W that with artificially generated data in which an a priori solution is known, the correct solution set is always identified. In Panel A of Fig 5, we show a set of 15 unordered assemblages each with 6 types. Using a threshold of 0.10 (i.e., the maximum acceptable difference between assemblage frequencies is no more thanFig 5. Example of the IDSS algorithm seriation output for 15 assemblages with 6 types. This seriation order was generated using a threshold of 0.10. Panel A takes the form of traditional centered-bar format where the empty bars indicate relative proportion of the type and small black bars represent confidence intervals of = 0.05 for the type proportions. Panel B is the same order in graph form. Note that while SP600125 biological activity hand-sorting of this example data could be relatively easily done, the IDSS algorithm ensures that the longest possible solution or set of solutions is found. In real-world cases, patterns of type frequencies often includes the effects of sample size, space and other transmission processes. In these cases, a systematic deterministic method is necessary to ensure comprehensive and statistically sound solutions. doi:10.1371/journal.pone.0124942.gPLOS ONE | DOI:10.1371/journal.pone.0124942 April 29,13 /The IDSS Frequency Seriation Algorithm10 ), the IDSS algorithm was able to locate the optimal seriation order of these assemblages out of all possible valid solutions in just over 1470 seconds, using a 2013-era quad-core computer. This length of time might appear slow relative to quick hand-sorting but the results of intuitive shuffling of graphical representations cannot ensure that the largest possible order is identified nor can it find all the equally valid solutions that might be present. Traditional brute force sorting approaches that evaluate the entire search space can easily take many years (Table 1). Using IDSS instead of hand-sorting allows identification of all valid solutions from groups of 20 or fewer assemblages on a single desktop computer. Twenty or so assemblages is a common scale of analysis, at least for many archaeological cases conducted within local regions, and it is important for a DFS algorithm to be able to produce optimal solutions for this scale of data, on commonly available hardware. In particular, many large sets of assemblages break down into much smaller subsets when ordered and thus can be analyzed quickly. Solutions with larger numbers of assemblages or few solution subsets require carefully setting the maximum differences between assemblages and using a computing cluster to further parallelize the evaluation of solutions. Graphical Representation. Fig 5, Panel A represents the traditional graphic form for seriations in which the width of the horizontal bars represents the magnitude of the frequencies of types for individual assemblages. This “stacked and centered bar” format is instantly recognizable by archaeologists, and is excellent for WP1066 biological activity displaying the results of a seriation if there is only one causal factor driving the ordering (typically, time) and if no assemblages participate in more than one seriation. When the situation becomes any more complex than a single chronological order, we need a better visual representation. Graphs, a collection of vertices and edges, provide an alternative means of visualization that accommodate linear orderings as well as more complex relations [86?0]. We can create a graph representation of our seriation results by connecting assemblages via ed.W that with artificially generated data in which an a priori solution is known, the correct solution set is always identified. In Panel A of Fig 5, we show a set of 15 unordered assemblages each with 6 types. Using a threshold of 0.10 (i.e., the maximum acceptable difference between assemblage frequencies is no more thanFig 5. Example of the IDSS algorithm seriation output for 15 assemblages with 6 types. This seriation order was generated using a threshold of 0.10. Panel A takes the form of traditional centered-bar format where the empty bars indicate relative proportion of the type and small black bars represent confidence intervals of = 0.05 for the type proportions. Panel B is the same order in graph form. Note that while hand-sorting of this example data could be relatively easily done, the IDSS algorithm ensures that the longest possible solution or set of solutions is found. In real-world cases, patterns of type frequencies often includes the effects of sample size, space and other transmission processes. In these cases, a systematic deterministic method is necessary to ensure comprehensive and statistically sound solutions. doi:10.1371/journal.pone.0124942.gPLOS ONE | DOI:10.1371/journal.pone.0124942 April 29,13 /The IDSS Frequency Seriation Algorithm10 ), the IDSS algorithm was able to locate the optimal seriation order of these assemblages out of all possible valid solutions in just over 1470 seconds, using a 2013-era quad-core computer. This length of time might appear slow relative to quick hand-sorting but the results of intuitive shuffling of graphical representations cannot ensure that the largest possible order is identified nor can it find all the equally valid solutions that might be present. Traditional brute force sorting approaches that evaluate the entire search space can easily take many years (Table 1). Using IDSS instead of hand-sorting allows identification of all valid solutions from groups of 20 or fewer assemblages on a single desktop computer. Twenty or so assemblages is a common scale of analysis, at least for many archaeological cases conducted within local regions, and it is important for a DFS algorithm to be able to produce optimal solutions for this scale of data, on commonly available hardware. In particular, many large sets of assemblages break down into much smaller subsets when ordered and thus can be analyzed quickly. Solutions with larger numbers of assemblages or few solution subsets require carefully setting the maximum differences between assemblages and using a computing cluster to further parallelize the evaluation of solutions. Graphical Representation. Fig 5, Panel A represents the traditional graphic form for seriations in which the width of the horizontal bars represents the magnitude of the frequencies of types for individual assemblages. This “stacked and centered bar” format is instantly recognizable by archaeologists, and is excellent for displaying the results of a seriation if there is only one causal factor driving the ordering (typically, time) and if no assemblages participate in more than one seriation. When the situation becomes any more complex than a single chronological order, we need a better visual representation. Graphs, a collection of vertices and edges, provide an alternative means of visualization that accommodate linear orderings as well as more complex relations [86?0]. We can create a graph representation of our seriation results by connecting assemblages via ed.