International audienceFor graph $G(V,E)$, a minimum path cover (MPC) is a minimum cardinality set of vertex disjoint paths that cover $V$ (i.e., every vertex of $G$ is in exactly one path in the cover). This problem is a natural generalization of the Hamiltonian path problem. Cocomparability graphs (the complements of graphs that have an acyclic transitive orientation of their edge sets) are a well studied subfamily of perfect graphs that includes many popular families of graphs such as interval, permutation, and cographs. Furthermore, for every cocomparability graph $G$ and acyclic transitive orientation of the edges of $\overline{G}$ there is a corresponding poset $P_G$; it is easy to see that an MPC of $G$ is a linear extension of $P_G$ that minimizes the bump number of $P_G$. Although there are directly graph-theoretical MPC algorithms (i.e., algorithms that do not rely on poset formulations) for various subfamilies of cocomparability graphs, notably interval graphs, until now all MPC algorithms for cocomparability graphs themselves have been based on the bump number algorithms for posets. In this paper we present the first directly graph-theoretical MPC algorithm for cocomparability graphs; this algorithm is based on two consecutive graph searches followed by a certifying algorithm. Surprisingly, except for a lexicographic depth first search (LDFS) preprocessing step, this algorithm is identical to the corresponding algorithm for interval graphs. The running time of the algorithm is $O({\rm min}(n^2, n + {\rm mloglogn}))$, with the nonlinearity coming from LDFS

For many meta-Fibonacci sequences it is possible to identify a partition of the sequence into successive intervals (sometimes called blocks) with the property that the sequence behaves "similarly" in each block. This partition provides insights into the sequence properties. To date, for any given sequence, only ad hoc methods have been available to identify this partition. We apply a new concept -the spot-based generation sequence -to derive a general methodology for identifying this partition for a large class of meta-Fibonacci sequences. This class includes the Conolly and Conway sequences and many of their well-behaved variants, and even some highly chaotic sequences, such as Hofstadter's famous Q-sequence.

Implementing summation when accuracy and throughput need to be balanced is a challenging endevour. We present experimental results that provide a sense when to start worrying and the expense of the various solutions that exist. We also present a new algorithm based on pairwise summation that achieves 89% of the throughput of the fastest summation algorithms when the data is not resident in L1 cache while eclipsing the accuracy of signifigantly slower compensated sums like Kahan summation and Kahan-Babuska that are typically used when accuracy is important.

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The concept of default and its associated painful repercussions have been a particular area of focus for financial institutions, especially after the 2007/2008 global financial crisis. Counterparty credit risk (CCR), i.e. risk associated with a counterparty default prior to the expiration of a contract, has gained tremendous amount of attention which resulted in new CCR measures and regulations being introduced. In particular users would like to measure the potential impact of each real time trade or potential real time trade against exposure limits for the counterparty using Monte Carlo simulations of the trade value, and also calculate the Credit Value Adjustment (i.e, how much it will cost to cover the risk of default with this particular counterparty if/when the trade is made). These rapid limit checks and CVA calculations demand more compute power from the hardware. Furthermore, with the emergence of electronic trading, the extreme low latency and high throughput real time compute requirement push both the software and hardware capabilities to the limit. Our work focuses on optimizing the computation of risk measures and trade processing in the existing Mark-to-future Aggregation (MAG) engine in the IBM Algorithmics product offering. We propose a new software approach to speed up the end-to-end trade processing based on a pre-compiled approach. The net result is an impressive speed up of 3-5x over the existing MAG engine using a real client workload, for processing trades which perform limit check and CVA reporting on exposures while taking Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Permissions@acm.org. WHPCF'