Efficient Implementation of a Synchronous Parallel Push-Relabel Algorithm

Motivated by the observation that FIFO-based push-relabel algorithms are able to outperform highest label-based variants on modern, large maximum flow problem instances, we introduce an efficient implementation of the algorithm that uses coarse-grained parallelism to avoid the problems of existing parallel approaches. We demonstrate good relative and absolute speedups of our algorithm on a set of large graph instances taken from real-world applications. On a modern 40-core machine, our parallel implementation outperforms existing sequential implementations by up to a factor of 12 and other parallel implementations by factors of up to 3

Impartial coloring games

Coloring games are combinatorial games where the players alternate painting uncolored vertices of a graph one of $k > 0$ colors. Each different ruleset specifies that game's coloring constraints. This paper investigates six impartial rulesets (five new), derived from previously-studied graph coloring schemes, including proper map coloring, oriented coloring, 2-distance coloring, weak coloring, and sequential coloring. For each, we study the outcome classes for special cases and general computational complexity. In some cases we pay special attention to the Grundy function

MSO definable string transductions and two-way finite state transducers

String transductions that are definable in monadic second-order (mso) logic (without the use of parameters) are exactly those realized by deterministic two-way finite state transducers. Nondeterministic mso definable string transductions (i.e., those definable with the use of parameters) correspond to compositions of two nondeterministic two-way finite state transducers that have the finite visit property. Both families of mso definable string transductions are characterized in terms of Hennie machines, i.e., two-way finite state transducers with the finite visit property that are allowed to rewrite their input tape.Comment: 63 pages, LaTeX2e. Extended abstract presented at 26-th ICALP, 199

Fast Parallel Fixed-Parameter Algorithms via Color Coding

Fixed-parameter algorithms have been successfully applied to solve numerous difficult problems within acceptable time bounds on large inputs. However, most fixed-parameter algorithms are inherently \emph{sequential} and, thus, make no use of the parallel hardware present in modern computers. We show that parallel fixed-parameter algorithms do not only exist for numerous parameterized problems from the literature -- including vertex cover, packing problems, cluster editing, cutting vertices, finding embeddings, or finding matchings -- but that there are parallel algorithms working in \emph{constant} time or at least in time \emph{depending only on the parameter} (and not on the size of the input) for these problems. Phrased in terms of complexity classes, we place numerous natural parameterized problems in parameterized versions of AC$^0$. On a more technical level, we show how the \emph{color coding} method can be implemented in constant time and apply it to embedding problems for graphs of bounded tree-width or tree-depth and to model checking first-order formulas in graphs of bounded degree

On the Memory Requirement of Hop-by-hop Routing: Tight Bounds and Optimal Address Spaces

Routing in large-scale computer networks today is built on hop-by-hop routing: packet headers specify the destination address and routers use internal forwarding tables to map addresses to next-hop ports. In this paper we take a new look at the scalability of this paradigm. We define a new model that reduces forwarding tables to sequential strings, which then lend themselves readily to an information-theoretical analysis. Contrary to previous work, our analysis is not of worst-case nature, but gives verifiable and realizable memory requirement characterizations even when subjected to concrete topologies and routing policies. We formulate the optimal address space design problem as the task to set node addresses in order to minimize certain network-wide entropy-related measures. We derive tight space bounds for many well-known graph families and we propose a simple heuristic to find optimal address spaces for general graphs. Our evaluations suggest that in structured graphs, including most practically important network topologies, significant memory savings can be attained by forwarding table compression over our optimized address spaces. According to our knowledge, our work is the first to bridge the gap between computer network scalability and information-theory