<chapter id='dependency-resolution-decision-making'>
<title>Decision Making</title>
<sect1 id='dependency-resolution-decision-making-dependency-expression-evaluation'>
	<title>Dependency Expression Evaluation</title>
	<para>
	In terms of boolean logic, a dependency expression can
	be expressed in disjunctive normal form (DNF), which is
	a disjunction of conjunctive clauses. Each conjunctive clause
	represents one possible alternative combination of dependency
	atoms capable of satisfying the dependency expression.
	</para>
	<sect2 id='dependency-resolution-decision-making-dependency-expression-evaluation-delayed-disjunction'>
		<title>Delayed Evaluation of Disjunctive Dependency Choices</title>
		<para>
		Disjunctive dependencies, of which virtuals are a special case,
		can be satisfied by multiple choices of dependency atoms. These
		choices are delayed until as late as possible in the dependency
		calculation, after packages have been selected to satisfy
		as many non-disjunctive dependencies as possible. As a consequence
		of this delayed evaluation, there is maximal information available
		which makes it possible to optimize choices such that the total
		number of packages required to satisfy all dependencies is minimized.
		</para>
	</sect2>
</sect1>
<sect1 id='dependency-resolution-decision-making-look-ahead'>
	<title>Look-Ahead</title>
	<para>
	When there are multiple combinations to choose from,
	a look-ahead mechanism will choose an optimal combination
	to satisfy constraints and minimize cost. The
	following package states influence the cost calculation for
	a given combination:
	</para>
	<itemizedlist>
	<listitem>
		<para>installed</para>
	</listitem>
	<listitem>
		<para>selected (for installation)</para>
	</listitem>
	<listitem>
		<para>not selected (for installation)</para>
	</listitem>
	</itemizedlist>
	<para>
	In cost calculations, virtual packages by themselves are
	considered to cost nothing since they do not directly install anything.
	It is the dependencies of a virtual package that contribute to it's cost.
	</para>
	<sect2 id='dependency-resolution-decision-making-look-ahead-constraint-propagation'>
		<title>Constraint Propagation</title>
		<para>
		Combinations that include packages from the "installed" or
		"selected" categories are less costly than those that
		include packages from the "not selected" category.
		When a package is chosen for installation, it transitions to the
		"selected" state. This state change propagates
		to the cost calculations of later decisions,
		influencing later decisions to be consistent with earlier decisions.
		This feedback mechanism serves to propagate constraints and can
		influence the modeling process to
		converge on a more optimal final state.
		</para>
	</sect2>
	<sect2 id='dependency-resolution-decision-making-look-ahead-expanded-search-space'>
		<title>Expanded Search Space</title>
		<para>
		When evaluating virtual atoms, an expanded search space is
		considered which recursively traverses
		the dependencies of virtual packages
		from all slots matching a given virtual atom. All combinations in
		this expanded search space are considered when choosing an optimal
		combination to satisfy constraints with minimal cost.
		</para>
	</sect2>
</sect1>
</chapter>