2795860
On-line seat reservations via off-line seating arrangements
When reservations are made to for instance a train, it is an on-line problem to accept or reject, i.e., decide if a person can be fitted in given all earlier reservations. However, determining a seating arrangement, implying that it is safe to accept, is an off-line problem with the earlier reservations and the current one as input. We develop algorithms with optimal running time to handle problems of this nature.
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.
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.
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.
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.
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.
5706272
The Power of Reachability Testing for Timed Automata
In this paper we provide a complete characterization of the class of properties of (networks of) timed automata for which model checking can be reduced to reachability checking in the context of testing automata.
6559743
A refinement logic for 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 |, whereas FC contains a unary fork operator. We provide FC with an operational semantics, together with a congruence relation between processes. Further, a refinement logic for program specification and design is presented. In this logic it is possible to freely mix programming constructs with specification constructs, thereby allowing us to define a compositional proof system. The proof rules of this system are applied to a non-trivial example.
8200399
Compositional and symbolic model-checking of real-time systems
Efficient automatic model-checking algorithms for real-time systems have been obtained in recent years based on the state-region graph technique of Alur, Courcoubetis and Dill (1990). However, these algorithms are faced with two potential types of explosion arising from parallel composition: explosion in the space of control nodes, and explosion in the region space over clock-variables. In this paper we attack these explosion problems by developing and combining compositional and symbolic model-checking techniques. The presented techniques provide the foundation for a new automatic verification tool UPPAAL. Experimental results indicate that UPPAAL performs time- and space-wise favorably compared with other real-time verification tools.
10855049
Automatic Synthesis of Real Time Systems
This paper presents a method for automatically constructing real time systems directly from their specifications. The model–construction problem is considered for implicit specifications of the form: (A1 | . . . |An |X) sat S where S is a real time (logical) specification, A1 . . . An are given (regular) timed agents and the problem is to decide whether there exists (and if possible exhibit) a real time agent X which when put in parallel with A1 . . . An will yield a network satisfying S. The method presented proceeds in two steps: first, the implicit specification of X is transformed into an equivalent direct specification of X; second, a model for this direct specification is constructed (if possible) using a direct model construction algorithm. A prototype implementation of our method has been added to the real time verification tool EPSILON.
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.