Synchronized sweep algorithms for scalable scheduling constraints

This report introduces a family of synchronized sweep based filtering algorithms for handling scheduling problems involving resource and precedence constraints. The key idea is to filter all constraints of a scheduling problem in a synchronized way in order to scale better. In addition to normal filtering mode, the algorithms can run in greedy mode, in which case they perform a greedy assignment of start and end times. The filtering mode achieves a significant speed-up over the decomposition into independent cumulative and precedence constraints, while the greedy mode can handle up to 1 million tasks with 64 resources constraints and 2 million precedences. These algorithms were implemented in both CHOCO and SICStus

Perseus: Randomized Point-based Value Iteration for POMDPs

Partially observable Markov decision processes (POMDPs) form an attractive and principled framework for agent planning under uncertainty. Point-based approximate techniques for POMDPs compute a policy based on a finite set of points collected in advance from the agents belief space. We present a randomized point-based value iteration algorithm called Perseus. The algorithm performs approximate value backup stages, ensuring that in each backup stage the value of each point in the belief set is improved; the key observation is that a single backup may improve the value of many belief points. Contrary to other point-based methods, Perseus backs up only a (randomly selected) subset of points in the belief set, sufficient for improving the value of each belief point in the set. We show how the same idea can be extended to dealing with continuous action spaces. Experimental results show the potential of Perseus in large scale POMDP problems

Fast Reliable Ray-tracing of Procedurally Defined Implicit Surfaces Using Revised Affine Arithmetic

Fast and reliable rendering of implicit surfaces is an important area in the field of implicit modelling. Direct rendering, namely ray-tracing, is shown to be a suitable technique for obtaining good-quality visualisations of implicit surfaces. We present a technique for reliable ray-tracing of arbitrary procedurally defined implicit surfaces by using a modification of Affine Arithmetic called Revised Affine Arithmetic. A wide range of procedurally defined implicit objects can be rendered using this technique including polynomial surfaces, constructive solids, pseudo-random objects, procedurally defined microstructures, and others. We compare our technique with other reliable techniques based on Interval and Affine Arithmetic to show that our technique provides the fastest, while still reliable, ray-surface intersections and ray-tracing. We also suggest possible modifications for the GPU implementation of this technique for real-time rendering of relatively simple implicit models and for near real-time for complex implicit models

Complexity, Heuristic, and Search Analysis for the Games of Crossings and Epaminondas

Games provide fertile research domains for algorithmic research. Often, game research helps solve real-world problems through the testing and refinement of search algorithms in game domains. Other times, game research finds limits for certain algorithms. For example, the game of Go proved intractable for the Min-Max with Alpha-Beta pruning algorithm leading to the popularity of Monte-Carlo based search algorithms. Although effective in Go, and game domains once ruled by Alpha-Beta such as Lines of Action, Monte-Carlo methods appear to have limits too as they fall short in tactical domains such as Hex and Chess. In a continuation of this type of research, two new games, Crossings and Epaminondas, are presented, analyzed and used to test two Monte-Carlo based algorithms: Upper Confidence Bounds applied to Trees (UCT) and Heuristic Guided UCT (HUCT). Results indicate that heuristic knowledge can positively affect UCT\u27s performance in the lower complexity domain of Crossings. However, both agents perform worse in the higher complexity domain of Epaminondas. This identifies Epaminondas as another domain that poses difficulties for Monte Carlo agents

Fast reliable interrogation of procedurally defined implicit surfaces using extended revised affine arithmetic.

Techniques based on interval and previous termaffine arithmetic next term and their modifications are shown to provide previous term reliable next term function range evaluation for the purposes of previous termsurface interrogation.next term In this paper we present a technique for the previous termreliable interrogation of implicit surfacesnext term using a modification of previous termaffine arithmeticnext term called previous term revised affine arithmetic.next term We extend the range of functions presented in previous termrevised affine arithmeticnext term by introducing previous termaffinenext term operations for arbitrary functions such as set-theoretic operations with R-functions, blending and conditional operators. The obtained previous termaffinenext term forms of arbitrary functions provide previous termfasternext term and tighter function range evaluation. Several case studies for operations using previous termaffinenext term forms are presented. The proposed techniques for previous termsurface interrogationnext term are tested using ray-previous termsurfacenext term intersection for ray-tracing and spatial cell enumeration for polygonisation. These applications with our extensions provide previous termfast and reliablenext term rendering of a wide range of arbitrary previous termprocedurally defined implicit surfacesnext term (including polynomial previous termsurfaces,next term constructive solids, pseudo-random objects, previous termprocedurally definednext term microstructures, and others). We compare the function range evaluation technique based on previous termextended revised affine arithmeticnext term with other previous termreliablenext term techniques based on interval and previous termaffine arithmeticnext term to show that our technique provides the previous termfastestnext term and tightest function range evaluation for previous termfast and reliable interrogation of procedurally defined implicit surfaces.next term Research Highlights The main contributions of this paper are as follows. ► The widening of the scope of previous termreliablenext term ray-tracing and spatial enumeration algorithms for previous termsurfacesnext term ranging from algebraic previous termsurfaces (definednext term by polynomials) to general previous termimplicit surfaces (definednext term by function evaluation procedures involving both previous termaffinenext term and non-previous termaffinenext term operations based on previous termrevised affine arithmetic)next term. ► The introduction of a technique for representing procedural models using special previous termaffinenext term forms (illustrated by case studies of previous termaffinenext term forms for set-theoretic operations in the form of R-functions, blending operations and conditional operations). ► The detailed derivation of special previous termaffinenext term forms for arbitrary operators

Verification and Simplification of DMN Decision Tables

Decision Model and Notation (DMN) on standardne notatsioon, mida kasutatakse ärirakendustes otsuste loogika kirjeldamiseks. Otsustabelid on DMNi üks peamisi osi. DMNi otsustabelite suurenev kasutatavus igapäevaste äriotsuste ülesmärkimiseks ja automatiseerimiseks on tõstatanud vajadust analüüsida otsustabeleid. See lõputöö annab ülevaate DMN otsustabelist ja kirjeldab kolme skaleeruvat algoritmi, mis on mõeldud leidmaks kattuvaid reegleid ja puuduvaid reegleid ning lihtsustada otsustabeleid kasutades reeglite ühendamist. Kõik välja pakutud algoritmid on implementeeritud avatud lähtekoodiga DMN redaktorisse ja katsetatud suurte otsustabelite peal, mis pärinevad krediidiandmise andmebaasist.The Decision Model and Notation (DMN) is a standard notation to specify decision logic in business applications. A central construct in DMN is a decision table. The rising use of DMN decision tables to capture and to automate everyday business decisions raises the need to support analysis tasks on decision tables. This thesis provides scalable algorithms to tackle three analysis tasks: detection of overlapping rules, detection of missing rules and simplification of decision tables via rule merging. All proposed algorithms have been implemented in an open-source DMN editor and are tested on large decision tables derived from a credit lending data-set