Revisiting the tree Constraint

International audienceThis paper revisits the tree constraint introduced in [2] which partitions the nodes of a n-nodes, m-arcs directed graph into a set of node-disjoint anti-arborescences for which only certain nodes can be tree roots. We introduce a new filtering algorithm that enforces generalized arc-consistency in O(n + m) time while the original filtering algorithm reaches O(nm) time. This result allows to tackle larger scale problems involving graph partitioning

Exploiting Air-Pressure to Map Floorplans on Point Sets

We prove a conjecture of Ackerman, Barequet and Pinter. Every floorplan with n segments can be embedded on every set of n points in generic position. The construction makes use of area universal floorplans also known as area universal rectangular layouts. The notion of area used in our context depends on a nonuniform density function. We, therefore, have to generalize the theory of area universal floorplans to this situation. The method is then used to prove a result about accommodating points in floorplans that is slightly more general than the conjecture of Ackerman et al

How to Tackle Integer Weighted Automata Positivity

International audienceThis paper is dedicated to candidate abstractions to capture relevant aspects of the integer weighted automata. The expected effect of applying these abstractions is studied to build the deterministic reachability graphs allowing us to semi-decide the positivity problem on these automata. Moreover, the papers reports on the implementations and experimental results, and discusses other encodings

Reasoning About Systems with Transition Fairness

Abstract. Formal verification methods model systems by Kripke structures. In order to model live behaviors of systems, Kripke structures are augmented with fairness conditions. Such conditions partition the computations of the systems into fair computations, with respect to which verification proceeds, and unfair computations, which are ignored. Reasoning about Kripke structures augmented with fairness is typically harder than reasoning about non-fair Kripke structures. We consider the transition fairness condition, where a computation π is fair iff each transition that is enabled in π infinitely often is also taken in π infinitely often. Transition fairness is a natural and useful fairness condition. We show that reasoning about Kripke structures augmented with transition fairness is not harder than reasoning about non-fair Kripke structures. We demonstrate it for fair CTL and LTL model checking, and the problem of calculating the dominators and postdominators.

Distilling Router Data Analysis for Faster and Simpler Dynamic IP Lookup Algorithms

We consider the problem of fast IP address lookup in the forwarding engines of Internet routers. Many hardware and software solutions available in the literature solve a more general problem on strings, the longest prefix match. These solutions are then specialized on real IPv4/IPv6 addresses to work well on the specific IP lookup problem. We propose to go the other way around. We first analyze over 2400 public snapshots of routing tables collected over five years, discovering what we call the "middle-class effect" of those routes. We then exploit this effect for tailoring a simple solution to the IP lookup scheme, taking advantage of the skewed distribution of Internet addresses in routing tables. Our algorithmic solution is easy to implement in hardware or software as it is tantamount to performing an indirect memory access. Its performance can be bounded tightly in the worst case and has very low memory dependence (e.g., just one memory access to off-chip memory in the hardware implementation). It can quickly handle route announcements and withdrawals on the fly, with a small cost which scales well with the number of routes. Concurrent access is permitted during these updates. Our ideas may be helpful for attaining state-of-art link speed and may contribute to setting up a general framework for designing lookup methods by data analysis

New streaming algorithms for counting triangles in graphs

Abstract. We present three streaming algorithms that (ɛ, δ) − approximate 1 the number of triangles in graphs. Similar to the previous algorithms [3], the space usage of presented algorithms are inversely proportional to the number of triangles while, for some families of graphs, the space usage is improved. We also prove a lower bound, based on the number of triangles, which indicates that our first algorithm behaves almost optimally on graphs with constant degrees.

Theory and Practice of Chunked Sequences

International audienceSequence data structures, i.e., data structures that provide operations on an ordered set of items, are heavily used by many applications. For sequence data structures to be efficient in practice, it is important to amortize expensive data-structural operations by chunking a relatively small, constant number of items together, and representing them by using a simple but fast (at least in the small scale) sequence data structure, such as an array or a ring buffer. In this paper, we present chunking techniques, one direct and one based on bootstrapping, that can reduce the practical overheads of sophisticated sequence data structures, such as finger trees, making them competitive in practice with special-purpose data structures. We prove amortized bounds showing that our chunking techniques reduce runtime by amortizing expensive operations over a user-defined chunk-capacity parameter. We implement our techniques and show that they perform well in practice by conducting an empirical evaluation. Our evaluation features comparisons with other carefully engineered and optimized implementations