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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptNIH Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Bioinformatics. Author manuscript; available in PMC Mar 10, 2008.
Published in final edited form as:
PMCID: PMC2266093

rh_tsp_map 3.0: End-to-end radiation hybrid mapping with improved speed and quality control



rh_tsp_map is a software package for computing radiation hybrid (RH) maps and for integrating physical and genetic maps. It solves the central mapping instances by reducing them to the traveling salesman problem (TSP) and using a modification of the CONCORDE package to solve the TSP instances. We present some of the features added between the initial rh_tsp_map version 1.0 and the current version 3.0, emphasizing the automation of many steps and addition of various checks designed to find problems with the input data. Iterations of improved input data followed by fast re-computation of the maps improves the quality of the final maps.


rh_tsp_map source code and documentation including a tutorial is available at ftp://ftp.ncbi.nih.gov/pub/agarwala/rhmapping/rh_tsp_map.tar.gz. CONCORDE modified for RH mapping is available in the directory http://www.isye.gatech.edu/~wcook/rh/. The QSopt library needed for CONCORDE is available at http://www2.isye.gatech.edu/~wcook/qsopt/downloads/downloads.htm.


vog.hin.xileh@ahcir, FAX: 301-480-2288 (Please send email concurrently with any fax.)


Radiation hybrid (RH) mapping projects produce physical maps of sequence tagged site markers on chromosomes and genomes. The input to the computational part of RH mapping is an M × P matrix of {0, 1, 2}, where M is the number of markers and P is the size of the “panel” of clones. Each row is called an “RHvector” for that marker. For each marker m and each clone c, a value of 0 means m is absent in c, 1 means m is present in c, and 2 means the experiment gave ambiguous results. M may range from hundreds to thousands for entire genomes and up to low hundreds for single chromosomes. P is usually between 90–94, due to the prevalence of 96-well plates (allowing a few control wells), although theoretical considerations strongly suggest that to get a reliable map, P should increase as M increases (Ben-Dor and Chor, 1997). The basic principle of RH map computation is that markers with similar RHvectors should be close together in the map. The theory of RH map computation (see e.g., Lange et al. (1995)) has been worked out under the assumption that the RHvectors contain all 0’s and 1’s, but this is hardly true in practice. For example, in the data set described in Murphy et al. (2007), only 0.68% of matrix entries are 2, but 39.82% of RHvectors contain at least one 2.

The initial publication describing rh_tsp_map 1.0 (Agarwala et al., 2000), a software package for constructing radiation hybrid maps and integrating physical and genetic maps, introduced explicit consideration of matrix entries of 2. Versions of rh_tsp_map have been used to compute whole-genome maps of human (Agarwala et al., 2000), dog (Guyon et al., 2003), cow (Everts-van der Wind et al., 2005), a fish called the sea bream (Senger et al., 2006), rhesus macaque (Murphy et al., 2006), and cat (Murphy et al., 2007) as well as chromosome maps of other vertebrates such as horse (Goh et al., 2007). In this note, we describe some of the most important features available in the current version 3.0 of rh_tsp_map that have been added since version 1.0. These features were driven by the practical experience gained when computing RH maps and point to the basic problems with RH mapping – the biology for making hybrids using radiation and the lab protocols provide minimal checks on the correctness of the RHvectors. This contrasts with genetic mapping with microsatellites, in which the combination of the rules of inheritance and the polymorphism of the markers provides a much stronger check on the correctness and consistency of the allele calls. However, RH mapping has some major advantages over genetic mapping, for example, markers need not be polymorphic, scoring markers is easier, and the DNA can be kept in cell lines eliminating the costs of animal care and breeding. Due to the complementary nature of the two techniques, an integrated RH and genetic map is likely to be the most informative map for a genome.

Two principal contributions of rh_tsp_map 1.0 were:

  1. An implementation of a known reduction from the marker ordering problem to the traveling salesman problem (TSP), for either the maximum likelihood estimate (MLE) or minimum obligate chromosome breaks (OCB) criteria, and use of the linkern program of CONCORDE (Applegate et al., 2006) to solve the TSP instances likely to optimality.
  2. Redefinition of the basic problem as selection of a set of markers that can be reliably ordered on a framework map. Ordering all markers is impractical at least because some markers are too close to have their ordered determined with current panel sizes and because the mathematically optimal order of some markers depends on how the ambiguous (2) entries are interpreted in the formulation of either the MLE or OCB criterion.

In contrast, other RH mapping packages such as RHMAP (Boehnke et al., 1991), RHMAPPER (Slonim et al., 1997), and MultiMap (Matise and Chakravarti, 1995) try to order all the markers, and use heuristics that are unlikely to produce optimal maps. An independent test of an early version of rh_tsp_map showed that it is much faster and more robust than the incremental approach used by MultiMap and RHMAPPER (Hitte et al., 2003). As described in the Methods section below, recent changes improve both the speed and robustness of rh_tsp_map.

Finally, we now provide a tutorial with examples to guide users at each step of rh_tsp_map.


With rh_tsp_map 3.0, the major steps to compute a genome-wide set of RH maps include:

  1. identifying linkage groups of markers that belong together,
  2. making a framework map for each linkage group,
  3. testing the robustness of each framework map and dropping or improving the RHvectors for markers as needed,
  4. placing additional markers with respect to each framework map, and
  5. making final maps, including the options to assign to bins markers that cannot be placed reliably and combining multiple linkage groups on a chromosome.

Data for all markers are available before step 1; the markers considered for placement at step 4 are those that do not make it onto the more reliably ordered framework maps that are constructed and tested in steps 2 and 3. Version 1.0 implemented only step 2. We have always allowed the alternative: to order all markers in a group. We now mention some of the modules for each step and highlight features specific to rh_tsp_map.

Identifying linkage groups

The key modules are pairlods_dists and make_groups, which compute pairwise LOD scores and make linkage groups by single linkage clustering using marker pairs with LOD scores above a user-specified threshold. One novel feature is a quality control program, discrepant pairs, that takes as input external evidence (e.g., from other maps, synteny, or fluorescence in situ hybridization (FISH)) and finds marker pairs whose linkage contradicts the chromosome assignments suggested by the external evidence.

Making framework maps

An important change is that the software now solves the TSP instances to guaranteed optimality rather than likely optimality by using the concorde module of CONCORDE (Applegate et al., 2006) rather than linkern. Furthermore, in this application, concorde is orders of magnitude faster than linkern with the conservative parameters we recommend for rh_tsp_map. For example, computing framework maps with the three MLE criteria on the data set described in Murphy et al. (2007) using concorde takes under 13 seconds while using linkern takes over 3 hour 20 minutes, although linkern also found optimal solutions. The cat framework maps contain a total of 1252 markers parititoned in 20 linkage groups.

To compare the running time of concorde to linkern in a case of a large number of markers in a linkage group, we considered all 1252 markers as one group, and randomly picked subsets of 626 markers and 313 markers. For these three sets of markers and the three MLE criteria, using concorde takes 1 minute 38 seconds, 30 seconds, and 9 seconds, respectively, while using linkern takes 1 hour 8 minutes, 1 hour 15 minutes, and 1 hour 10 minutes, respectively. Partitioning markers into 20 linkage groups took less time with concorde compared to having all the markers in one group because each individual problem was easier for concorde. However, the same behavior is not seen with linkern because the parameters specified find a solution from 10 starting points (called restarts) for each linkage group (for a total of 600 restarts with 3 criteria and 20 groups) compared to only a total of 30 restarts when all markers were in one group. As before, linkern also found an optimal solution for the set with 313 markers. However, linkern did not always find an optimal solution for the set with 626 and 1252 markers, suggesting that the parameters for linkern are not conservative enough for large problem sizes.

Because of decades of research into better algorithms and provable upper bounds for the length of TSP tours, instances with thousands of cities can be solved to guaranteed optimality quickly using concorde, even though TSP is NP-complete (Applegate et al., 2006). The linkern module was used in the original rh_tsp_map primarily because the concorde module could only be run together with commercial linear programming software at the time; once this limitation was overcome, some additional software integration was completed to put the RH distance functions into the concorde code.

Another recent addition allows users to express preferences for which marker to use in a framework map when two markers are too close to each other and, at most, one of them can be selected. This makes it possible to systematically increase the number of markers on the framework map about which one also has external evidence, improving the utility of the resulting framework maps for comparative genomics.

Testing framework maps

We added modules map_eval and flips for this step. map_eval removes one marker at a time from the input map and tests how much better its best position is to its second best position in the depleted map. flips tests the input map against all alternatives that locally permute any set of up to 9 consecutive markers; this functionality is also available in CARTHAGENE (de Givry et al., 2005).

Placing more markers

Using the new module place_interpolate, each marker not on the framework map can be placed in its best framework map interval. The MLE or OCB score of the best placement is compared to the score of the second best placement, and only markers with a score difference above some user-specified threshold are retained on the map. To produce a globally integrated map combining framework markers and placed markers, we define and solve instances of a restricted TSP in which the framework markers are required to stay in the framework map order, placed markers are required to stay in their best intervals, but if there are multiple placed markers in the same framework interval, their order is chosen optimally. Order for placed markers is tested using flips in a restricted mode that considers only those permutations that retain placed markers in the same interval. This global positioning of the placed markers avoids the incremental addition of markers used by other packages that causes the resulting maps to be highly sensitive to the order in which placed markers are added (Hitte et al., 2003).

Making final maps

We include new code to systematically handle markers with identical RHvectors, so that although only one of them is used in any flips test, all identical markers can appear in the final map with identical position. We include new options to assign markers that cannot be placed with high enough score to bins that are wider than intervals bounded by adjacent framework markers. This allows users to increase the number of markers shown with some positional information, without corrupting the robustness of the total ordering of framework and placed markers.


rh_tsp_map is implemented as a set of C programs. Some of these programs create UNIX shell scripts. For example, the frame_markers program creates a separate concorde_script for each distance criterion used. The CONCORDE package is implemented in C and available as source code. The concorde program solves TSP instances to optimality using the QSopt library, which is available as a file for numerous versions of UNIX.


This research was supported by the Intramural Research Program of the National Institutes of Health, National Library of Medicine, and Office of Naval Research Grant N00014-03-1-0040. Thanks to William Murphy, Bhanu Chowdhary, Terje Raudsepp, and Elisabete Amaral for giving us practical experience in constructing RH maps, which led to many of the improvements in rh_tsp_map.


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