International Journal of Foundations of Computer Science

For two points p and q in the plane, a straight line h, called a highway, and a real v > 1, we define the travel time (also known as the city distance) from p and q to be the time needed to traverse a quickest path from p to q, where the distance is measured with speed v on h and with speed 1 in the underlying metric elsewhere.

Given a set S of n points in the plane and a highway speed v, we consider the problem of finding a highway that minimizes the maximum travel time over all pairs of points in S. If the orientation of the highway is fixed, the optimal highway can be computed in linear time, both for the L₁- and the Euclidean metric as the underlying metric. If arbitrary orientations are allowed, then the optimal highway can be computed in O(n²log n) time. We also consider the problem of computing an optimal pair of highways, one being horizontal, one vertical.

We prove #P-completeness for counting the number of forests in regular graphs and chordal graphs. We also present algorithms for this problem, running in O*(1.8494^m) time for 3-regular graphs, and O*(1.9706^m) time for unit interval graphs, where m is the number of edges in the graph and O*-notation ignores a polynomial factor. The algorithms can be generalized to the Tutte polynomial computation.

The advance of wireless and mobile technology introduces a new type of Video-on-Demand (VOD) systems, namely the mobile VOD systems, that provide VOD services to mobile clients. It is a challenge to design broadcasting protocols for such systems because of the following special requirements: (1) fixed maximum bandwidth requirement: the maximum bandwidth required for broadcasting a movie should be fixed and independent of the number of requests, (2) load adaptivity: the total bandwidth usage should be dependent on the number of requests; the fewer the requests the smaller the total bandwidth usage, and (3) clients sensitivity: the system should be able to support clients with a wide range of heterogeneous capabilities. In the literature, there are some partial solutions that give protocols meeting one or two of the above requirements. In this paper, we give the first protocol that meets all of the three requirements. The performance of our protocol is optimal up to a small constant factor.

We present a general theorem capturing conditions required for the termination of abstract reduction systems. We show that our theorem generalises another similar general theorem about termination of such systems. We apply our theorem to give interesting proofs of termination for typed combinatory logic. Thus, our method can handle most path-orderings in the literature as well as the reducibility method typically used for typed combinators. Finally we show how our theorem can be used to prove termination for incrementally defined rewrite systems, including an incremental general path ordering. All proofs have been formally machine-checked in Isabelle/HOL.

In order to represent, compute and reason with advanced data types like lists with a fixed length, finite sets or well scoped λ-terms one must go beyond the traditional treatment of data types as being inductive types and, instead, consider them as inductive families, or more precisely Strictly Positive Families (SPFs). We have previously shown that the grammar of strictly positive types (SPT) can be given as an inductively defined family. In the present paper we go one step further an show that the universe of SPFs can be encoded as an SPF. We show that SPFs can be used to represent and compute with a variety of advanced data types and that generic programs can be naturally written over the universe of SPFs.

The concept of universal designated verifier signatures was introduced by Steinfeld, Bull, Wang and Pieprzyk at Asiacrypt 2003. These signatures can be used as standard publicly verifiable digital signatures but have an additional functionality which allows any holder of a signature to designate the signature to any desired verifier. This designated verifier can check that the message was indeed signed, but is unable to convince anyone else of this fact. We propose new efficient constructions for pairing-based short signatures. Our first scheme is based on Boneh-Boyen signatures and its security can be analyzed in the standard security model. We prove its resistance to forgery assuming the hardness of the so-called strong Diffie-Hellman problem, under the knowledge-of-exponent assumption. The second scheme is compatible with the Boneh-Lynn-Shacham signatures and is proven unforgeable, in the random oracle model, under the assumption that the computational bilinear Diffie-Hellman problem is untractable. Both schemes are designed for devices with constrained computation capabilities since the signing and the designation procedure are pairing-free. Finally, we present extensions of these schemes in the multi-user setting proposed by Desmedt in 2003.

Given a connected geometric graph G, we consider the problem of constructing a t-spanner of G having the minimum number of edges. We prove that for every real number t with , there exists a connected geometric graph G with n vertices, such that every t-spanner of G contains Ω(n^1+1/t) edges. This bound almost matches the known upper bound, which states that every connected weighted graph with n vertices contains a t-spanner with O(n^1+2/(t-1)) edges. We also prove that the problem of deciding whether a given geometric graph contains a t-spanner with at most K edges is NP-hard. Previously, this NP-hardness result was only known for non-geometric graphs.

In the algebraic study of words and languages it is often convenient to analyze words as numerical quantities. One such now-famous example is the study of words by using their attached Parikh mapping (or vector). However, the Parikh vector abstracts away too much of the structure of the word. Parikh matrices were introduced as a means to obtain more than just the number of occurrences of single letters. When studying properties of words, an important property is that a word is uniquely determined by the number of occurrences of certain predetermined subwords. In the context of Parikh matrices, the problem is translated in finding which words are completely characterized by their associated Parikh matrix. This paper links this problem with that of the print of a word, i.e. the word obtained by considering consecutive occurrences of the same letter as only one letter. We obtain results regarding finiteness and context-freeness of such classes of words.

Multiprocessor systems with a global shared memory provide logically uniform data access. To hide latencies when accessing global memory each processor makes use of a private cache. Several copies of a data item may exist concurrently in the system. To guarantee consistency when updating an item a processor must invalidate copies of the item in other private caches. To exclude the effect of classical paging faults, one assumes that each processor knows its own data access sequence, but does not know the sequence of future invalidations requested by other processors. Performance of a processor with this restriction can be measured against the optimal behavior of a theoretical omniscient processor, using competitive analysis. We present a -competitive randomized online algorithm for this problem for cache size of 2, and prove a matching lower bound on the competitiveness. The algorithm is derived with the help of a new concept we call knowledge states. Finally, we show a lower bound of on the competitiveness for larger cache sizes.

Three variants of determinism are introduced for CD-systems of restarting automata, called strict determinism, global determinism, and local determinism. In mode = 1 globally deterministic CD-systems of restarting automata are of the same expressive power as nonforgetting deterministic restarting automata of the same type, which corresponds to the situation for nondeterministic CD-systems. On the other hand, for the various types of restarting automata without auxiliary symbols, strictly deterministic CD-systems of restarting automata are strictly less expressive than the corresponding deterministic types of nonforgetting restarting automata. Further, globally deterministic CD-systems of restarting automata can be simulated by locally deterministic CD-systems of restarting automata of the same type. In fact, we conjecture that, for all types of restarting automata without auxiliary symbols, the latter are strictly more expressive than the former, but they are strictly less expressive than the corresponding nondeterministic CD-systems of restarting automata.