Patent Publication Number: US-2018032872-A1

Title: Interactive constraint solver

Description:
BENEFIT CLAIM 
     This application claims the benefit as a Continuation of patent application Ser. No. 14/692,602, filed Apr. 21, 2015, the entire contents of which is hereby incorporated by reference as if fully set forth herein, which claims benefit of priority to Provisional Application No. 62/054,260, filed Sep. 23, 2014, the entire contents of which is hereby incorporated by reference as if fully set forth herein, under 35 U.S.C. §119(e). Therefore, the effective filing date of this application is Sep. 23, 2014. The applicant(s) hereby rescind any disclaimer of claim scope in the parent application(s) or the prosecution history thereof and advise the USPTO that the claims in this application may be broader than any claim in the parent application(s). 
    
    
     FIELD 
     This patent application is generally directed to constraint programming and more specifically, to an interactive constraint solver. 
     BACKGROUND 
     Constraint programming is a programming paradigm that is used to solve problems that depend on a number of different variables that have relationships with one another. The relationships between variables are expressed as constraints. Examples of problems that have been solved using constraint programming include scheduling (e.g., of people and other resources) and combinatorial optimization problems (e.g., configurations of automobiles or computers). Constraint programming is used to find feasible assignments to a set of variables subject to one or more constraints defining a problem. When the problem is successfully solved, values will be assigned to all the variables in the solution such that all constraints are satisfied. Conflicts occur when it is not possible or permissible to satisfy all the constraints. When constraints conflict the problem is not successfully solved. A valid solution requires that all constraints be satisfied. 
     Constraint solving systems can communicate with client applications to receive constraints between variables. In some systems, client applications do not have the ability to assign priorities or weights to constraints. 
     These systems, by definition, provide only two categories of constraints: user-selections made by the end-user, and non-override-able constraints that have been added by the client application. 
     Further, these systems do not have the capability to provide additional categories of constraints and have profound limits in how conflicts are resolved. For example, in current systems, any conflict within the non-override-able constraints will always reject a subsequently received user-selection or a subsequently received non-override-able constraint. Resolution of conflicts between two or more of the user-selections involves re-ordering past user-selection to determine if the new user-selection can be implemented in a solution. Conflicts between selections and non-overrideable choices are always resolved in favor of the non-override-able choices. 
     As such, in existing systems, users of client applications do not have the ability to decide which user-selections are given greater weight when more than one user is submitting user-selections. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an illustration of an environment in which various embodiments can be implemented. 
         FIG. 2  is a block diagram of an example interactive constraint solver application, according to various embodiments. 
         FIG. 3A  is a flowchart of an example method of ordering constraints within priority groups, according to various embodiments. 
         FIG. 3B  is a chart depicting example ways a conflict can be resolved, according to various embodiments. 
         FIGS. 4  depicts a general format of queues or groups that are used to order choice-constraints. 
         FIG. 5  depicts examples of constraints being ordered within priority groups according to business rules during a first session, according to various embodiments. 
         FIG. 6  depicts examples of constraints being ordered within priority groups according to business rules during a second session, according to various embodiments. 
         FIG. 7  depicts examples of constraints being ordered within priority groups according to business rules during a third session, according to various embodiments. 
         FIG. 8  is a block diagram of a computer system upon which various embodiments may be implemented. 
     
    
    
     DETAILED DESCRIPTION 
     In the following description, for the purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be apparent, however, that the present invention may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to avoid unnecessarily obscuring the present invention. 
     Embodiments are described herein according to the following outline:
         1.0 General Overview   2.0 Example Interactive Constraint Solver Application   3.0 Example Interactive Constraint Solver Process   4.0 Example Implementation of the Constraint Solver Process   5.0 Hardware Overview   6.0 Extensions and Alternatives       

     1.0. General Overview 
     The interactive constraint solver application finds feasible assignments of values to a set of variables subject to one or more model-constraints defining a problem. The interactive constraint solver application can change the current value of a variable defined in the problem and can handle conflicts between choice-constraints and model-constraints. The interactive constraint solver application can affect the value of a variable by introducing new constraints between variables (e.g., by adding a choice-constraint). The interactive constraint solver application maintains a queue of the choice-constraints. When the problem is successfully solved, all variables in the solution are bound such that all constraints are satisfied. Elsewhere in this document, the concept of variable assignment is used interchangeably with variable binding. 
     Described herein are approaches that allow client applications using the interactive constraint solver applications to have partial control of the order of choice-constraints while allowing the interactive constraint solver to control the absolute order of the processing of choice-constraints to the solution. The interactive constraint solver application resolves conflicts according to model-constraints that have been set by an application developer. The ability to provide model-constraints, allows the application developer to tailor the client application to the problem being solved. 
     Techniques described herein improve the operation of the client application by giving the application developer more control over the process of processing submitted choice-constraints and handling any conflicts that result. The priority group mechanism eases the application developer&#39;s task by allowing the developer to implement this complexity in their application. 
     2.0 Example Interactive Constraint Solver Application 
       FIG. 1  is an illustration of an environment  100  in which various embodiments can be implemented. The environment  100  includes an interactive constraint solver application  102  in electronic communication with one or more client applications  104 A-C. 
     The interactive constraint solver application  102  is configured to receive a set of variables and a set of model-constraints that define relationships between the variables in the set of variables from a client application, into which a developer of that client application has coded the model-constraints. The set of model-constraints can comprise non-override-able constraints and other types of constraints. For example, for each of the client applications, the set of model-constraints can include one or more business rules defined for the client application. In some embodiments, the application developer, defines and builds the client applications  104 A, B, and C for users to interact with the interactive constraint solver application  102 . Users interact with various instances of client applications  104 A-C to submit user choice-constraints. Model-constraints are defined by the application developer and choice-constraints are submitted by a user of one of the client application  104  A, B, or C. 
     The client application  104  is also configured to receive business rules from the application developer to establish a set of queues to which respective user choice-constraints can be added according to the business rules. Logical relationships between the established queues can be dictated by one or more business rules, as described below. In some embodiments, each queue can correspond to a role of a stakeholder submitting a choice-constraint. A stakeholder, as used herein, refers to a person, or a person acting on behalf of an entity, who submits a choice-constraint. A stakeholder or user has a role. The role of the stakeholder or user is used by the business rules to place choice-constraints into a priority group. 
     After receiving user choice-constraints, the interactive constraint solver application  102  assigns each user choice-constraint to a priority group according to business rules dictating how the user choice-constraints are allocated to the priority groups. The business rules are received from a client application  104 , into which a developer of that client application  104  has defined the business rules. In some embodiments, the client application  104  can provide a “modeling toolkit” that can be used to define business rules or to select business rules that are defined in the toolkit and stored in a database. These rules are retrieved when the client application  104  starts a session. In other embodiments, client application  104  can be used by an application developer to code the business rules directly into their application. For each priority group, the user choice-constraints are arranged into a queue corresponding to a priority group according to one or more business rules. 
     The interactive constraint solver application  102  provides capabilities that allow users to interact with the interactive constraint solver application  102 . One capability is to add user selections (assignment of values to one or more variables in the form of choice-constraints), through user interface interaction, to the solution. These user choice-constraints can result in the interactive constraint solver application  102  providing a user-preferred solution. 
     In an embodiment, the assignment of choice-constraints to priority groups in an interactive constraint solver application  102  is achieved as a consequence of the following factors. The client application can create any number of priority groups, each having a unique priority. The priority groups, and therefore the choice-constraints contained within different priority groups, are processed from highest priority to lowest priority. Client applications can add choice-constraints to priority groups and remove choice-constraints from priority groups. Client applications can also move choice-constraints between priority groups. These operations are subject to validation. That is, moving a choice-constraint from one group to another can cause conflicts. For each priority group, client applications are prevented from creating priority among choice-constraints within that priority group. Within each priority group, the interactive constraint solver application maintains the order of choice-constraints to support other interactive constraint solver application  102  functions such as conflict resolution. A conflict occurs when one or more choice-constraints cannot co-exist in the solution without violating one or more model-constraints or choice-constraints. 
     The client applications  104  are each dedicated to solving one or more separate problems that are solved by assigning values to a set of variables. The client applications  104  can provide model-constraints or pre-defined business rules. The received constraints can be stored and maintained by the interactive constraint solver application  102 . In addition, each client application can define one or more priority groups into which choice-constraints are assigned. Each client application  104  may present a user interface via which a stakeholder can submit choice-constraints. The client application  104  can add the stakeholder-submitted choice-constraints to a respective priority group based on a role of the stakeholder. Examples of roles include “company”, “manager”, and “employee”. The role of the stakeholder is used when processing choice-constraints submitted by the stakeholder. 
     Upon receiving choice-constraints from one of the client applications  104 , the interactive constraint solver application  102  can determine a solution to the problem that satisfies the model-constraints and the choice-constraints. 
       FIG. 2  is a block diagram of an example interactive constraint solver application  102 , according to various embodiments. The interactive constraint solver application  102  comprises a choice-constraint database  204  and a model-constraint database  202 . The databases  202  and  204  can be combined into a single database or be further divided into additional databases. 
     The interactive constraint solver application  102  is configured to obtain and store, for later retrieval, constraints used to solve a problem for the client application  104 . The constraints include both model-constraints (stored in the model-constraint database  202 ) and choice-constraints (stored in the choice-constraint database  204 ). Using various instances of client applications  104 A-C, users of those client applications can submit choice-constraints. A choice-constraint is a constraint generated by one of the client applications  104 A,  104 B, or  104 C from a selection submitted by the user via one of the client applications  104 A,  104 B, or  104 C. The interactive constraint solver application  102  optionally receives an indication of a priority group in which the choice-constraint belongs. 
     The interactive constraint solver application  102  is configured to control an ordering of choice-constraints received from the client application  104 . According to some embodiments, the client application  104  controls the ordering of the choice-constraints when certain choice-constraints are more important than others. The order of the choice-constraints is treated with priority by virtue of being assigned to a priority group. For example, a client application  104  can assign choice-constraints to three priority groups. In embodiments where choice-constraints are defined by virtue of a role of a stakeholder, the priority groups can be: company-required, employee-must-have, and employee-like-to have, where choice-constraints assigned to the company-required priority group are given the highest priority. The interactive constraint solver application  102  controls the order of choice-constraints within the priority groups to fulfill pre-defined constraints such as product requirements or business rules. When adding a new choice-constraint, the interactive constraint solver application  102  determines where to add the choice-constraint to the set of the choice-constraints within each priority group. 
     The interactive constraint solver application  102  is configured to resolve conflicts between choice-constraints according to the relative priority of the priority group to which the conflicting choice-constraints are assigned. As part of conflict resolution, the interactive constraint solver manipulates the set of choice-constraints within each priority group. 
     An example of a conflict follows. The user first submits the choice-constraint “carBodyColor=Red” and later attempts to submit the choice-constraint “carBodyColor=Blue”. The second choice-constraint conflicts with the first because the carBodyColor is limited to one color. To resolve the conflict, the interactive constraint solver application  102  changes the order of the choice-constraints. The interactive constraint solver application  102  moves the conflicting choice-constraint whose addition is being attempted, “carBodyColor=Blue”, to the highest priority within its priority group according to a business rule indicating that more recent choice-constraints supersede earlier choice-constraints. In some instances, one or more other choice-constraints may be automatically removed from the solution. In this example, the choice-constraint “carBodyColor=Red” is removed while the choice-constraint “carBodyColor=Blue is preserved. 
     3.0 Example Interactive Constraint Solver Process 
       FIG. 3  is a flowchart of an example method  300  of resolving a conflict between two or more choice-constraints, according to various embodiments. The method  300  can be performed by the interactive constraint solver application  102  and/or the client application  104 , as described herein. 
     Choice-constraints are initially added to one or more corresponding queues. The queues are each associated with a relative priority to the other queues. The rules dictate the placement of each choice-constraint among other choice-constraints within a particular queue including, for example, based on a chronology of when the choice-constraints were received. 
     The client application  104  has some control over the ordering of choice-constraints by virtue of the priority groups corresponding to the queues. The client application  104  defines the priority groups, including the number of priority groups and their relative priorities. The client application  104  further identifies which choice-constraints are added to or retracted from which priority groups, when choice-constraints can be moved between priority groups, and how to handle conflicts between choice-constraints. For example, the client application  104  can define priority groups such as: company-required, employee-must-have, and employee-like-to-have choice-constraints, where company-required choice-constraints having a highest relative priority. 
     In an operation  302 , a new choice-constraint is added to one of the queues according to a characteristic of the choice-constraint. The characteristics of the choice-constraint may be defined by the client application  104  or based on a pre-existing business rules such as a time that the choice-constraint was received, a role of a stakeholder from whom the choice-constraint was received, and/or one or more constraints. 
     In an operation  304 , a conflict, between the new choice-constraint of operation  302  and one or more choice-constraints contained in the queue into which the new choice-constraint was added, is detected. In an operation  306 , in response to the detection of the conflict between the new choice-constraint and another choice-constraint, information is provided to the client application  104 . This information allows the client application  104  to distinguish between various situations and allows the client application  104  to decide how to resolve the conflict based on the business rules defined by the client application. 
     The interactive constraint solver application  102  distinguishes between various types of conflicts. A first type of conflict is a conflict that occurs between two choice-constraints within the same priority group. A second type of conflict is a conflict that occurs between a later choice-constraint that was chronologically added to a higher priority group following the addition, to a lower priority group, of an earlier choice-constraint that conflicts with the later choice-constraint. For an example of this second type of conflict, a company-required choice-constraint (highest priority group) might be chronologically added after an employee-like-to-have choice-constraint (low priority group) has been added. A third type of conflict is a conflict that occurs when a choice-constraint in a lower priority group is chronologically added after a choice-constraint in a higher priority group; e.g., an employee-like-to-have choice-constraint chronologically is added after an employee-must-have choice-constraint. 
     In an operation  308 , the interactive constraint solver application  102  provides a prompt to the user requesting a further constraint that, when applied, resolves said conflict. The prompt can include information about the constraints that are in conflict. In some instances, the prompt can include a menu of constraints from which the user can choose to resolve the conflict. 
     In an operation  310 , the conflict is resolved by the interactive constraint solver application  102  based on the model-constraint and which priority group and/or choice-constraints are in conflict. Situations where the attempt to resolve the conflict are discussed below. In situations where the attempt to resolve the conflict in successful, the conflict can be resolved in one of five ways as depicted in  FIG. 3B . First, the conflict can be resolved by rejecting the choice-constraint that caused the conflict (box  350 ). This results in no change to a current solution (box  352 ). Second, the conflict can be resolved by keeping the company-required (higher priority group) choice-constraint and removing the conflicting employee-like-to-have (lower priority group) choice-constraint (box  354 ). Only the company-required choice-constraint remains in the current solution (box  356 ). Third, the conflict can be resolved by keeping the employee-like-to-have (lower priority group) choice-constraint and removing the conflicting company-required (higher priority group) choice-constraint (box  358 ). Only the like-to-have choice-constraint remains both in the current solution and in the employee-like-to-have priority group (box  360 ). Fourth, the conflict can be resolved by swapping the like-to-have choice-constraint in the lower priority group with its conflicting must-have choice-constraint in the higher priority group (box  362 ). Both choice-constraints remain in the solution but their priorities have changed (subject to additional validation and conflict resolution if the re-ordering also conflicts) (box  364 ). Fifth, the conflict can be resolved by removing the choice-constraints that are in conflict (box  366 ). The original choice-constraint is not added to its priority group, and the other choice-constraint is removed from the solution resulting in both choice-constraints being removed (box  368 ). 
     The interactive constraint solver application  102  determines or updates feasible assignments to a set of variables subject to the one or more model-constraints and business rules defining a problem. When the problem is successfully solved, values are assigned to all the variables in the solution such that the constraints are satisfied. 
     In an interactive constraint solver application  102 , the users add choice-constraints to direct the solver application to a user-preferred solution. When the users have finished adding choice-constraints, the client application directs the solver application complete the solution. 
     In some embodiments, the interactive constraint solver application  102  maintains a queue of the choice-constraints. Each choice-constraint is added to the end of the queue. The interactive constraint solver application  102  processes the choice-constraints (processing the choice-constraints is known as propagation) to find any conflicts with earlier choice-constraints and/or model-constraints defined in the problem. 
     The client application  104  can add any number of queues as priority groups. Each priority group is added to a session of the client application  104 . A session is a semi-permanent interactive information interchange between the client application and a user. A session is set up or established at a certain point in time, and then torn down at some later point. Within a priority group, the user does not further specify the order of choice-constraints as the ordering is controlled by the interactive solver application  102 . Each priority group is assigned a priority relative to the other priority groups. There is precedence among the priority groups: choice-constraints in higher priority groups are applied to the solution before choice-constraints in lower priority groups are applied to the solution. The client application  104  can add, retract, and query for choice-constraints in the priority groups. As the client application  104  adds choice-constraints to the various priority groups, the interactive constraint solver application  102  can add each choice-constraint to the end of the queue of respective priority group containing the choice-constraint and can apply the choice-constraint(s) to the solution. If there is no conflict, the user choice-constraints remain in the solution. 
     However, when the interactive constraint solver application  102  discovers a conflict between choice-constraints and/or model-constraints, the interactive constraint solver application  102  stops processing and signals the conflict. The interactive constraint solver application  102  recognizes conflicts between choice-constraints within the same priority group and choice-constraints in different priority groups. The interactive constraint solver application  102  provides capabilities to handle conflicts between the choice-constraints. These capabilities allow the application developer to resolve the conflict in a way that meets his business requirements as well as user interface needs. The interactive constraint solver application  102  only determines that a conflict is resolved. 
     The interactive constraint solver application  102  resolves conflicts occurring between two choice-constraints within the same priority group. The interactive constraint solver application  102  can resolve a conflict in a variety of ways. For example, the interactive constraint solver application  102  can reject the choice-constraint and revert to the previous state of the solution. For another example, the interactive constraint solver application  102  can override the conflict. 
     To override the conflict, the interactive constraint solver application  102  can update the priority group&#39;s queue order by moving the latest choice-constraint from the end of the priority group&#39;s queue to the front. The interactive constraint solver application  102  again processes all the choice-constraints. If no further conflict is found, the recently moved choice-constraint remains at the front of the queue. Additionally, under such circumstances, the set of choice-constraints that conflicted with the recently moved choice-constraint are dropped from the solution and the priority group. The override sets the recently moved choice-constraint to the highest priority in the priority group until either the recently moved choice-constraint is removed or a future conflict occurs. 
     The interactive constraint solver application  102  also resolves conflicts occurring between choice-constraints in different priority groups. In one embodiment, a client application  104  has defined two priority groups. These priority groups are “must-have” and “like-to-have.” The “must-have” priority group has a higher priority than the “like-to-have” priority group. 
     The conflict can be between a new choice-constraint in the higher priority group and an existing choice-constraint in the lower priority group. For example, the “must-have” choice-constraint can be created after the “like-to-have” choice-constraint. The interactive constraint solver application  102  can resolve the conflict in one of two ways. The interactive constraint solver application  102  can reject the “must-have” choice-constraint and revert to the previous state of the solution. Or the interactive constraint solver application  102  can retain the “must-have” choice-constraint (at the end of the queue for the “must-have” priority group) and remove the “like-to-have” choice-constraint from its priority group. 
     The conflict can be between a new user choice-constraint in the lower priority group and an existing choice-constraint in the higher priority group. For example, the “like-to-have” choice-constraint might be created chronologically after the “must-have” choice-constraint. The interactive constraint solver application  102  resolves the conflict in one of three ways. First, the interactive constraint solver application  102  can reject the “like-to-have” choice-constraint and revert to the previous state of the solution. Second, the interactive constraint solver application  102  can retain the “like-to-have” choice-constraint (at the end of the queue for the “like-to-have” priority group) and remove the “must-have” choice-constraint from the “must-have” priority group. Third, the interactive constraint solver application  102  can swap the “like-to-have” choice-constraint with the “must-have” user choice-constraint. Both choice-constraints remain in the solution but are in different priority groups. 
     In some cases, the resolution itself can fail. Even after re-ordering choice-constraints in the priority groups, the interactive constraint solver application  102  can still find other conflicts during propagation. When this situation occurs, neither the resolution nor the original choice-constraint can be completed. The interactive constraint solver application  102  reverts to the state before the original choice-constraint was attempted and sends a message to the client application  104  to that effect. 
     4.0 Example Implementation of the Constraint Solver Process 
       FIGS. 4, 5, 6, and 7  depict examples of ordering choice-constraints, according to various embodiments. In these examples, the priority groups are used in an employee scheduling application that uses the interactive constraint solver application  102  to create monthly shift schedules. The client application  104  allows for company, managerial, and employee choice-constraints to be made before the final schedule is calculated. 
     In this example, for every day in the schedule, and for every employee in the schedule, a selection is made from this set: {OFF, WORK, VACATION, TRAINING}. An example choice-constraint can be: Arthur.May07=TRAINING. 
     The client application  104  collates these choice-constraints into three priority groups: COMPANY, MANAGER, and EMPLOYEE. The priority of processing the priority groups is the same order. Therefore, COMPANY choice-constraints have the highest priority and are processed before the MANAGER and EMPLOYEE choice-constraints. The COMPANY choice-constraints are also processed before the final calculation of the full schedule by the interactive constraint solver application  102 .  FIG. 4  depicts a representation of these three priority groups that will be populated by the choice-constraints. 
     The client application  104  has these business rules: Rule R 1 : TRAINING and VACATION days are added to COMPANY group. TRAINING cannot be removed during an interactive session. Rule R 2  is that a manager can add or remove choice-constraints for employees for OFF and WORK days. These choice-constraints are added to the MANAGER group. Rule R 3  is that an employee can add or remove choice-constraints for themselves for OFF and WORK days. These choice-constraints are added to the EMPLOYEE group. Rule R 4  is that an employee can add or remove choice-constraints for VACATION. These choice-constraints are added to the COMPANY group. 
     Client application  104  also defines business rules that deal with circumstances in which a new choice-constraint is being added and conflicts with existing choice-constraints. Examples of these rules follow. Rule R 5  is that a manager or employee cannot override a TRAINING day. Rule R 6  is that an employee can override his own VACATION day but a manager cannot. Rule R 7  is that an employee cannot override any manager selection. Rule R 8  is that a manager can override any employee selection (but will be prompted). 
     In the following examples, each choice-constraint is represented by a circle. Each choice-constraint is named in chronological order and shown in the correct priority position in its respective priority group. The propagation order of the choice-constraint is shown below the choice-constraint. 
     In  FIG. 5 , choice-constraints submitted during a first session are depicted. First, as shown in state  502 , the application adds mandatory training: C 1  {Leonard.May07=TRAINING} and C 2  {Arthur.May07=TRAINING}. According to rule R 1 , these choice-constraints are added to the COMPANY group. Second, as shown in state  504 , the user chooses a vacation day: C 3  {Arthur.May08=VACATION}. According to rule R 4 , this choice-constraint is added to the COMPANY group. 
     In  FIG. 6 , a second session begins by reloading choice-constraints C 1 , C 2 , and C 3  as shown in state  602 . The user, Arthur, having the role of “employee”, submits choice-constraint C 4  {Arthur.May07=OFF}. The choice-constraint C 4  is made by the employee. The choice-constraint is added to the EMPLOYEE group, according to rule R 3  as shown in state  602 . 
     The choice-constraint C 4 , {Arthur.May07=OFF}, conflicts with choice-constraint C 2 , {Arthur.May07=TRAINING}. Because C 2  is in the COMPANY group and not a “vacation” constraint, the rule R 1  requires the rejection of C 4 . C 4  is removed as shown in state  604 . The client application  104  decides what, if any, information to provide to Arthur. Examples of information that can be provided include the constraint C 2 , the role (e.g., COMPANY) of the user who submitted the constraint C 2 , and the role (e.g., EMPLOYEE) of Arthur when he submitted constraint C 4 . In some embodiments, the information informs Arthur as to why his choice is invalid, including information about company policy and that his choice conflicts with that policy. This information can imply or explicitly include information about Arthur&#39;s role. The client application  104 , based on instructions received from an application developer, can determine how to communicate the conflict. In some instances, the employee may not have been aware of the company policy, or that their request would conflict. 
     The employee, Arthur, chooses a work day: C 5  {Arthur.May08=WORK}, which is added to the EMPLOYEE group according to rule R 3  as shown in state  606 . 
     Because choice-constraint C 3  is VACATION and the employee submitted the C 5  choice-constraint, the business rule R 6  requires the employee to decide which choice-constraint to keep. The client application&#39;s user interface notifies Arthur of the conflict and the options. Arthur decides to work instead of taking vacation, and user choice-constraint C 3  is retracted as shown in state  608 . 
     During the second interactive session, Arthur selects a non-work day: C 6  {Arthur.May10=OFF}. The user choice-constraint is added to the EMPLOYEE group according to rule R 3  as shown in state  610 . There is no other choice-constraint concerning May 10 th , and this selection does not violate any business rules. 
       FIG. 7  depicts choice-constraints added during a third interactive session, where a stakeholder having the role of “manager” inputs one or more choice-constraints. The choice-constraints submitted at the end of the second session are depicted as shown in state  702 . 
     The manager submits a choice-constraint that Arthur is scheduled to work on the 9th. Choice-constraint C 7  is created for {Arthur.May09=WORK} and added to the MANAGER group according to rule R 2  as shown in state  704 . There are no other choice-constraints by Arthur or the Company about May 9th, and thus no conflict. 
     The manager submits a choice-constraint indicating that Arthur is scheduled to work on the 10th. Choice-constraint C 8  is created for {Arthur.May10=WORK} and added to the MANAGER group according to rule R 2  as shown in state  708 . 
     Arthur&#39;s choice-constraint C 6  {Arthur.May10=OFF} conflicts with the manager&#39;s choice-constraint C 8  {Arthur.May10=WORK}. Rule R 8  requires that the manager decide which choice-constraint to keep. The interactive constraint solver  102  provides information about the conflict. The application displays the information in the user interface of the client application  104 . The manager decides to have Arthur work. Choice-constraint C 6  is removed as shown in state  708 . 
     The manager has finished making choice-constraints and closes or exits the client application  104 . The interactive constraint solver application  102  can now solve the problem and create the schedule. 
     5.0 Hardware Overview 
       FIG. 8  is a block diagram of a computer system upon which various embodiments may be implemented. According to one embodiment, the techniques described herein are implemented by one or more special-purpose computing devices. The special-purpose computing devices may be hard-wired to perform the techniques, or may include digital electronic devices such as one or more application-specific integrated circuits (ASICs) or field programmable gate arrays (FPGAs) that are persistently programmed to perform the techniques, or may include one or more general purpose hardware processors programmed to perform the techniques pursuant to program instructions in firmware, memory, other storage, or a combination. Such special purpose computing devices may also combine custom hard-wired logic, ASICs, or FPGAs with custom programming to accomplish the techniques. The special-purpose computing devices may be desktop computer systems, portable computer systems, handheld devices, networking devices or any other device that incorporates hard-wired and/or program logic to implement the techniques. 
     For example,  FIG. 8  is a block diagram that illustrates a computer system  800  upon which an embodiment of the invention may be implemented. Computer system  800  includes a bus  802  or other communication mechanism for communicating information, and a hardware processor  804  coupled with bus  802  for processing information. Hardware processor  804  may be, for example, a general purpose microprocessor. 
     Computer system  800  also includes a main memory  806 , such as a random access memory (RAM) or other dynamic storage device, coupled to bus  802  for storing information and instructions to be executed by processor  804 . Main memory  806  also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor  804 . Such instructions, when stored in non-transitory storage media accessible to processor  804 , render computer system  800  into a special-purpose machine that is customized to perform the operations specified in the instructions. 
     Computer system  800  further includes a read only memory (ROM)  808  or other static storage device coupled to bus  802  for storing static information and instructions for processor  804 . A storage device  810 , such as a magnetic disk or optical disk, is provided and coupled to bus  802  for storing information and instructions. 
     Computer system  800  may be coupled via bus  802  to a display  812 , such as a cathode ray tube (CRT), for displaying information to a computer user. An input device  814 , including alphanumeric and other keys, is coupled to bus  802  for communicating information and command selections to processor  804 . Another type of user input device is cursor control  816 , such as a mouse, a trackball, or cursor direction keys for communicating direction information and command selections to processor  804  and for controlling cursor movement on display  812 . This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), that allows the device to specify positions in a plane. 
     Computer system  800  may implement the techniques described herein using customized hard-wired logic, one or more ASICs or FPGAs, firmware and/or program logic which in combination with the computer system causes or programs computer system  800  to be a special-purpose machine. According to one embodiment, the techniques herein are performed by computer system  800  in response to processor  804  executing one or more sequences of one or more instructions contained in main memory  806 . Such instructions may be read into main memory  806  from another storage medium, such as storage device  810 . Execution of the sequences of instructions contained in main memory  806  causes processor  804  to perform the process steps described herein. In alternative embodiments, hard-wired circuitry may be used in place of or in combination with software instructions. 
     The term “storage media” as used herein refers to any non-transitory media that store data and/or instructions that cause a machine to operation in a specific fashion. Such storage media may comprise non-volatile media and/or volatile media. Non-volatile media includes, for example, optical or magnetic disks, such as storage device  810 . Volatile media includes dynamic memory, such as main memory  806 . Common forms of storage media include, for example, a floppy disk, a flexible disk, hard disk, solid state drive, magnetic tape, or any other magnetic data storage medium, a CD-ROM, any other optical data storage medium, any physical medium with patterns of holes, a RAM, a PROM, and EPROM, a FLASH-EPROM, NVRAM, any other memory chip or cartridge. 
     Storage media is distinct from but may be used in conjunction with transmission media. Transmission media participates in transferring information between storage media. For example, transmission media includes coaxial cables, copper wire and fiber optics, including the wires that comprise bus  802 . Transmission media can also take the form of acoustic or light waves, such as those generated during radio-wave and infra-red data communications. 
     Various forms of media may be involved in carrying one or more sequences of one or more instructions to processor  804  for execution. For example, the instructions may initially be carried on a magnetic disk or solid state drive of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system  800  can receive the data on the telephone line and use an infra-red transmitter to convert the data to an infra-red signal. An infra-red detector can receive the data carried in the infra-red signal and appropriate circuitry can place the data on bus  802 . Bus  802  carries the data to main memory  806 , from which processor  804  retrieves and executes the instructions. The instructions received by main memory  806  may optionally be stored on storage device  180  either before or after execution by processor  804 . 
     Computer system  800  also includes a communication interface  818  coupled to bus  802 . Communication interface  818  provides a two-way data communication coupling to a network link  820  that is connected to a local network  822 . For example, communication interface  818  may be an integrated services digital network (ISDN) card, cable modem, satellite modem, or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, communication interface  818  may be a local area network (LAN) card to provide a data communication connection to a compatible LAN. Wireless links may also be implemented. In any such implementation, communication interface  818  sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information. 
     Network link  820  typically provides data communication through one or more networks to other data devices. For example, network link  820  may provide a connection through local network  822  to a host computer  824  or to data equipment operated by an Internet Service Provider (ISP)  826 . ISP  826  in turn provides data communication services through the world wide packet data communication network now commonly referred to as the “Internet”  828 . Local network  822  and Internet  828  both use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on network link  820  and through communication interface  818 , which carry the digital data to and from computer system  800 , are example forms of transmission media. 
     Computer system  800  can send messages and receive data, including program code, through the network(s), network link  820  and communication interface  818 . In the Internet example, a server  830  might transmit a requested code for an application program through Internet  828 , ISP  826 , local network  822  and communication interface  818 . 
     The received code may be executed by processor  804  as it is received, and/or stored in storage device  170 , or other non-volatile storage for later execution. 
     The techniques described herein are implemented using one or more processing solutions, examples of which include distributed systems, clustered computing systems, and cloud computing systems. In an embodiment, the interactive constraint solver application is part of a cloud computing system. A cloud computing system implements one or more of: cloud storage, cloud processing, cloud communication, and any other kind of cloud computing service. Further, cloud computing systems may operate under a pay-for-what-you-use-as-you-use-it model, under a fixed subscription model, etc. In this embodiment, any part (or the whole of) the functionality attributed to the entities within this description, is controllable via an interface that is exposed at a cloud computing system. 
     6.0 Extensions and Alternatives 
     In the foregoing specification, embodiments of the invention have been described with reference to numerous specific details that may vary from implementation to implementation. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. The sole and exclusive indicator of the scope of the invention, and what is intended by the applicants to be the scope of the invention, is the literal and equivalent scope of the set of claims that issue from this application, in the specific form in which such claims issue, including any subsequent correction.