has been developed during an investigation of the programming language CML, an extension of ML with concurrency primitives, amongst them a fork operator.
16545835
UPPAAL Implementation Secrets
In this paper we present the continuous and on-going development of datastructures and algorithms underlying the verification engine of the tool UPPAAL. In particular, we review the datastructures of Difference Bounded Matrices, Minimal Constraint Representation and Clock Difference Diagrams used in symbolic state-space representation and -analysis for real-time systems.In addition we report on distributed versions of the tool, and outline the design and experimental results for new internal datastructures to be used in the next generation of UPPAAL.Finally, we mention work on complementing methods involving acceleration, abstraction and compositionality.
9243889
Generality in design and compositional verification usingTav
It is a well recognised fact that design errors in parallel systems are often hard to identify—due to their non-deterministic nature. It is therefore important that designs are analysedbefore the implementation phase begins. Even small parallel systems often have an intrinsic structure which is hard to fully understand, and the support of automated tools is therefore indispensable. In order to be of any practical use, the computations of such tools must be (polynomially) effective in terms of the system size, and furthermore it must be possible to reason about the system in terms of the properties of its (parallel) components—in order to avoid state-space explosion. Finally, the well-establishedstepwise refinement design strategy must be supported.The tools of theTav-system fulfil the above requirements, and in this paper we present its features by analysing a simple transmission protocol. The cornerstone of the system is the theory ofmodal transition systems, which allows for efficient decidability, stepwise refinement, and compositionality. The theory also supports a unique feature ofTav, namely the ability to provide explanations in case of design errors.
9332520
Compact Data Structures and State-Space Reduction for Model-Checking Real-Time Systems
During the past few years, a number of verification tools have been developed for real-time systems in the framework of timed automata. One of the major problems in applying these tools to industrial-sized systems is the huge memory-usage for the exploration of the state-space of a network (or product) of timed automata, as the model-checkers must keep information about not only the control structure of the automata but also the clock values specified by clock constraints. In this paper, we present a compact data structure for representing clock constraints. The data structure is based on an O(n3) algorithm which, given a constraint system over real-valued variables consisting of bounds on differences, constructs an equivalent system with a minimal number of constraints. In addition, we have developed an on-the-fly reduction technique to minimize the space-usage. Based on static analysis of the control structure of a network of timed automata, we are able to compute a set of symbolic states that cover all the dynamic loops of the network in an on-the-fly searching algorithm, and thus ensure termination in reachability analysis. The two techniques and their combination have been implemented in the tool UPPAAL. Our experimental results demonstrate that the techniques result in truly significant space-reductions: for six examples from the literature, the space saving is between 75% and 94%, and in (nearly) all examples time-performance is improved. Noteworthy is also the observation that the two techniques are completely orthogonal.